Hans Gottinger, Essays on Decision, Information, Computation and Technology
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ESSAYS ON
DECISION,
INFOR MATION,
COMPUTATION &
TECHNOLOGY
ESSAYS ON
DECISION,
INFOR MATION,
COMPUTATION &
TECHNOLOGY
STRATEC Munich, Germany
www.stratec-con.net
stratec_c@yahoo.com
gottingerhans@gmail.com
Aggregate Keywords:
Utility, Measurement/Scaling, Preference Orderings, Decisions, Decision-Making under Uncertainty,
Strategy, Game Theory, Statistical Games/Decisions, Mathematical Economics, Information Economics,
Organizations, Behavioral Economics, Bounded/Limited Rationality, Optimal Search, Complexity
Measures, Intelligent Decision Systems, Statistical Expert Systems, Policy Decisions, Regulatory
Decisions, Social/Environmental Decisions.
CONTENTS
HANS W. GOTTINGER
CONTENTS
ESSAYS ON DECISIONS , INFORMATION,
COMPUTATION AND SYSTEMS
Contents ................................................................................................ I
Foreword. .............................................................................................. III
Preface and Introduction ............................................................................... V
1. Preferences, Information and Decision ................................................. 1
1.1 Über die Existenz einer stetigen, reellen Nutzenfunktion
(On the Existence of a continuous, real-valued utility function) ................................... 3
1.2 Methodologische Entwicklungen in der Meßtheorie
(Methodological Developments in Measurement Theory) ....................................... 11
1.3 Existence of a Utility on a Topological Semigroup ............................................... 45
1.4 Conditional Utility ............................................................................. 59
1.5 Foundations of Lexicographic Utility . ........................................................... 69
1.6 Decision problems under uncertainty based on entropy functionals ............................. 79
1.7 Choice and Complexity . ....................................................................... 109
1.8 Computational Costs and Bounded Rationality (Philosophy of Economics, 223-238) ............. 127
1.9 Krohn-Rhodes Complexity on Decision Rules . .................................................. 143
1.10 An Information Theoretic Approach to Large Organizations .................................... 157
1.11 Some Measures of Information arising in Statistical Games ..................................... 169
1.12 Subjective Qualitative Information Structures based on Orderings .............................. 175
1.13 Qualitative Information and Comparative Informativeness ..................................... 205
1.14 On a Problem of Optimal Search .............................................................. 219
2. Intelligent Decision Systems ........................................................ 229
2.1 Intelligent Decision Support Systems (with Peter Weimann) ..................................... 231
2.2 Statistical Expert Systems ...................................................................... 247
2.3 Artificial Intelligence and Economic Modeling .................................................. 261
3. Applications ....................................................................... 269
3.1 Assessment of Social Value in the Allocation of CT Scanners in the Munich Metropolitan Area ... 271
3.2 Adoption Decisions and Diffusion ............................................................. 299
3.3 Choosing Regulatory Options when Environmental Costs are Uncertain ........................ 317
3.4 Dynamic Portfolio Strategies with Transaction Costs ........................................... 331
I
HANS W. GOTTINGER
CONTENTS
II
FOREWORD
HANS W. GOTTINGER
FOREWORD
Selected writings of a very prolific author over a long-time period typically open a window both on the
evolution of his thinking and on the changing focusses and fads of the scientific community.
are no exception.
The essays, some of which are in German, are hard to subsume. They span across economics, mathematics,
operations research, expert systems, and then some. They include provocative advances, more standard
efforts, and uncontroversial applications. At their best, they delineate new venues of research that could
significantly impact the way we are doing economics. It has been widely argued, rightfully so in my
opinion, that the imperialistic spread of neo-classical thinking has stuck much of the economic profession
in an increasingly noxious Newtonian vision of the economy together with a very narrow conception of
rational decision-making. As usual with theoretical approaches that struggle to cope with the reality, most
improvements efforts at improvement are purely incremental and do not go beyond patching up the main
deficiencies by twisting standard relationships, adding new one, introducing more and more epicycles while
rejecting any true change in paradigm. Not so
suggest radically new ways of addressing fundamental economic questions.
