13.02.2018 Views

Hans Gottinger, Essays on Decision, Information, Computation and Technology

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

<str<strong>on</strong>g>Hans</str<strong>on</strong>g> W. <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g><br />

ESSAYS ON<br />

DECISION,<br />

INFOR MATION,<br />

COMPUTATION &<br />

TECHNOLOGY


<str<strong>on</strong>g>Hans</str<strong>on</strong>g> W. <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g><br />

ESSAYS ON<br />

DECISION,<br />

INFOR MATION,<br />

COMPUTATION &<br />

TECHNOLOGY<br />

<str<strong>on</strong>g>Hans</str<strong>on</strong>g> W. <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g><br />

STRATEC Munich, Germany<br />

www.stratec-c<strong>on</strong>.net<br />

stratec_c@yahoo.com<br />

gottingerhans@gmail.com


Aggregate Keywords:<br />

Utility, Measurement/Scaling, Preference Orderings, Decisi<strong>on</strong>s, Decisi<strong>on</strong>-Making under Uncertainty,<br />

Strategy, Game Theory, Statistical Games/Decisi<strong>on</strong>s, Mathematical Ec<strong>on</strong>omics, Informati<strong>on</strong> Ec<strong>on</strong>omics,<br />

Organizati<strong>on</strong>s, Behavioral Ec<strong>on</strong>omics, Bounded/Limited Rati<strong>on</strong>ality, Optimal Search, Complexity<br />

Measures, Intelligent Decisi<strong>on</strong> Systems, Statistical Expert Systems, Policy Decisi<strong>on</strong>s, Regulatory<br />

Decisi<strong>on</strong>s, Social/Envir<strong>on</strong>mental Decisi<strong>on</strong>s.


CONTENTS<br />

HANS W. GOTTINGER<br />

CONTENTS<br />

ESSAYS ON DECISIONS , INFORMATION,<br />

COMPUTATION AND SYSTEMS<br />

C<strong>on</strong>tents ................................................................................................ I<br />

Foreword. .............................................................................................. III<br />

Preface <strong>and</strong> Introducti<strong>on</strong> ............................................................................... V<br />

1. Preferences, Informati<strong>on</strong> <strong>and</strong> Decisi<strong>on</strong> ................................................. 1<br />

1.1 Über die Existenz einer stetigen, reellen Nutzenfunkti<strong>on</strong><br />

(On the Existence of a c<strong>on</strong>tinuous, real-valued utility functi<strong>on</strong>) ................................... 3<br />

1.2 Methodologische Entwicklungen in der Meßtheorie<br />

(Methodological Developments in Measurement Theory) ....................................... 11<br />

1.3 Existence of a Utility <strong>on</strong> a Topological Semigroup ............................................... 45<br />

1.4 C<strong>on</strong>diti<strong>on</strong>al Utility ............................................................................. 59<br />

1.5 Foundati<strong>on</strong>s of Lexicographic Utility . ........................................................... 69<br />

1.6 Decisi<strong>on</strong> problems under uncertainty based <strong>on</strong> entropy functi<strong>on</strong>als ............................. 79<br />

1.7 Choice <strong>and</strong> Complexity . ....................................................................... 109<br />

1.8 Computati<strong>on</strong>al Costs <strong>and</strong> Bounded Rati<strong>on</strong>ality (Philosophy of Ec<strong>on</strong>omics, 223-238) ............. 127<br />

1.9 Krohn-Rhodes Complexity <strong>on</strong> Decisi<strong>on</strong> Rules . .................................................. 143<br />

1.10 An Informati<strong>on</strong> Theoretic Approach to Large Organizati<strong>on</strong>s .................................... 157<br />

1.11 Some Measures of Informati<strong>on</strong> arising in Statistical Games ..................................... 169<br />

1.12 Subjective Qualitative Informati<strong>on</strong> Structures based <strong>on</strong> Orderings .............................. 175<br />

1.13 Qualitative Informati<strong>on</strong> <strong>and</strong> Comparative Informativeness ..................................... 205<br />

1.14 On a Problem of Optimal Search .............................................................. 219<br />

2. Intelligent Decisi<strong>on</strong> Systems ........................................................ 229<br />

2.1 Intelligent Decisi<strong>on</strong> Support Systems (with Peter Weimann) ..................................... 231<br />

2.2 Statistical Expert Systems ...................................................................... 247<br />

2.3 Artificial Intelligence <strong>and</strong> Ec<strong>on</strong>omic Modeling .................................................. 261<br />

3. Applicati<strong>on</strong>s ....................................................................... 269<br />

3.1 Assessment of Social Value in the Allocati<strong>on</strong> of CT Scanners in the Munich Metropolitan Area ... 271<br />

3.2 Adopti<strong>on</strong> Decisi<strong>on</strong>s <strong>and</strong> Diffusi<strong>on</strong> ............................................................. 299<br />

3.3 Choosing Regulatory Opti<strong>on</strong>s when Envir<strong>on</strong>mental Costs are Uncertain ........................ 317<br />

3.4 Dynamic Portfolio Strategies with Transacti<strong>on</strong> Costs ........................................... 331<br />

I


HANS W. GOTTINGER<br />

CONTENTS<br />

II


FOREWORD<br />

HANS W. GOTTINGER<br />

FOREWORD<br />

Selected writings of a very prolific author over a l<strong>on</strong>g-time period typically open a window both <strong>on</strong> the<br />

evoluti<strong>on</strong> of his thinking <strong>and</strong> <strong>on</strong> the changing focusses <strong>and</strong> fads of the scientific community. <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g>s’s<br />

<str<strong>on</strong>g>Essays</str<strong>on</strong>g> <strong>on</strong> Decisi<strong>on</strong>, Informati<strong>on</strong>, Computati<strong>on</strong> & <strong>Technology</strong>, which cover roughly the period 1970-2000,<br />

are no excepti<strong>on</strong>.<br />

The essays, some of which are in German, are hard to subsume. They span across ec<strong>on</strong>omics, mathematics,<br />

operati<strong>on</strong>s research, expert systems, <strong>and</strong> then some. They include provocative advances, more st<strong>and</strong>ard<br />

efforts, <strong>and</strong> unc<strong>on</strong>troversial applicati<strong>on</strong>s. At their best, they delineate new venues of research that could<br />

significantly impact the way we are doing ec<strong>on</strong>omics. It has been widely argued, rightfully so in my<br />

opini<strong>on</strong>, that the imperialistic spread of neo-classical thinking has stuck much of the ec<strong>on</strong>omic professi<strong>on</strong><br />

in an increasingly noxious Newt<strong>on</strong>ian visi<strong>on</strong> of the ec<strong>on</strong>omy together with a very narrow c<strong>on</strong>cepti<strong>on</strong> of<br />

rati<strong>on</strong>al decisi<strong>on</strong>-making. As usual with theoretical approaches that struggle to cope with the reality, most<br />

improvements efforts at improvement are purely incremental <strong>and</strong> do not go bey<strong>on</strong>d patching up the main<br />

deficiencies by twisting st<strong>and</strong>ard relati<strong>on</strong>ships, adding new <strong>on</strong>e, introducing more <strong>and</strong> more epicycles while<br />

rejecting any true change in paradigm. Not so <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g>, who did not hesitate to enter terra incognita <strong>and</strong><br />

suggest radically new ways of addressing fundamental ec<strong>on</strong>omic questi<strong>on</strong>s.<br />

The first <strong>and</strong> by far larger secti<strong>on</strong> of the book focusses <strong>on</strong> decisi<strong>on</strong>-theoretic problems. Some early works,<br />

published largely in the period 1970-1975, centre about c<strong>on</strong>diti<strong>on</strong>s under which preferences can be represented<br />

by a utility functi<strong>on</strong> with agreeable properties. The issue was acute at the time but has largely been exhausted<br />

nowadays <strong>and</strong> arguably stalled rather than promoted our mastering of the very large <strong>and</strong> most important<br />

class of situati<strong>on</strong>s where st<strong>and</strong>ard utility functi<strong>on</strong>s do not exist. Still, it remains at the very core of neoclassical<br />

ec<strong>on</strong>omics. A st<strong>and</strong>al<strong>on</strong>e c<strong>on</strong>tributi<strong>on</strong> reviews the foundati<strong>on</strong>al work in measurement theory that<br />

was carried out at the time by such authors as Krantz, Luce, Pfanzagl, Suppes, <strong>and</strong> Tversky. The logical<br />

link between utility, decisi<strong>on</strong>-making, <strong>and</strong> measurement is immediate, utility is nothing but a measure of<br />

preferences, <strong>and</strong> decisi<strong>on</strong>-making typically requires measurement. N<strong>on</strong>etheless, the theory of measurement<br />

has been largely, <strong>and</strong> unfortunately, overlooked by the ec<strong>on</strong>omic professi<strong>on</strong>. To my knowledge, <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g>’s<br />

paper is <strong>on</strong>e of the very few attempts to remedy this <strong>and</strong> remind ec<strong>on</strong>omists that much work relevant for<br />

the very core of their discourse is being d<strong>on</strong>e outside of their narrow disciplinary circles.<br />

Several later papers in the <str<strong>on</strong>g>Essays</str<strong>on</strong>g>’ first secti<strong>on</strong> are disruptive in their attempt to enrich <strong>and</strong> transcend the<br />

st<strong>and</strong>ard neo-classical framework by introducing c<strong>on</strong>cepts <strong>and</strong> methods from other disciplines, predominantly<br />

informati<strong>on</strong> theory, statistical inference, computing, <strong>and</strong> abstract automata theory. Thus, <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g> suggested<br />

in a 1990 paper using the maximum entropy principle to tackle decisi<strong>on</strong>-making under uncertainty. This<br />

was brave – entropy is not easy to interpret, underst<strong>and</strong> or visualize in a socio-ec<strong>on</strong>omic c<strong>on</strong>text. The use of<br />

the c<strong>on</strong>cept in ec<strong>on</strong>omics remains marginal up to now but is the subject of active research in the innovative<br />

fringe <strong>and</strong> increasingly used in such field as game theory, finance, robust optimizati<strong>on</strong>, <strong>and</strong> organizati<strong>on</strong><br />

theory. Other lines of research suggested in several articles hint to the nowadays very active <strong>and</strong> promising<br />

efforts in complexity ec<strong>on</strong>omics <strong>and</strong> agent-based ec<strong>on</strong>omics. Other papers combine informati<strong>on</strong> theory as<br />

the mathematics of communicati<strong>on</strong> <strong>and</strong> storage of informati<strong>on</strong> with more st<strong>and</strong>ard ec<strong>on</strong>omic issues. Here<br />

again, <strong>on</strong>e recognizes some early precursors of complexity <strong>and</strong> agent-based ec<strong>on</strong>omics, but also of boundedrati<strong>on</strong>ality<br />

models <strong>and</strong> computati<strong>on</strong>al games, am<strong>on</strong>g others. Inexplicably, <strong>and</strong> unfortunately, the <str<strong>on</strong>g>Essays</str<strong>on</strong>g> do<br />

not include the nice paper <strong>on</strong> Structure <strong>and</strong> Complexity in Socio-Ec<strong>on</strong>omic Systems that <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g> jointly<br />

published with the late Peter Albin in Mathematical Social Sciences 1983.<br />

III


HANS W. GOTTINGER<br />

FOREWORD<br />

The sec<strong>on</strong>d part of the book is devoted to expert systems, which were the main focus of research in AI in<br />

the 80s. Together with the informatician Peter Weimann, <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g> published towards the end of the decade<br />

a number of papers <strong>on</strong> the topic. The <strong>on</strong>e reproduced here outlines a flexible shell that allows c<strong>on</strong>sidering<br />

c<strong>on</strong>diti<strong>on</strong>al probabilities <strong>and</strong> all informati<strong>on</strong> available at the time of decisi<strong>on</strong>. A c<strong>on</strong>temporaneous paper<br />

with <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g> as sole author discusses in broad terms the c<strong>on</strong>cept of a statistical c<strong>on</strong>sultati<strong>on</strong> system,<br />

which can help a user with little statistical knowledge to design a proper statistical analysis. Another <strong>on</strong>e,<br />

which sketches an approach for building a ruled-based qualitative model of the macro-ec<strong>on</strong>omy, has again<br />

some reflexi<strong>on</strong> in recent agent-based ec<strong>on</strong>omic models. I felt pleased <strong>and</strong> h<strong>on</strong>oured to find that the author’s<br />

argumentati<strong>on</strong> echoes some idea that G.R. (Robert) Boynt<strong>on</strong> <strong>and</strong> myself expressed independently in a<br />

1987 paper.<br />

The last secti<strong>on</strong> of the <str<strong>on</strong>g>Essays</str<strong>on</strong>g> is devoted to “applicati<strong>on</strong>s”, showing that with advancing age <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g> has<br />

been increasingly attracted to less abstract <strong>and</strong> even to empirical research. It includes a cost-benefits analysis<br />

of PT scanners locati<strong>on</strong> <strong>and</strong> a paper <strong>on</strong> dynamic envir<strong>on</strong>mental regulati<strong>on</strong> under uncertainty. Two other<br />

papers address the questi<strong>on</strong>s of optimal dynamic portfolio selecti<strong>on</strong> <strong>and</strong> suggest a novel micro-ec<strong>on</strong>omic<br />

foundati<strong>on</strong> for diffusi<strong>on</strong> curves.<br />

Reading the <str<strong>on</strong>g>Essays</str<strong>on</strong>g> requires, for most part, a solid knowledge of mathematics. It is hard, abstract reading.<br />

But it is also a rewarding lecture, for a wide circle of senior academics <strong>and</strong> graduate students alike. In<br />

additi<strong>on</strong> to providing valuable insights bey<strong>on</strong>d the mainstream wisdom it sheds light <strong>on</strong> the way science<br />

advances. Not <strong>on</strong>ly by taking the safe way of incremental improvement in accepted ideas, but also <strong>and</strong><br />

more dangerously by combining ideas, by reaching across disciplines, in the hope that some of these efforts<br />

will bloom <strong>and</strong> survive.<br />

Prof. Dr. Christophe Deissenberg, Luxembourg<br />

April 26, 2018<br />

IV


PREFACE AND INTRODUCTION<br />

HANS W. GOTTINGER<br />

<str<strong>on</strong>g>Essays</str<strong>on</strong>g> <strong>on</strong> Decisi<strong>on</strong>s , Informati<strong>on</strong>, Computati<strong>on</strong> <strong>and</strong> Systems<br />

PREFACE AND INTRODUCTION<br />

Not <strong>on</strong>ly in ec<strong>on</strong>omics, psychology <strong>and</strong> business but generally in most human activities, decisi<strong>on</strong>s <strong>and</strong> decisi<strong>on</strong><br />

making, whether deliberate or routine, play a crucial part in the human pursuit of happiness, prosperity,<br />

individual <strong>and</strong> collective satisfacti<strong>on</strong>. A precursor of decisi<strong>on</strong>-making , strategy <strong>and</strong> planning, dates back<br />

to the classical Greeks <strong>and</strong> Chinese up to modern European times. The c<strong>on</strong>ceptual tools developed with<br />

game theory, statistical decisi<strong>on</strong> theory, operati<strong>on</strong>s research, systems analyis/engineering <strong>and</strong> management<br />

science all originated in the twentiest century <strong>and</strong> are fast exp<strong>and</strong>ing in the digital world with intelligent<br />

decisi<strong>on</strong> systems. Applicati<strong>on</strong>s proliferate in health care (medical decisi<strong>on</strong>-making), logistics, transportati<strong>on</strong>,<br />

industrial <strong>and</strong> public services facilitated through enhanced tools involving artificial intelligence (AI),<br />

machine learning, human-machine interacti<strong>on</strong>s, <strong>and</strong> machine-to-machine cooperati<strong>on</strong>s (Internet of Things).<br />

Within ec<strong>on</strong>omics the behavioral foundati<strong>on</strong>s emerged from game theory with links to<br />

competiti<strong>on</strong> theory <strong>and</strong> policy, competitiveness, organizati<strong>on</strong>s <strong>and</strong> teams up to managerial ec<strong>on</strong>omics<br />

with decisi<strong>on</strong> analysis of multiple objectives, risk <strong>and</strong> uncertainty. New subdisciplines have emerged such<br />

as informati<strong>on</strong> ec<strong>on</strong>omics, computati<strong>on</strong>al ec<strong>on</strong>omics, behavioral <strong>and</strong> experimental ec<strong>on</strong>omics.The latter<br />

got recent prominence through Nobel Prizes in ec<strong>on</strong>omics for D.Kahneman (2002) <strong>and</strong> R. Thaler (2017).<br />

The collecti<strong>on</strong> of selected essays to follow emphasizes some limited foundati<strong>on</strong>al, theme related key issues<br />

subsumed under the title. We proceed partly in chr<strong>on</strong>ological order which also moves from more theoretical,<br />

c<strong>on</strong>ceptual themes to further applicati<strong>on</strong>. All are categorized in three parts. At the end a brief bibliography<br />

points to relevant related literature.<br />

1. Preferences, Informati<strong>on</strong> <strong>and</strong> Decisi<strong>on</strong>s<br />

1.1. Über die Existenz einer stetigen, reellen Nutzenfunkti<strong>on</strong> (On the Existence of a c<strong>on</strong>tinuous,<br />

real-valued utility functi<strong>on</strong>)<br />

The article pursues a simple representati<strong>on</strong> of binary relati<strong>on</strong>s , preference-indifference or strict preference,<br />

<strong>on</strong> a bundle of objects X (commodity bundles) by a numerical functi<strong>on</strong> (utility) <strong>on</strong> the real line. For its<br />

representati<strong>on</strong> it <strong>on</strong>ly uses ordering properties compatible for c<strong>on</strong>tinuous functi<strong>on</strong>s <strong>on</strong> the real line. This<br />

distinguishes itself from G. Debreu’s representati<strong>on</strong> theorems (Debreu [1]) as he uses<br />

ordered topological spaces <strong>and</strong> structural topological properties later extended to c<strong>on</strong>tinuity properties of<br />

Paretian utility (Debreu [2]). The reas<strong>on</strong> behind is that basic rati<strong>on</strong>al preferences can be shown for “ordinal<br />

utility functi<strong>on</strong>s“ in deterministic settings (or c<strong>on</strong>sumer choice theory) without taking recourse to more<br />

aadvanced topological tools. The latter lead to more elegant representati<strong>on</strong>s but less intuitive ec<strong>on</strong>omic<br />

interpretati<strong>on</strong>s.<br />

1.2. Methodologische Entwicklungen in der Messtheorie (Methodological Developments in<br />

Measurement Theory)<br />

This piece serves as a limited survey <strong>on</strong> measurement theory following a comprehensive , seminal treatment<br />

by Pfanzagl [3]. It complements issues of measurement of utility theory as used in ec<strong>on</strong>omic <strong>and</strong> psychology<br />

research. We show the similarity in the structure of measurement theory to that of utility theory.<br />

It lends itself to (a) algebraic metric operati<strong>on</strong>s , (b) axiomatic models, (c) order relati<strong>on</strong>s linking various<br />

entities, (d) topology <strong>on</strong> ordered sets <strong>and</strong> (e) transformati<strong>on</strong>s of empirical relati<strong>on</strong>al systems <strong>on</strong> numerical<br />

scales.<br />

1.3 Existence of a Utility <strong>on</strong> a Topological Semigroup<br />

Here we go bey<strong>on</strong>d ordinal utility of Sec. 1.1. <strong>and</strong> explore the c<strong>on</strong>necti<strong>on</strong> between cardinal <strong>and</strong> expected<br />

utility theory. Again the work of G. Debreu [4]<br />

has been seminal. To prove existence for an additive utility representati<strong>on</strong> we need specific algebraic<br />

V


HANS W. GOTTINGER<br />

PREFACE AND INTRODUCTION<br />

assumpti<strong>on</strong>s in additi<strong>on</strong> to those of the order topology comm<strong>on</strong>ly found in an orderd to topological semigroup<br />

(tsg). The use of an order topology <strong>on</strong> a semigroup suggests a wide variety of embeddings of preference<br />

orderings into real numbers through dimensi<strong>on</strong>al transformati<strong>on</strong>s. That is, a tsg would allow a collecti<strong>on</strong><br />

of metrics (bey<strong>on</strong>d additivity) to be transformed into real numbers to “cardinalize“ utilities. Utilities <strong>on</strong><br />

tsgs would fit as <strong>on</strong>e category of several algebraic-topological c<strong>on</strong>structs to clasif diverse preference orders<br />

<strong>and</strong> utilities (Vind [5]).<br />

1.4 C<strong>on</strong>diti<strong>on</strong>al Utility<br />

Here I c<strong>on</strong>sider a situati<strong>on</strong> where the utility of a risky/uncertain prospect in a V<strong>on</strong> Neumann-Morgenstern<br />

utility c<strong>on</strong>text is affected by an “extraneous chance mechanism“, sort of stochastic shock through changes<br />

of states of nature which additi<strong>on</strong>ally affects its utility valuati<strong>on</strong>. Putting it in Savage’s system [6] of<br />

decisi<strong>on</strong> acts would yield the difference between prior utility (n<strong>on</strong> c<strong>on</strong>diti<strong>on</strong>alized) <strong>and</strong> posterior utility<br />

(c<strong>on</strong>diti<strong>on</strong>alized) as a revealed measure of the value of informati<strong>on</strong> (VI) provided <strong>on</strong>e would know about<br />

the extraneous chance mechanism.<br />

1.5 Foundati<strong>on</strong>s of Lexicographic Utility<br />

A comm<strong>on</strong> preference order <strong>on</strong> the choice of sure or r<strong>and</strong>om prospects would be open to tradeoff or<br />

compensatory choices reflected simply in microec<strong>on</strong>omic st<strong>and</strong>ard indifference diagrams. Lexicographic<br />

utility can no l<strong>on</strong>ger be represented as a real-valued functi<strong>on</strong> but is multidimensi<strong>on</strong>al <strong>on</strong> a vector space.<br />

In between we could think of mixed preferences, lexicographic or compensatory, or lexicographic subject<br />

to 2nd, ... , nth order fixed c<strong>on</strong>straints making a feasible preference set. Also stochastic preferences over<br />

lexicographic choices allow lexicographic tradeoff structures.<br />

1.6 Decisi<strong>on</strong> Problems under Uncertainty based <strong>on</strong> Entropy Functi<strong>on</strong>als (Theory <strong>and</strong> Decisi<strong>on</strong>,<br />

1990)<br />

In this paper it is shown how various criteria of optimal decisi<strong>on</strong>s under uncertainty relate to the entropy<br />

functi<strong>on</strong> known from classical informati<strong>on</strong> theory.<br />

Of particular interest is the “Expected Utility of Perfect Informati<strong>on</strong>“(EUPI) being closely linked to Shann<strong>on</strong>’s<br />

informati<strong>on</strong> measure. This gives rise to other decisi<strong>on</strong> theoretic noti<strong>on</strong>s such as expected opportunity loss,<br />

payoff relevant informati<strong>on</strong> emerging from statistical decisi<strong>on</strong> analysis . They are c<strong>on</strong>ceptually applied<br />

to optimality at equilibrium in many pers<strong>on</strong> games as well as to specific types of ec<strong>on</strong>omic organizati<strong>on</strong>s<br />

such as teams.<br />

1.7 Choice <strong>and</strong> Complexity<br />

Here we relate human choice processes to computati<strong>on</strong> <strong>and</strong> machines. We move from the noti<strong>on</strong>s of<br />

effective computability, effective algorithms to computati<strong>on</strong>al complexity with respect to computable<br />

relati<strong>on</strong>s identified as preference relati<strong>on</strong>s generating choice processes. In the center of observati<strong>on</strong>s will<br />

be a basic model of a social choice machine (SCM). The basic features from a SCM would be threefold:<br />

(i) characterizing computati<strong>on</strong>al rati<strong>on</strong>ality as a sort of bounded or limited human/machine rati<strong>on</strong>ality. (ii)<br />

computati<strong>on</strong>al rati<strong>on</strong>ality being bound by the computati<strong>on</strong>al complexity of the choice process, (iii) rati<strong>on</strong>al<br />

choice processes being restricted by the computati<strong>on</strong>al difficulty of effectively realizing rati<strong>on</strong>al choice<br />

functi<strong>on</strong>s. Exploring recursive computati<strong>on</strong>al functi<strong>on</strong>s in recursive topological spaces yield a descripti<strong>on</strong><br />

of effective computability <strong>and</strong> corresp<strong>on</strong>ding complexity. They end up being “simulated“ by sequential<br />

finite state machines as Turing machines. The complexity number of a Turing machine simulating a choice<br />

functi<strong>on</strong> is the minimal length of the program which simulates this machine.<br />

1.8 Computati<strong>on</strong>al Costs <strong>and</strong> Bounded Rati<strong>on</strong>ality<br />

The bound will be achieved by the fact that computati<strong>on</strong>s are not costless, that is they use procedures that<br />

require the use of scarce resources . In such situati<strong>on</strong>s decisi<strong>on</strong> may use simple heuristics or “rules of<br />

thumb“ to reduce the cost of computati<strong>on</strong>. A device to measure computati<strong>on</strong>al bounds could be finite state<br />

sequential machines or Turing machines. Some applicati<strong>on</strong>s relate to the c<strong>on</strong>structi<strong>on</strong> of aggregati<strong>on</strong> of a<br />

c<strong>on</strong>sumer price index up to decentralized resource allocati<strong>on</strong> in the theory of the firm.<br />

VI


PREFACE AND INTRODUCTION<br />

HANS W. GOTTINGER<br />

1.9 Krohn-Rhodes Complexity <strong>on</strong> Decisi<strong>on</strong> Rules<br />

This is designed as an updated review of algebraic complexity of Krohn-Rhodes [7] <strong>and</strong> its c<strong>on</strong>necti<strong>on</strong> to<br />

bounded rati<strong>on</strong>ality properties of H. Sim<strong>on</strong> [8], its intrinsic applicati<strong>on</strong> to chess-playing programs, heuristics<br />

<strong>and</strong> problem solving with interface issues of ec<strong>on</strong>omics to computer <strong>and</strong> management science.<br />

1.10 An Informati<strong>on</strong>-Theoretic Approach to Large Organizati<strong>on</strong>s<br />

Here we look at the interacti<strong>on</strong> of decisi<strong>on</strong> , informati<strong>on</strong> <strong>and</strong> performance in large ec<strong>on</strong>omic organizati<strong>on</strong>s<br />

<strong>and</strong> challenges that would arise from issues of bounded rati<strong>on</strong>ality treated in previous secti<strong>on</strong>s. Decisi<strong>on</strong><br />

theoretic <strong>and</strong> computable models of organizati<strong>on</strong>s have been advanced by March <strong>and</strong> Sim<strong>on</strong> [9] <strong>and</strong><br />

Marschak <strong>and</strong> Radner [10]. I build processing tasks in terms of a “machine model“ that face payoff relevant<br />

informati<strong>on</strong> <strong>and</strong> complexity limits.<br />

1.11 Some Measures of Informati<strong>on</strong> arising in Statistical Games<br />

Payoff relevant informati<strong>on</strong> with respect to an expected utility/loss functi<strong>on</strong> arises from statistical decisi<strong>on</strong><br />

functi<strong>on</strong>s embedded in game theory (Blackwell <strong>and</strong> Girshick [11]). They serve as value of informati<strong>on</strong><br />

(VI) provided by experiments. In a best sense VI, positive or negative, is the amount that payoff-relevant<br />

informati<strong>on</strong> adds to or reduces from the payoff functi<strong>on</strong> associated with a decisi<strong>on</strong> in a statistical game. I<br />

propose various measures of informati<strong>on</strong> emerging from statistical decisi<strong>on</strong> theory that reflect the ec<strong>on</strong>omic<br />

aspects of usefulness of informati<strong>on</strong> (based <strong>on</strong> some kind of utility or loss functi<strong>on</strong>) rather than the original<br />

physical/engineering viewpoint of transmitting <strong>and</strong> c<strong>on</strong>trolling informati<strong>on</strong> flows through a large (noisy<br />

or noiseless) communicati<strong>on</strong> channel (Shann<strong>on</strong> <strong>and</strong> Weaver [12]). Thus it creates an informati<strong>on</strong>al metric<br />

for payoff functi<strong>on</strong>s in terms of an ec<strong>on</strong>omic value of informati<strong>on</strong>.<br />

1.12 Subjective Qualitative Informati<strong>on</strong> Structures based <strong>on</strong> Orderings<br />

In this essay I reverse the qualitative relati<strong>on</strong> “not more probable than“ as a “primitive“ of probability to<br />

informati<strong>on</strong> in review of Savage’s [6] introducti<strong>on</strong> to subjective probability. This is an attempt to axiomatize<br />

subjective informati<strong>on</strong> as a c<strong>on</strong>ceptual precursor to generating subjective probabilities <strong>on</strong> corresp<strong>on</strong>ding<br />

(informati<strong>on</strong> induced) events. The primitive relati<strong>on</strong> “not more informative than“ is c<strong>on</strong>structed <strong>on</strong> the basis<br />

of order topopologies by the Hungarian mathematician A. Cszaszar called topogenous structures. I then<br />

show that semi-topogeneous informati<strong>on</strong> structures (also named experiments) have a natural mapping <strong>on</strong><br />

subjective probability structures of the Savage type. With the more recent advance of artificial intelligence,<br />

machine learning <strong>and</strong> big data potential applicati<strong>on</strong>s can be foreseen that such qualitative informati<strong>on</strong><br />

structures could be machine-generated in terms of qualitative orderings.<br />

1.13 Qualitative Informati<strong>on</strong> <strong>and</strong> Comparative Informativeness<br />

This essay provides a c<strong>on</strong>ceptual qualificati<strong>on</strong> , refinement <strong>and</strong> expansi<strong>on</strong> of the previous Secti<strong>on</strong> 1.12 <strong>and</strong><br />

a diversificati<strong>on</strong> into various directi<strong>on</strong>s.<br />

1.14 On a Problem of Optimal Search<br />

A simple search as a classical opertai<strong>on</strong>s research (OR) problem (St<strong>on</strong>e [13]) is treated as a sequential<br />

statistical decisi<strong>on</strong> problem <strong>and</strong> involves some optimal stopping. Given a sequential decisi<strong>on</strong> problem, in<br />

order to find the best decisi<strong>on</strong> (policy) now is whether to stop <strong>and</strong> make a decisi<strong>on</strong> or to go <strong>on</strong> <strong>and</strong> take<br />

another observati<strong>on</strong> it is desirable to know the best decisi<strong>on</strong> in the future., C<strong>on</strong>sequently, the search for an<br />

optimal decisi<strong>on</strong> should not proceed according to chr<strong>on</strong>ological time but in reverse order to work backwards<br />

in time since the present optimum involves the future optimum. This is incorporated in the principle of<br />

dynamic programming (Bellman [14]). In a grid type search, with T [(pk, N] formally denoting the minimum<br />

average number of comparis<strong>on</strong>s of cells per successful search, given N cells <strong>and</strong> prior distributi<strong>on</strong> (pk) <strong>on</strong><br />

k trials. Then the search procedure starts with the selecti<strong>on</strong> of a cell for the first comparis<strong>on</strong> . T [(pk, N] is<br />

subject to the formalism of dynamic programming.<br />

VII


HANS W. GOTTINGER<br />

PREFACE AND INTRODUCTION<br />

2. Intelligent Decisi<strong>on</strong> Systems<br />

2.1 Intelligent Decisi<strong>on</strong> Support systems<br />

We describe intelligent decisi<strong>on</strong> systems as a prototype of a decisi<strong>on</strong> technology that subjects itself to<br />

computerizati<strong>on</strong>, therefore opening itself up to computati<strong>on</strong>al tools such as artificial intelligence techniques<br />

through expert systems, neural networks <strong>and</strong> machine learning. The “intelligence“ <strong>and</strong> computati<strong>on</strong>al parts<br />

have increased tremendously though the Internet over the last 30 years (<str<strong>on</strong>g>Gottinger</str<strong>on</strong>g> [15]) but the underlying<br />

statistical decisi<strong>on</strong> models are still valid <strong>and</strong> ramificati<strong>on</strong>s in applicati<strong>on</strong> areas are widely perceived.<br />

2.2 Statistical Expert Systems<br />

On the interface of machine generated “Big Data“ <strong>and</strong> proper statistical treatment an advice giving program<br />

such as an expert system or decisi<strong>on</strong> support system suggests a targeted range of statistical tools <strong>and</strong> expert<br />

judgements for data analysis involving classificati<strong>on</strong> <strong>and</strong> regressi<strong>on</strong> analysis, decisi<strong>on</strong> trees, variable selecti<strong>on</strong><br />

<strong>and</strong> ec<strong>on</strong>ometrics. The fast computati<strong>on</strong>al generati<strong>on</strong> of <strong>on</strong>line data could also activate built-in-intelligent<br />

mechanisms of classifying, categorizing, visualizing, aggregating diverse unstructured data types thus<br />

allowing data analytic tools for statistical metrics – useful for statistical inference <strong>and</strong> decisi<strong>on</strong>s.<br />

2.3 Artificial Intelligence <strong>and</strong> Ec<strong>on</strong>omic Modelling<br />

Here is <strong>on</strong>e of the early attempts to explore artificial intelligence/expert system techniques for micromacro<br />

ec<strong>on</strong>omic models. It discusses some methodological issues in implementing those tools c<strong>on</strong>necting<br />

influence diagrams with qualitative reas<strong>on</strong>ing <strong>on</strong> graphs <strong>and</strong> data fusi<strong>on</strong> as similar lines of modeling have<br />

been pursued in AI based “qualitative physics“ modeling.<br />

3. Applicati<strong>on</strong>s<br />

3.1 Assessment of Social Value in the Allocati<strong>on</strong> of CT Scanners in the Munich Metropolitan<br />

Area<br />

This is an illustrative case study of a synthetic benefit/risk/cost analysis of an allocati<strong>on</strong> problem of a medical<br />

technology that calculates the social value as a decisi<strong>on</strong> criteri<strong>on</strong>. The empirical inputs are based <strong>on</strong> this<br />

specific case, the value judgements <strong>on</strong> “value of life“ as given in the mid 1980s <strong>and</strong> the medical technology<br />

parameters at that time. The methodology used for this case may be possibly adapted to a comparative case<br />

of resource allocati<strong>on</strong> decisi<strong>on</strong> at any time for other “technology assessment“ purposes with appropriate<br />

impacts <strong>and</strong> overall checked by sensitivity analysis <strong>on</strong> the major input variables.<br />

3.2 Adopti<strong>on</strong> Decisi<strong>on</strong>s <strong>and</strong> Diffusi<strong>on</strong> (Swiss Journal of Ec<strong>on</strong>omics <strong>and</strong> Statistics, 1991)<br />

The article applies the use of decisi<strong>on</strong> modelling under risk/uncertainty to describe the decisi<strong>on</strong>-making<br />

process of a firm in its drive of technology adopti<strong>on</strong> <strong>and</strong> the diffusi<strong>on</strong> of innovati<strong>on</strong>. It shows that adopti<strong>on</strong><br />

decisi<strong>on</strong>s are inheretly linked to risk behavior of firms.<br />

3.3 Choosing Regulatory Opti<strong>on</strong>s when Envir<strong>on</strong>mental Costs are Uncertain<br />

This applicati<strong>on</strong> area is c<strong>on</strong>cerned with the potential of public policies against l<strong>on</strong>g-term climate change.<br />

A model of optimal statistical decisi<strong>on</strong>s is used to determine the value of informati<strong>on</strong> (VI) <strong>on</strong> restricting<br />

greenhouse gas emissi<strong>on</strong>s against choosing effective regulatory measures (including carb<strong>on</strong> taxes) for<br />

implementati<strong>on</strong> of emissi<strong>on</strong> c<strong>on</strong>trol. Since a balancing process evolves over time with collecting of<br />

informati<strong>on</strong> the appropriate algorithmic h<strong>and</strong>ling is through dynamic programming (as in Secs. 1.11 <strong>and</strong><br />

1.14). A crucial parameter in the evaluati<strong>on</strong> of the decisi<strong>on</strong> model is the “critical probability“ or threshold<br />

to determine the differential cost of delaying additi<strong>on</strong>al emissi<strong>on</strong> restricti<strong>on</strong>s when such restricti<strong>on</strong>s will<br />

be necessary in later periods as against the cost of imposing additi<strong>on</strong>al restricti<strong>on</strong>s now that later prove<br />

unnecessary. Alternatively, a “critical probability“ could also determine when the costs of stringently<br />

restricting emissi<strong>on</strong>s are small in the future relative to the foreg<strong>on</strong>e benefits of limiting emissi<strong>on</strong>s in the<br />

VIII


PREFACE AND INTRODUCTION<br />

HANS W. GOTTINGER<br />

current period. Though composed at a time when climate treaties have <strong>on</strong>ly started to be discussed in the<br />

Kyoto Protocol, the method would fit to a scaled-up applicati<strong>on</strong> of the Paris Climate Accord (PCA,2016).<br />

3.4 Dynamic Portfolio Strategies with Transacti<strong>on</strong> Costs (Journal of Policy Studies, 2005)<br />

Here I explore a portfolio investment choice model , in financial ec<strong>on</strong>omics, with a mixed single risky/<br />

riskless asset. to maximize the investor’s expected utility at terminal wealth assuming different forms <strong>and</strong><br />

size of transacti<strong>on</strong> costs in trading of assets.<br />

The vintage collecti<strong>on</strong> of essays over forty years pursues a path from the foundati<strong>on</strong>s of decisi<strong>on</strong> theory,<br />

its mathematical representati<strong>on</strong>s <strong>and</strong> c<strong>on</strong>ceptual ramificati<strong>on</strong>s to aspects of informati<strong>on</strong>, computati<strong>on</strong>,<br />

complexity <strong>and</strong> intelligent decisi<strong>on</strong> systems.<br />

Special applicati<strong>on</strong> areas cover policy analysis of health care delivery, technology adopti<strong>on</strong> in innovating<br />

firms <strong>and</strong> industries, , <strong>and</strong> when to induce effective <strong>and</strong> efficient dynamic regulatory c<strong>on</strong>trol in policies<br />

toward envir<strong>on</strong>mental damage c<strong>on</strong>tainment of climate change processes <strong>and</strong> optimal investment decisi<strong>on</strong>s<br />

with c<strong>on</strong>straints.<br />

<str<strong>on</strong>g>Hans</str<strong>on</strong>g> W. <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g>, Feb. 2018<br />

References<br />

[1] Debreu, G., “Representati<strong>on</strong> of a Preference Ordering by a Numerical Functi<strong>on</strong>“, in Decisi<strong>on</strong> Processes,<br />

R.M. Thrall, C.H. Coombs <strong>and</strong> R.G. Davis, eds., Wiley: New York 1954, 159-165<br />

[2] Debreu, G., “C<strong>on</strong>tinuity Properties of Paretian Utility“, Internati<strong>on</strong>al Ec<strong>on</strong>omic Review 5, 1964, 285-293<br />

[3] Pfanzagl, J., Theory of Measurement, Physica Verlag: Würzburg-Wien 1968<br />

[4] Debreu, G., “Topological Methods in Cardinal Utility Theory“, in Mathematical Methods in the Social<br />

Sciences, K.J.Arrow, S. Karlin <strong>and</strong> P. Suppes, eds., Stanford Univ. Press: Stanford,Ca., 1960,16-26<br />

[5] Vind, K., Independence, Additivity <strong>and</strong> Uncertainty (Studies in Ec<strong>on</strong>omic Theory),<br />

Springer: New York 2003<br />

[6] Savage, L.J., The Foundati<strong>on</strong>s of Statistics, Wiley: New York 1954<br />

[7] Rhodes, J., Applicati<strong>on</strong> of Automata Theory <strong>and</strong> Algebra, World Scientific: Singapore 2010<br />

[8] Sim<strong>on</strong>, H., Models of Bounded Rati<strong>on</strong>ality, Vol. 2, MIT Press: Cambridge,Ma. 1982<br />

[9] March, J.G. <strong>and</strong> H. Sim<strong>on</strong>, Organizati<strong>on</strong>s, Wiley: New York 1958<br />

[10] Marschak, J. <strong>and</strong> R. Radner, The Ec<strong>on</strong>omic Theory of Teams, Yale Univ. Press: New Haven,Cn. 1972<br />

[11] Blackwell, D. <strong>and</strong> M.A. Girshick, Theory of Games <strong>and</strong> Statistical Decisi<strong>on</strong>s, Wiley: New York 1955<br />

[12] Shann<strong>on</strong>, C.E. <strong>and</strong> W. Weaver, The Mathematical Theory of Communicati<strong>on</strong>, The Univ. of Illinois<br />

Press: Urbana, Il. 1949<br />

[13] St<strong>on</strong>e, L.D., Theory of Optimal Search, Academic Press: New York 1975<br />

[14] Bellman, R., Dynamic Programming, Princet<strong>on</strong> Univ. Press: Princet<strong>on</strong>,NJ 1957<br />

[15] <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g>, H.W., Internet Ec<strong>on</strong>omics-Models,Methods <strong>and</strong> Management, Bentham Science: L<strong>on</strong>d<strong>on</strong>.<br />

IX


HANS W. GOTTINGER<br />

PREFACE AND INTRODUCTION<br />

X


1.<br />

PREFERENCES,<br />

INFOR MATION<br />

AND DECISION


1.1 ÜBER DIE EXISTENZ EINER STETIGEN, REELLEN NUTZENFUNKTION<br />

HANS W. GOTTINGER<br />

3


HANS W. GOTTINGER<br />

1.1 ÜBER DIE EXISTENZ EINER STETIGEN, REELLEN NUTZENFUNKTION<br />

4


1.1 ÜBER DIE EXISTENZ EINER STETIGEN, REELLEN NUTZENFUNKTION<br />

HANS W. GOTTINGER<br />

5


HANS W. GOTTINGER<br />

1.1 ÜBER DIE EXISTENZ EINER STETIGEN, REELLEN NUTZENFUNKTION<br />

6


1.1 ÜBER DIE EXISTENZ EINER STETIGEN, REELLEN NUTZENFUNKTION<br />

HANS W. GOTTINGER<br />

7


HANS W. GOTTINGER<br />

1.1 ÜBER DIE EXISTENZ EINER STETIGEN, REELLEN NUTZENFUNKTION<br />

8


1.1 ÜBER DIE EXISTENZ EINER STETIGEN, REELLEN NUTZENFUNKTION<br />

HANS W. GOTTINGER<br />

9


HANS W. GOTTINGER<br />

1.1 ÜBER DIE EXISTENZ EINER STETIGEN, REELLEN NUTZENFUNKTION<br />

290 H.-vV. <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g>: Eine stetige, reelle Nutzenfunkti<strong>on</strong><br />

Doch w 2 P y P w 1 impliziert, wegen w 2 I x 2 , w 1 I x 1 und S. 4, x 2 P<br />

h (y) P x 1 , und das bedeutet lf (y) - f (x) 1 < e. Da x e X und e > 0 willkürlich<br />

gewählt werden können, gewinnen wir die Stetigkeit v<strong>on</strong> f.<br />

Literatur<br />

[l] C. Caratheo dory: Vorlesungen über reelle Funkti<strong>on</strong>en. Leipzig und<br />

Berlin: B. G. Teubner, 1939.<br />

[2] G. De b r e u: Theory of Value. Cowles Foundati<strong>on</strong> for Research in Ec<strong>on</strong>omics<br />

(M<strong>on</strong>ogr. 17), New York: John Wiley & S<strong>on</strong>s, 1959.<br />

[3] H. S<strong>on</strong>nenschein : The Relati<strong>on</strong>ship between Transitive Preference<br />

<strong>and</strong> the Structure of the Choice Space. Ec<strong>on</strong>ometrica 33 (1965), S. 624-634.<br />

[4] H. Wold (in Verbindung mit L. Jureen): Dem<strong>and</strong> Analysis.<br />

New York: John Wiley & S<strong>on</strong>s, 1953.<br />

[5] T. Y ok o y am a: On Uniformity <strong>and</strong> C<strong>on</strong>tinuity C<strong>on</strong>diti<strong>on</strong>s in the<br />

Theory of C<strong>on</strong>sumer's Choice. Osaka Ec<strong>on</strong>omic Papers 3 (1954), S. 29-35.<br />

Anschrift des Verfassers: Dr. <str<strong>on</strong>g>Hans</str<strong>on</strong>g>-Werner <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g>, Research Associate,<br />

Department of Ec<strong>on</strong>omics, University of California, Berkeley, California 94 704,<br />

USA.<br />

Prlnted In A ustrla<br />

10


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

Methodologische Entwicklungen in der Meßtheorie':")<br />

V<strong>on</strong> <str<strong>on</strong>g>Hans</str<strong>on</strong>g> - Werner Gott in g er, München<br />

'') Eberhard Fels (1924-1970) zum Gedenken.<br />

11


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

12


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

13


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

14


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

15


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

16


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

17


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

18


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

19


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

20


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

21


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

22


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

23


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

24


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

25


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

26


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

27


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

28


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

29


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

30


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

31


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

32


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

33


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

34


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

35


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

36


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

37


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

38


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

39


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

40


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

41


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

42


1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

HANS W. GOTTINGER<br />

43


HANS W. GOTTINGER<br />

1.2 METHOLOGISCHE ENTWICKLUNGEN IN DER MESSTHEORIE<br />

44


1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

HANS W. GOTTINGER<br />

45


HANS W. GOTTINGER<br />

1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

46


1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

HANS W. GOTTINGER<br />

47


HANS W. GOTTINGER<br />

1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

48


1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

HANS W. GOTTINGER<br />

49


HANS W. GOTTINGER<br />

1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

50


1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

HANS W. GOTTINGER<br />

51


HANS W. GOTTINGER<br />

1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

52


1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

HANS W. GOTTINGER<br />

53


HANS W. GOTTINGER<br />

1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

54


1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

HANS W. GOTTINGER<br />

55


HANS W. GOTTINGER<br />

1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

56


1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

HANS W. GOTTINGER<br />

57


HANS W. GOTTINGER<br />

1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP<br />

58


1.4 CONDITIONAL UTILITY<br />

HANS W. GOTTINGER<br />

59


HANS W. GOTTINGER<br />

1.4 CONDITIONAL UTILITY<br />

60


1.4 CONDITIONAL UTILITY<br />

HANS W. GOTTINGER<br />

61


HANS W. GOTTINGER<br />

1.4 CONDITIONAL UTILITY<br />

62


1.4 CONDITIONAL UTILITY<br />

HANS W. GOTTINGER<br />

63


HANS W. GOTTINGER<br />

1.4 CONDITIONAL UTILITY<br />

64


1.4 CONDITIONAL UTILITY<br />

HANS W. GOTTINGER<br />

65


HANS W. GOTTINGER<br />

1.4 CONDITIONAL UTILITY<br />

66


1.4 CONDITIONAL UTILITY<br />

HANS W. GOTTINGER<br />

67


HANS W. GOTTINGER<br />

1.4 CONDITIONAL UTILITY<br />

68


1.5 FOUNDATIONS OF LEXICOGRAPHIC UTILITY<br />

HANS W. GOTTINGER<br />

69


HANS W. GOTTINGER<br />

1.5 FOUNDATIONS OF LEXICOGRAPHIC UTILITY<br />

70


1.5 FOUNDATIONS OF LEXICOGRAPHIC UTILITY<br />

HANS W. GOTTINGER<br />

71


HANS W. GOTTINGER<br />

1.5 FOUNDATIONS OF LEXICOGRAPHIC UTILITY<br />

72


1.5 FOUNDATIONS OF LEXICOGRAPHIC UTILITY<br />

HANS W. GOTTINGER<br />

73


HANS W. GOTTINGER<br />

1.5 FOUNDATIONS OF LEXICOGRAPHIC UTILITY<br />

74


1.5 FOUNDATIONS OF LEXICOGRAPHIC UTILITY<br />

HANS W. GOTTINGER<br />

75


HANS W. GOTTINGER<br />

1.5 FOUNDATIONS OF LEXICOGRAPHIC UTILITY<br />

76


1.5 FOUNDATIONS OF LEXICOGRAPHIC UTILITY<br />

HANS W. GOTTINGER<br />

77


HANS W. GOTTINGER<br />

1.5 FOUNDATIONS OF LEXICOGRAPHIC UTILITY<br />

78


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

79


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

80


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

81


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

82


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

83


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

84


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

85


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

86


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

87


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

88


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

89


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

90


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

91


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

92


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

93


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

94


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

95


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

96


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

97


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

98


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

99


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

100


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

101


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

102


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

103


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

104


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

105


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

106


1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

HANS W. GOTTINGER<br />

107


HANS W. GOTTINGER<br />

1.6 DECISION PROBLEMS UNDER UNCERTAINTY BASED ON ENTROPY FUNCTIONALS<br />

108


1.7 CHOICE AND COMPLEXITY<br />

HANS W. GOTTINGER<br />

Mathematical Social Sciences 14 (1987) 1-17<br />

North-Holl<strong>and</strong><br />

1<br />

CHOICE AND COMPLEXITY<br />

<str<strong>on</strong>g>Hans</str<strong>on</strong>g> W. GOTTINGER<br />

The University of Maastricht (RU), Institute of Management Science, PO Box 591, Maastricht,<br />

The Netherl<strong>and</strong>s<br />

<strong>and</strong><br />

Department of Systems Engineering, University of Virginia, Charlol/esville, VA 22901, U.S.A.<br />

Communicated by F.W. Roush<br />

Received 6 May 1986<br />

An attempt is made to propose a c<strong>on</strong>cept of limited rati<strong>on</strong>ality for choice functi<strong>on</strong>s based <strong>on</strong><br />

computability theory in computer science.<br />

Starling with the observati<strong>on</strong> that it is possible to c<strong>on</strong>struct a machine simulating strategies of<br />

each individual in society, <strong>on</strong>e machine for each individual's preference structure, we identify<br />

internal states of this machine with strategies or strategic preferences. Inputs are possible acti<strong>on</strong>s<br />

of other agents in society, thus society is effectively operating as a social choice machine. The<br />

main result states that effective realizati<strong>on</strong> of choice functi<strong>on</strong>s is bound by the 'complexity of<br />

computing machines'. Given a certain social choice machine, this complexity is simply the length<br />

of the shortest program which simulates this machine.<br />

Key words: Limited rati<strong>on</strong>ality; computability; cognitive science; complexity; social choice.<br />

1. Introducti<strong>on</strong><br />

1<br />

Ever since choice theory has established itself as part of ec<strong>on</strong>omic theory <strong>and</strong><br />

mathematical ec<strong>on</strong>omics there have been attempts to axiomatize it <strong>on</strong> the basis<br />

of set theory <strong>and</strong> topology. To the extent that 'human rati<strong>on</strong>ality' <strong>and</strong> 'human<br />

problem-solving' has been taken as an anchor point for c<strong>on</strong>stmcting 'artificial intelligence'<br />

it would be natural to model human choice processes by computati<strong>on</strong>al<br />

procedures <strong>and</strong> by representati<strong>on</strong>s of computati<strong>on</strong>al theory.<br />

In ec<strong>on</strong>omic theory the problem of representati<strong>on</strong> of rati<strong>on</strong>al choice or rati<strong>on</strong>al<br />

decisi<strong>on</strong> mles has obtained primary attenti<strong>on</strong>. The realizability of such representati<strong>on</strong>,<br />

however, in terms of computati<strong>on</strong>al viability has so far been neglected .. In<br />

ec<strong>on</strong>omic theory, with the excepti<strong>on</strong> of Sim<strong>on</strong>'s path-breaking work, the matter of<br />

effective computability of choice <strong>and</strong> decisi<strong>on</strong> mies has essentially been c<strong>on</strong>fined to<br />

the problem of costliness of mies. As A. Rubinstein (1985) pointed out, ec<strong>on</strong>omists<br />

have found it 'difficult to embed the procedural aspects of decisi<strong>on</strong>-making in formal<br />

ec<strong>on</strong>omics models'. As Lewis (1985) has put it: ' .. .if rati<strong>on</strong>ality is c<strong>on</strong>strained by<br />

effective computability within the framework of recursive functi<strong>on</strong>s ... , the noti<strong>on</strong><br />

0165-4896/87/$3.50 © 1987, Elsevier Science Publishers B.V. (North-Holl<strong>and</strong>)<br />

109


HANS W. GOTTINGER<br />

1.7 CHOICE AND COMPLEXITY<br />

110


1.7 CHOICE AND COMPLEXITY<br />

HANS W. GOTTINGER<br />

111


HANS W. GOTTINGER<br />

1.7 CHOICE AND COMPLEXITY<br />

112


1.7 CHOICE AND COMPLEXITY<br />

HANS W. GOTTINGER<br />

113


HANS W. GOTTINGER<br />

1.7 CHOICE AND COMPLEXITY<br />

114


1.7 CHOICE AND COMPLEXITY<br />

HANS W. GOTTINGER<br />

115


HANS W. GOTTINGER<br />

1.7 CHOICE AND COMPLEXITY<br />

116


1.7 CHOICE AND COMPLEXITY<br />

HANS W. GOTTINGER<br />

117


HANS W. GOTTINGER<br />

1.7 CHOICE AND COMPLEXITY<br />

118


1.7 CHOICE AND COMPLEXITY<br />

HANS W. GOTTINGER<br />

119


HANS W. GOTTINGER<br />

1.7 CHOICE AND COMPLEXITY<br />

120


1.7 CHOICE AND COMPLEXITY<br />

HANS W. GOTTINGER<br />

121


HANS W. GOTTINGER<br />

1.7 CHOICE AND COMPLEXITY<br />

122


1.7 CHOICE AND COMPLEXITY<br />

HANS W. GOTTINGER<br />

123


HANS W. GOTTINGER<br />

1.7 CHOICE AND COMPLEXITY<br />

124


1.7 CHOICE AND COMPLEXITY<br />

HANS W. GOTTINGER<br />

125


HANS W. GOTTINGER<br />

1.7 CHOICE AND COMPLEXITY<br />

126


1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

HANS W. GOTTINGER<br />

127


HANS W. GOTTINGER<br />

1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

128


1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

HANS W. GOTTINGER<br />

129


HANS W. GOTTINGER<br />

1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

130


1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

HANS W. GOTTINGER<br />

131


HANS W. GOTTINGER<br />

1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

132


1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

HANS W. GOTTINGER<br />

133


HANS W. GOTTINGER<br />

1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

134


1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

HANS W. GOTTINGER<br />

135


HANS W. GOTTINGER<br />

1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

136


1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

HANS W. GOTTINGER<br />

137


HANS W. GOTTINGER<br />

1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

138


1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

HANS W. GOTTINGER<br />

139


HANS W. GOTTINGER<br />

1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

140


1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

HANS W. GOTTINGER<br />

141


HANS W. GOTTINGER<br />

1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY<br />

142


1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

HANS W. GOTTINGER<br />

!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-)3)4,-567)8,59)<br />

:2;-*&$


HANS W. GOTTINGER<br />

1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

144<br />

!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-)3!++.14)<br />

5,-678)9((2'):)!;/*-?@)<br />

)<br />

&,I;2B*%H)"'#*&'()3*%"*DD'/'%&')(B$B'I'%B()$/')J';B),2B)K'&$2('),D);,((*K-')#$H2'%'((46)L0')<br />

"'&*(*,%


1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

HANS W. GOTTINGER<br />

!<br />

"#$$%&'()*!+,!-,!./0123,!4)#5&675#8(9!:#;%$?!#&!@(A%9%#&!7B=(9,!!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-3)C456)C06DC,!<br />

!<br />

!<br />

9":,:!+5!4;!


HANS W. GOTTINGER<br />

1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-)3!++.14)<br />

5,-678)9((2'):)!;/*-?@)<br />

)<br />

$--,J()B,)"'B'/I*%')B0')&,I;-'K*BC)-'#'-),%)B0')&,I;2B$L*-*BC)/'(B/*&B*,%()$(),2B-*%'")*%)B0')<br />

%'KB)('&B*,%6)<br />

)<br />

*+,-./.01234+-254360<br />

9%) B/$"*B*,%$-) "'&*(*,%) B0',/C) *B) *() H'%'/$--C) $&M%,J-'"H'") B0$B) $B) -'$(B) BJ,) "'D*%*B*,%() ,D)<br />

/$B*,%$-*BC)$/')&,%&'*#$L-'8)"';'%"*%H),%)J0'B0'/)B0')$;;/,$&0)*()$L(B/$&B)3%,/I$B*#'48)L$('")<br />

,%)%,%


1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

HANS W. GOTTINGER<br />

!<br />

"#$$%&'()*!+,!-,!./0123,!4)#5&675#8(9!:#;%$?!#&!@(A%9%#&!7B=(9,!!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-3)C456)C06DC,!<br />

!<br />

9::;!,4#?!:,?'+=#+*@!+@!:,*AB?C!;$4=?DE!+F!#"?!4=#>4B!$,*AB?C5!+@G*BG?!4=#+@-!>$*@!#"?!<br />

?(#?,@4B! H*,B'!


HANS W. GOTTINGER<br />

1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-)3!++.14)<br />

5,-678)9((2'):)!;/*-?@)<br />

)<br />

K0*() *() (B*--) B/2') B,"$C) B0,2H0) B0') (0''/) (*L') ,D) &,I;2B$B*,%$-) ;,M'/) 0$() B*-B'") B0')<br />

N$-$%&')B,M$/")ON/2B')D,/&'P)('$/&0);/,&'"2/'()3&,I;2B$B*,%$-)&,I;-'Q*BC4)D*/(B)$B)B0')<br />

'Q;'%(') $%") B0'%) *%) &,IN*%$B*,%) ,D) O('-D4) ;/,;,('") BM,) ;/*%&*;-'() ,%)<br />

M0*&0)$%)$-H,/*B0I)D,/);-$C*%H)&0'(()&,2-")N')D,/I2-$B'"^)<br />

?6 +&$%) $--) B0') ;,((*N*-*B*'() 3I,#'(4) $%") &,%(B/2&B) $) ('$/&0) B/'') M*B0) N/$%&0'() ,D) 'T2$-)<br />

-'%HB06)U'%&'8)$--)B0')#$/*$%B(),D)B0')I,#'()B,)N')('$/&0'")D,/)$/')&,I;2B'")B,)B0')($I')<br />

"';B06)!B)B0')'%"),D)'$&0)#$/*$B*,%)3$B)B0')'%"),D)B0')N/$%&04)B0');,(*B*,%)*()'#$-2$B'")<br />

NC)I'$%(),D)$)%2I'/*&$-)'#$-2$B*,%)D2%&B*,%6)XC)&,I;$/*%H)B0')%2I'/*&$-)#$-2'(8),%')<br />

&$%) &0,,(') B0') N'(B) I,#') *%) $%C) H*#'%) (B$/B*%H) ;,(*B*,%8) (*I;-C) NC) $) I*%*I$Q*%H)<br />

;/,&'"2/'8)*6'6)$#'/$H*%H)(B/$B'H*'()NC)B0')'#$-2$B*,%)D2%&B*,%6)<br />

=6 _,B)$--);,((*N*-*B*'()$/')(&$%%'"8)(,I')$/')'Q&-2"'")D/,I)&,%(*"'/$B*,%)NC)$)(;'&*$-)/2-'8)<br />

(;'&*$-) ('$/&0) ,/) ;/'


1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

HANS W. GOTTINGER<br />

!<br />

"#$$%&'()*!+,!-,!./0123,!4)#5&675#8(9!:#;%$?!#&!@(A%9%#&!7B=(9,!!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-3)C456)C06DC,!<br />

!<br />

#":! ;*,:! ?5:=:55@! +):)! A*#! =:4'+A-! #*! 4! ':5+,4>=:! -*4=! BC":C=:!<br />

4D*?A#!*G!C*D$?#4#+*AM)!<br />

!<br />

OA! 5?DD4,+P+A-! #":! :($:,+:AC:! *G! H4,+*?5! C":55N$=4J+A-! $,*-,4D5@! ;:! *>5:,H:! #"4#! 5*D:!<br />

$,*-,4D5!"4H:!$?#!D*,:!:D$"45+5!*A!C*D$?#+A-!$*;:,!4=*A-!#,::!5:4,C"!+A!#":!'+,:C#+*A!*G!<br />

*$#+*A! B.E@! ;":,:45! *#":,5! "4H:! #,4':'! *GG! C*D$?#+A-! 5$::'! 4-4+A5#! 5*$"+5#+C4#+*A! *,!<br />

5:=:C#+H+#J! 45! 5*?,C:5! *G! +D$,*H:D:A#! +A! C*D$=:(! $,*-,4D5)! Q:=:C#+H+#J! +5! 4! H:,J! $*;:,G?=!<br />

':H+C:!4A'!5$::'!4!H:,J!;:4J!$?,5?+A-!'+GG:,:A#!,*?#:5!#":!<br />

C*D$?#4#+*A4=!H5)!#":!":?,+5#+C!4$$,*4C"%!#":!G+,5#!>J!?5+A-!A*!5:=:C#+H+#J!4A'!>:+A-!H:,J!G45#@!<br />

#":!5:C*A'!>J!?5+A-!4!=4,-:!4D*?A#!*G!5:=:C#+H+#J!>?#!A*#!,:=J+A-!*A!C*D$?#4#+*A4=!5$::')!Q*@!+A!<br />

4!;4J@!R:,A5#:+AM5!$,*-,4D!+A#,*'?C:5!D*,:!5*$"+5#+C4#+*A!#*!#":!C":55!$,*-,4D)!V*5#!*G!#":!<br />

D46*,!-4D:N$=4J+A-!$,*-,4D5!4,:!>45:'!?$*A!B=*C4=E!=**+-!'4#4)!<br />

!<br />

&"'(#)*+,'#-./0%<br />

S:#!?5!5#4,#!;+#"!4!':G+A+#+*A!*G!4!$,*>=:D!4CC*,'+A-!#*!W:;:==@!Q"4;!4A'!Q+D*A!B.7924E%!L!T!<br />

$,*>=:D! :(+5#5! ;":A:H:,! 4! $,*>=:DN5*=H:,! ':5+,:5! 5*D:! *?#C*D:! *,! 5#4#:! *G! 4GG4+,5! #"4#! ":!<br />

'*:5!A*#!+DD:'+4#:=J!=:DN5*=H+A-M! +5! #*! +AH*=H:! ":?,+5#+C5! #"4#! ,:G=:C#! $,4C#+C4=! ,4+C!5J5#:D5!4A'!C*D$=:(+#J)!<br />

!<br />

T55?D:!#":!:(+5#:AC:!*G!4!G+A+#:!*,!C*?A#4>=:!5:#!Z!*G!5#4#:5@!4A'!4!5:#![!*G!*$:,4#*,5!C*A5+5#+A-!<br />

*G!5:D+-,*?$5!Q!4C#+A-!?$*A!Z)!F":!$,*>=:DN5*=H:,!+5!5::A!45!D*H+A-!#",*?-"!5$4C:!':G+A:'!>J!<br />

#":!5#4#:5!+A!4A!4##:D$#!#*!,:4C"!*A:!*G!4!':5+,:'!5:#!*G!-*4=!5#4#:5)!)!T!$,*>=:D!+5!5*=H:'!;":A!4!<br />

!<br />

!<br />

!"#$%"##$%&&'()'*+)*,-&./).0123&455,6)20).787)% 29!<br />

149


HANS W. GOTTINGER<br />

1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-)3!++.14)<br />

5,-678)9((2'):)!;/*-?@)<br />

)<br />

('K2'%&'),D)('I*H/,2;),;'/$B,/()+)L)+?8+=8666+%)&,2-")M')D,2%")D,/)(,I')"'&,I;,(*B*,%),D)B0')<br />

(B$B'


1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

HANS W. GOTTINGER<br />

!<br />

"#$$%&'()*!+,!-,!./0123,!4)#5&675#8(9!:#;%$?!#&!@(A%9%#&!7B=(9,!!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-3)C456)C06DC,!<br />

!<br />

9,*:;5*;?+@-! +5! A;+@=4C+@-!E5+@-!5*;?+@-! =


HANS W. GOTTINGER<br />

1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-)3!++.14)<br />

5,-678)9((2'):)!;/*-?@)<br />

)<br />

#'/C)/$;*"-C6)K,/)*%(B$%&'8)D,/)%)L)?>)B0')%2IM'/)*()$M,2B)?N>8>>>)$%")D,/)%L)??)*B)*()%'$/-C)=)<br />

I*--*,%6) +'#'/$-) 'O$&B) I$B0'I$B*&$-) (,-2B*,%() ,D) B0*() ;/,M-'I) 0$#') M''%) ;/,;,('"8) M2B) B0'C)<br />

$I,2%B)B,)('%(*M-')&,I;-'B')'%2I'/$B*,%),D)B0')$-B'/%$B*#'(8)B0$B)*(8)'%2I'/$B*,%),D)B0')I,/')<br />

-*P'-C)&*B*'(6)+2&0)I'B0,"()(''I)B,)Q,/P)2;)B,)$M,2B)%)L)=>)$%")B0'%)M/'$P)",Q%)M'&$2('),D)<br />

'O&'((*#')"'I$%")2;,%)&,I;2B'/)B*I'6)<br />

)<br />

R0')B/$#'-*%H)($-'(I$%);/,M-'I)*()&-,('-C)/'-$B'")B,)I$%C),B0'/);/,M-'I()B0$B)$/')&,%(*"'/'")<br />

B,) M') ST


1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

HANS W. GOTTINGER<br />

!<br />

"#$$%&'()*!+,!-,!./0123,!4)#5&675#8(9!:#;%$?!#&!@(A%9%#&!7B=(9,!!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-3)C456)C06DC,!<br />

!<br />

9#! +5! :*;455+?@! ,=:*-;+#+*;! $,*A>=B5! +;#*! :*B$>=(+#@! :>455=5! '=?+;='! +;! #=,B5! *?!<br />

C*,5#D:45=! 4;'! 5$4:=! A*E;'5F! C"+:"! 4,=! =($,=55='! 45! 4! ?E;:#+*;! *?! #"=! >=;-#"! *?! #"=! +;$E#!<br />

5#,+;-F!?*,!=(4B$>=F!#"=!:>455!*?!$,*A>=B5!45!$*>@;*B+4>!5$4:=!:*;5+5#5!*?!4>>!$,*A>=B5!C"+:"!<br />

:4;! A=! '=:+'='! A@! 4! GE,+;-! B4:"+;=! E5+;-! 4;! 4B*E;#! *?! #4$=! #"4#! ;=@;*B+4>!A*E;'='!;EBA=,!*?!B4:"+;=!5#=$5)!<br />

!<br />

G"=!:*B$>=(+#@!#"=*,@!*?!5$=:+?+:!$,*A>=B5F!4>*;-!#"=!>+;=5!6E5#!'=5:,+A='F!"4!4,=4!*?!,=5=4,:")!K#!"+-"=,!>=5!*?!:*B$>=(+#@!L#"4#!+5F!<br />

C"=,=!#"=!#+B=!4;'!5$4:=!A*E;'5!4,=!! >*-+:4>! #"=*,+=5F! 4;'! #"=! C*,N! "45! 5=,=B5! #"4#! 4,=! ?*,B4>>@! '=:+'4A>=! 4,=!<br />

;=*-+:4>! #"=*,+=5)! K#! #"+5! >=F!<br />

$*>@;*B+4>! 5$4:=! :*;#4+;5! B4;@! $,*A>=B5! *?! -,=4#! $,4:#+:4>! +;#=,=5#! 5E:"! 45! #"=! #,4+;-!<br />

54>=5B4;! $,*A>=BF! :*BA+;4#+*;4>! 455+-;B=;#! $,*A>=B5! 4;'! ;=#C*,N! $,*A>=B5! =#:)! C"+:"!<br />

5==B!#*!A=!:*B$E#4#+*;4>>@!+;?=45+A>=F!+;!#"4#!4>>!N;*C;!4>-*,+#"B5!"4>@!C+#"!#"=!5+P=!*?!#"=!+;$E#)!K>#"*E-"!#"=!OE=5#+*;!*?!C"=#"=,!#"+5!<br />

=($*;=;#+4>!-,*C#"!+5!E;4*C=,! A*E;'5! *;! #"=! :*B$>=(+#@! *?! #"=5=! $,*A>=B5F! ,=>4#+=(+#@!"44@!4;!+B$*,#4;#!,*>=)!9#!+5!+;!B4;@!:45=5!$*55+A>=!#*!<br />

,='E:=!*;=!$,*A>=B!#*!4;*#"=,F!#"4#!+5F!#*!?+;'!4!C4@!*?!B4$$+;-!*;=!$,*A>=B!+;#*!4;*#"=,F!5*!<br />

#"4#!+?!4;!=??+:+=;#!5*>E#+*;!C=,=!44A>=!?*,!#"=!>4##=,!$,*A>=BF!#"=;!#"+5!C*E>'!4>5*!-+=B! *?! ,='E:+A+>+#@! +5! #"4#! *?! 4! I:*B$>=#=J!<br />

$,*A>=B)!K!$,*A>=B!+5!:*B$>=#=!+;!4!:*B$>=(+#@!:>455!+?!+#!>+=5!+;!#"=!:>455!4;'!==B!+;!<br />

#"=!:>455!+5!,='E:+A>=!#*!+#)!HE:"!4!$,*A>=B!:4;!A=!#"*E-"#!*?!45!4!"4,'=5#!$,*A>=B!?*,!#"=!:>455F!<br />

,=>4#+=(+#@!<br />

:>455F! :*B$>=#=;=55! B4@! :*;5#+#E#=! =#@)! T*,! =(4B$>=F! +?! 4!<br />

$,*A>=B! +5! :*B$>=#=! +;! $*>@;*B+4>! 5$4:=! *,! :*B$>=#=! +;! UV! #"=;! +#! 5==B5! >+N=>@! #"4#! #"=!<br />

$*>@;*B+4>D#+B=!4>-*,+#"B!?*,!#"=!$,*A>=B!'*=5!;*#!=(+5#)!G"+5!"45!$,4:#+:4>!E=!+;!#"4#!#"=!<br />

'=:+5+*;DB4N=,! *,! ,=5=4,:"=,F! N;*C+;-! #"=! $,*A>=B! +5! :*B$>=#=F! :4;! 4-*,+#"B)!<br />

!<br />

H=:*;'F!:*B$>=#=!$,*A>=B5!$,*=#=!+;!$*>@;*B+4>!5$4:=!5=,


HANS W. GOTTINGER<br />

1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-)3!++.14)<br />

5,-678)9((2'):)!;/*-?@)<br />

)<br />

&$(')D,/)B0'),;'%)J2'(B*,%),D)K0'B0'/);,-C%,I*$-)B*I')'J2$-();,-C%,I*$-)(;$&'6)L0*()J2'(B*,%)<br />

0$() $%) $DD*/I$B*#') $%(K'/) *D) $%") ,%-C) *D) B0'/') 'M*(B() $) ;,-C%,I*$-


1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

HANS W. GOTTINGER<br />

!<br />

"#$$%&'()*!+,!-,!./0123,!4)#5&675#8(9!:#;%$?!#&!@(A%9%#&!7B=(9,!!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-3)C456)C06DC,!<br />

!<br />

"9:,+5#+;! $,+$:#4#+*9'!4#!<br />

5*=D+46*,!#45H5!*E!4!$,*A=9>B5*=D+95!4!#,9>9!5#,:;#:,9)!<br />

!<br />

G"9! #,4'9*EE! A4=4$4,+4H9!4!5#4#9>95%!<br />

!<br />

JG*! 4! ,*:-"! 4$$,*(+>4#+*5! #"4#! 4;"+9D9! #"9! 54>9! V:4=+#?! *E!<br />

$9,E*,>49! #*#4=! 9EE*,#! A?! #C*! '+EE9,9*D95!'99$!+*5!$,*-,4>!C*:='!#4H9!4A*:#!<br />

.///!#+>95!P2/8S!45!=**D9@!C"9,945!M9,*D9K)!<br />

!<br />

W,*>! #"+5! C9! >4?! ;**D95! +95!<br />

;*,,95$*9! $*+$:#4#+*$=9(+#?@! E*,! 5*$"+5#+;4#9'!<br />

"9:,+5#+;!594,;"!$,*;9':,95!-+D9$=9(+#?)!<br />

!<br />

"&'&(&)*&+%<br />

LA,9:@! X+=+$! 495! C+#"! W+4#4@!Z;*9#,+;4!QR!$$)!.8Q7B.833)!<br />

L5$D4==@! \)M)! 4+F4#+*


HANS W. GOTTINGER<br />

1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES<br />

!"#$%&'()*%)+,&*$-)+&*'%&'().'('$/&0)1,2/%$-)3!++.14)<br />

5,-678)9((2'):)!;/*-?@)<br />

)<br />

J,BB*%H'/8K6L63?MM?48)NO,I;2B$B*,%$-)O,(B()$%")P,2%"'").$B*,%$-*BCQ8)*%)+B'HIR--'/8)L68P$-S'/8L6)$%")L6)+;,0%8)<br />

'"(68)T0*-,(,;0C),D)E&,%,I*&(8))+;/*%H'/U)P'/-*%8)==7>M48)O,I;-'X*BC)>=48) O,I;2B$B*,%) $%") O,I;-'X*BC) *%) E&,%,I*&) P'0$#*,/) $%") c/H$%*S$B*,%8)<br />

O$I`/*"H')F%*#6)T/'((U)O$I`/*"H')<br />

]'CI$%8) !6) 3?MVY48) NP,2%"'") O,I;-'X*BC) d2(B*D*'() &,,;'/$B*,%) *%) B0') D*%*B'-C) .';'$B'") T/*(,%'/() ^*-'II$Q8)<br />

E&,%,I*&)\'BB'/()?M8)==Z


1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

HANS W. GOTTINGER<br />

157


HANS W. GOTTINGER<br />

1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

158


1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

HANS W. GOTTINGER<br />

159


HANS W. GOTTINGER<br />

1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

160


1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

HANS W. GOTTINGER<br />

161


HANS W. GOTTINGER<br />

1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

228 H. W. <str<strong>on</strong>g>Gottinger</str<strong>on</strong>g> / An informati<strong>on</strong> theoretic approach<br />

Zh=inf{z;}. Let Z1,=0 <strong>and</strong> for i-:;:.h Jet z;=z;+(Zhl(n-1)). Then by (b)<br />

f(z1, ... , z) v1. So by minimality f(z1, ... , z) = v1. This is a c<strong>on</strong>tradicti<strong>on</strong> since<br />

(z1, ... , Zn ) had a maximum number of zeros am<strong>on</strong>g its coordinates. So some Zi are<br />

zero\ By (c) we now apply this same argument to the functi<strong>on</strong> Uk(m -1) where<br />

No= {J}. Then we find that at least two of the Zi must be zero. By c<strong>on</strong>tinuing this<br />

process we find that all but <strong>on</strong>e of the Zi must be zero.<br />

5. The input machine<br />

The input machine collects certain inputs Xj from sources outside or inside the<br />

organizti<strong>on</strong>, <strong>and</strong> c<strong>on</strong>verts them in a <strong>on</strong>e-to-<strong>on</strong>e fashi<strong>on</strong> into a form that the output<br />

machine can process them. The collecti<strong>on</strong> <strong>and</strong> c<strong>on</strong>versi<strong>on</strong> of Xj will in general<br />

require a certain processing time also, for which the notati<strong>on</strong> tY> was introduced.<br />

(The superscript (i) will henceforth be omitted, for notati<strong>on</strong>al simplicity.)<br />

The allowances for the complexity of an input processing task are different from<br />

those of an output machine, in fact, they appear to have no counterpart <strong>on</strong> the output<br />

machine.<br />

According to a !arge volume of psychometric data, the processing time ('the<br />

reacti<strong>on</strong> time') for an input symbol Xj varies with the probability with which the<br />

symbol arrives. The input machine in other words, somehow quickly accumulates<br />

statistical evidence c<strong>on</strong>cerning the relative frequency with which the various Xj are<br />

received <strong>and</strong> then adapts its processing times accordingly. Symbols that occur rarely<br />

are processed more slowly <strong>and</strong> those that come up frequently are disposed of<br />

quickly. There are, in fact, indicati<strong>on</strong>s that the variati<strong>on</strong> of t i with the probability P i<br />

is roughly logarithmic, i.e.<br />

lj = foj - Cj log Pj J (4)<br />

but this observati<strong>on</strong> does not seem to be uniformly acepted by experimental psychologists.<br />

Under these circumstances it may be appropriate to define load dependence for<br />

input machines in a way that is roughly analogous to Definiti<strong>on</strong> 1 for output<br />

machines, but includes eq. (4) as a special possibility. In such a case the analogy<br />

should further make plausible allowance for the complexity of alternate <strong>and</strong> parallel<br />

processing tasks. The size of an input alphabet can be quite !arge. lt may be appropriate<br />

to associate the noti<strong>on</strong> of the complexity of the task of input processing with<br />

the numbers of input symbols, <strong>and</strong> the probability of their occurrence in roughly the<br />

same way in which this noti<strong>on</strong> was associated with the number of destinati<strong>on</strong>s (or of<br />

permutati<strong>on</strong>s) for the output machine. The qualitative analogy that suggests itself<br />

here would then be this: an input processing task would be the easier, the smaller the<br />

number n of symbols in the output alphabet, <strong>and</strong> if n remains the same the task<br />

should become easier if the frequency of the processing is increased.<br />

162


1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

HANS W. GOTTINGER<br />

163


HANS W. GOTTINGER<br />

1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

164


1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

HANS W. GOTTINGER<br />

165


HANS W. GOTTINGER<br />

1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

166


1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

HANS W. GOTTINGER<br />

167


HANS W. GOTTINGER<br />

1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS<br />

168


1.11 SOME MEASURES OF INFORMATION ARISING IN STATISTICAL GAMES<br />

HANS W. GOTTINGER<br />

169


HANS W. GOTTINGER<br />

1.11 SOME MEASURES OF INFORMATION ARISING IN STATISTICAL GAMES<br />

170


1.11 SOME MEASURES OF INFORMATION ARISING IN STATISTICAL GAMES<br />

HANS W. GOTTINGER<br />

171


HANS W. GOTTINGER<br />

1.11 SOME MEASURES OF INFORMATION ARISING IN STATISTICAL GAMES<br />

172


1.11 SOME MEASURES OF INFORMATION ARISING IN STATISTICAL GAMES<br />

HANS W. GOTTINGER<br />

173


HANS W. GOTTINGER<br />

1.11 SOME MEASURES OF INFORMATION ARISING IN STATISTICAL GAMES<br />

174


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

175


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

176


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

177


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

178


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

179


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

180


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

181


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

182


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

183


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

184


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

185


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

186


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

187


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

188


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

189


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

190


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

191


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

192


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

193


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

194


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

195


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

196


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

197


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

198


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

199


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

200


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

201


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

202


1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

HANS W. GOTTINGER<br />

203


HANS W. GOTTINGER<br />

1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS<br />

204


1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

HANS W. GOTTINGER<br />

205


HANS W. GOTTINGER<br />

1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

206


1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

HANS W. GOTTINGER<br />

207


HANS W. GOTTINGER<br />

1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

208


1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

HANS W. GOTTINGER<br />

209


HANS W. GOTTINGER<br />

1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

210


1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

HANS W. GOTTINGER<br />

211


HANS W. GOTTINGER<br />

1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

212


1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

HANS W. GOTTINGER<br />

213


HANS W. GOTTINGER<br />

1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

214


1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

HANS W. GOTTINGER<br />

215


HANS W. GOTTINGER<br />

1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

216


1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

HANS W. GOTTINGER<br />

217


HANS W. GOTTINGER<br />

1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS<br />

218


1.14 ON A PROBLEM OF OPTIMAL SEARCH<br />

HANS W. GOTTINGER<br />

219


HANS W. GOTTINGER<br />

1.14 ON A PROBLEM OF OPTIMAL SEARCH<br />

220


1.14 ON A PROBLEM OF OPTIMAL SEARCH<br />

HANS W. GOTTINGER<br />

221


HANS W. GOTTINGER<br />

1.14 ON A PROBLEM OF OPTIMAL SEARCH<br />

222


1.14 ON A PROBLEM OF OPTIMAL SEARCH<br />

HANS W. GOTTINGER<br />

223


HANS W. GOTTINGER<br />

1.14 ON A PROBLEM OF OPTIMAL SEARCH<br />

224


1.14 ON A PROBLEM OF OPTIMAL SEARCH<br />

HANS W. GOTTINGER<br />

225


HANS W. GOTTINGER<br />

1.14 ON A PROBLEM OF OPTIMAL SEARCH<br />

226


1.14 ON A PROBLEM OF OPTIMAL SEARCH<br />

HANS W. GOTTINGER<br />

227


HANS W. GOTTINGER<br />

1.14 ON A PROBLEM OF OPTIMAL SEARCH<br />

228


2.<br />

INTELLIGENT<br />

DECISION<br />

SYSTEMS


2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

HANS W. GOTTINGER<br />

231


HANS W. GOTTINGER<br />

2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

232


2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

HANS W. GOTTINGER<br />

233


HANS W. GOTTINGER<br />

2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

234


2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

HANS W. GOTTINGER<br />

235


HANS W. GOTTINGER<br />

2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

236


2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

HANS W. GOTTINGER<br />

237


HANS W. GOTTINGER<br />

2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

238


2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

HANS W. GOTTINGER<br />

239


HANS W. GOTTINGER<br />

2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

240


2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

HANS W. GOTTINGER<br />

241


HANS W. GOTTINGER<br />

2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

242


2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

HANS W. GOTTINGER<br />

243


HANS W. GOTTINGER<br />

2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

244


2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

HANS W. GOTTINGER<br />

245


HANS W. GOTTINGER<br />

2.1 INTELLIGENT DECISION SUPPORT SYSTEMS<br />

246


2.2 STATISTICAL EXPERT SYSTEMS<br />

HANS W. GOTTINGER<br />

247


HANS W. GOTTINGER<br />

2.2 STATISTICAL EXPERT SYSTEMS<br />

248


2.2 STATISTICAL EXPERT SYSTEMS<br />

HANS W. GOTTINGER<br />

249


HANS W. GOTTINGER<br />

2.2 STATISTICAL EXPERT SYSTEMS<br />

250


2.2 STATISTICAL EXPERT SYSTEMS<br />

HANS W. GOTTINGER<br />

251


HANS W. GOTTINGER<br />

2.2 STATISTICAL EXPERT SYSTEMS<br />

252


2.2 STATISTICAL EXPERT SYSTEMS<br />

HANS W. GOTTINGER<br />

253


HANS W. GOTTINGER<br />

2.2 STATISTICAL EXPERT SYSTEMS<br />

254


2.2 STATISTICAL EXPERT SYSTEMS<br />

HANS W. GOTTINGER<br />

255


HANS W. GOTTINGER<br />

2.2 STATISTICAL EXPERT SYSTEMS<br />

256


2.2 STATISTICAL EXPERT SYSTEMS<br />

HANS W. GOTTINGER<br />

257


HANS W. GOTTINGER<br />

2.2 STATISTICAL EXPERT SYSTEMS<br />

258


2.2 STATISTICAL EXPERT SYSTEMS<br />

HANS W. GOTTINGER<br />

259


HANS W. GOTTINGER<br />

2.2 STATISTICAL EXPERT SYSTEMS<br />

260


2.3 ARTIFICIAL INTELLIGENCE AND ECONOMIC MODELLING<br />

HANS W. GOTTINGER<br />

261


HANS W. GOTTINGER<br />

2.3 ARTIFICIAL INTELLIGENCE AND ECONOMIC MODELLING<br />

262


2.3 ARTIFICIAL INTELLIGENCE AND ECONOMIC MODELLING<br />

HANS W. GOTTINGER<br />

263


HANS W. GOTTINGER<br />

2.3 ARTIFICIAL INTELLIGENCE AND ECONOMIC MODELLING<br />

264


2.3 ARTIFICIAL INTELLIGENCE AND ECONOMIC MODELLING<br />

HANS W. GOTTINGER<br />

265


HANS W. GOTTINGER<br />

2.3 ARTIFICIAL INTELLIGENCE AND ECONOMIC MODELLING<br />

266


2.3 ARTIFICIAL INTELLIGENCE AND ECONOMIC MODELLING<br />

HANS W. GOTTINGER<br />

267


HANS W. GOTTINGER<br />

2.3 ARTIFICIAL INTELLIGENCE AND ECONOMIC MODELLING<br />

268


3.<br />

APPLICATIONS


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

271


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

272


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

273


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

274


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

275


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

276


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

277


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

278


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

279


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

280


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

281


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

282


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

283


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

284


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

285


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

286


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

287


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

288


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

289


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

290


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

291


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

292


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

293


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

294


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

295


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

296


3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

HANS W. GOTTINGER<br />

297


HANS W. GOTTINGER<br />

3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA<br />

298


3.2 ADOPTION DECISION AND DIFFUSION<br />

HANS W. GOTTINGER<br />

299


HANS W. GOTTINGER<br />

3.2 ADOPTION DECISION AND DIFFUSION<br />

300


3.2 ADOPTION DECISION AND DIFFUSION<br />

HANS W. GOTTINGER<br />

301


HANS W. GOTTINGER<br />

3.2 ADOPTION DECISION AND DIFFUSION<br />

302


3.2 ADOPTION DECISION AND DIFFUSION<br />

HANS W. GOTTINGER<br />

303


HANS W. GOTTINGER<br />

3.2 ADOPTION DECISION AND DIFFUSION<br />

304


3.2 ADOPTION DECISION AND DIFFUSION<br />

HANS W. GOTTINGER<br />

305


HANS W. GOTTINGER<br />

3.2 ADOPTION DECISION AND DIFFUSION<br />

306


3.2 ADOPTION DECISION AND DIFFUSION<br />

HANS W. GOTTINGER<br />

307


HANS W. GOTTINGER<br />

3.2 ADOPTION DECISION AND DIFFUSION<br />

308


3.2 ADOPTION DECISION AND DIFFUSION<br />

HANS W. GOTTINGER<br />

309


HANS W. GOTTINGER<br />

3.2 ADOPTION DECISION AND DIFFUSION<br />

310


3.2 ADOPTION DECISION AND DIFFUSION<br />

HANS W. GOTTINGER<br />

311


HANS W. GOTTINGER<br />

3.2 ADOPTION DECISION AND DIFFUSION<br />

312


3.2 ADOPTION DECISION AND DIFFUSION<br />

HANS W. GOTTINGER<br />

313


HANS W. GOTTINGER<br />

3.2 ADOPTION DECISION AND DIFFUSION<br />

314


3.2 ADOPTION DECISION AND DIFFUSION<br />

HANS W. GOTTINGER<br />

315


HANS W. GOTTINGER<br />

3.2 ADOPTION DECISION AND DIFFUSION<br />

316


3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

HANS W. GOTTINGER<br />

317


HANS W. GOTTINGER<br />

3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

318


3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

HANS W. GOTTINGER<br />

319


HANS W. GOTTINGER<br />

3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

320


3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

HANS W. GOTTINGER<br />

321


HANS W. GOTTINGER<br />

3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

322


3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

HANS W. GOTTINGER<br />

323


HANS W. GOTTINGER<br />

3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

324


3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

HANS W. GOTTINGER<br />

325


HANS W. GOTTINGER<br />

3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

326


3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

HANS W. GOTTINGER<br />

327


HANS W. GOTTINGER<br />

3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

328


3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

HANS W. GOTTINGER<br />

329


HANS W. GOTTINGER<br />

3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN<br />

330


3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

HANS W. GOTTINGER<br />

331


HANS W. GOTTINGER<br />

3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

332


3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

HANS W. GOTTINGER<br />

333


HANS W. GOTTINGER<br />

3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

334


3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

HANS W. GOTTINGER<br />

335


HANS W. GOTTINGER<br />

3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

336


3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

HANS W. GOTTINGER<br />

337


HANS W. GOTTINGER<br />

3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

338


3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

HANS W. GOTTINGER<br />

339


HANS W. GOTTINGER<br />

3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

340


3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

HANS W. GOTTINGER<br />

341


HANS W. GOTTINGER<br />

3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

342


3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

HANS W. GOTTINGER<br />

343


HANS W. GOTTINGER<br />

3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

344


3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS<br />

HANS W. GOTTINGER<br />

345

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!