The first and by far larger section of the book focusses on decision-theoretic problems. Some early works,
published largely in the period 1970-1975, centre about conditions under which preferences can be represented
by a utility function with agreeable properties. The issue was acute at the time but has largely been exhausted
nowadays and arguably stalled rather than promoted our mastering of the very large and most important
class of situations where standard utility functions do not exist. Still, it remains at the very core of neoclassical
economics. A standalone contribution reviews the foundational work in measurement theory that
was carried out at the time by such authors as Krantz, Luce, Pfanzagl, Suppes, and Tversky. The logical
link between utility, decision-making, and measurement is immediate, utility is nothing but a measure of
preferences, and decision-making typically requires measurement. Nonetheless, the theory of measurement
has been largely, and unfortunately, overlooked by the economic profession. To my knowledge,
paper is one of the very few attempts to remedy this and remind economists that much work relevant for
the very core of their discourse is being done outside of their narrow disciplinary circles.
Several later papers in the
standard neo-classical framework by introducing concepts and methods from other disciplines, predominantly
information theory, statistical inference, computing, and abstract automata theory. Thus,
in a 1990 paper using the maximum entropy principle to tackle decision-making under uncertainty. This
was brave – entropy is not easy to interpret, understand or visualize in a socio-economic context. The use of
the concept in economics remains marginal up to now but is the subject of active research in the innovative
fringe and increasingly used in such field as game theory, finance, robust optimization, and organization
theory. Other lines of research suggested in several articles hint to the nowadays very active and promising
efforts in complexity economics and agent-based economics. Other papers combine information theory as
the mathematics of communication and storage of information with more standard economic issues. Here
again, one recognizes some early precursors of complexity and agent-based economics, but also of boundedrationality
models and computational games, among others. Inexplicably, and unfortunately, the
not include the nice paper on Structure and Complexity in Socio-Economic Systems that
published with the late Peter Albin in Mathematical Social Sciences 1983.
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HANS W. GOTTINGER
FOREWORD
The second part of the book is devoted to expert systems, which were the main focus of research in AI in
the 80s. Together with the informatician Peter Weimann,
a number of papers on the topic. The one reproduced here outlines a flexible shell that allows considering
conditional probabilities and all information available at the time of decision. A contemporaneous paper
with
which can help a user with little statistical knowledge to design a proper statistical analysis. Another one,
which sketches an approach for building a ruled-based qualitative model of the macro-economy, has again
some reflexion in recent agent-based economic models. I felt pleased and honoured to find that the author’s
argumentation echoes some idea that G.R. (Robert) Boynton and myself expressed independently in a
1987 paper.
The last section of the
been increasingly attracted to less abstract and even to empirical research. It includes a cost-benefits analysis
of PT scanners location and a paper on dynamic environmental regulation under uncertainty. Two other
papers address the questions of optimal dynamic portfolio selection and suggest a novel micro-economic
foundation for diffusion curves.
Reading the
But it is also a rewarding lecture, for a wide circle of senior academics and graduate students alike. In
addition to providing valuable insights beyond the mainstream wisdom it sheds light on the way science
advances. Not only by taking the safe way of incremental improvement in accepted ideas, but also and
more dangerously by combining ideas, by reaching across disciplines, in the hope that some of these efforts
will bloom and survive.
Prof. Dr. Christophe Deissenberg, Luxembourg
April 26, 2018
IV
PREFACE AND INTRODUCTION
HANS W. GOTTINGER
PREFACE AND INTRODUCTION
Not only in economics, psychology and business but generally in most human activities, decisions and decision
making, whether deliberate or routine, play a crucial part in the human pursuit of happiness, prosperity,
individual and collective satisfaction. A precursor of decision-making , strategy and planning, dates back
to the classical Greeks and Chinese up to modern European times. The conceptual tools developed with
game theory, statistical decision theory, operations research, systems analyis/engineering and management
science all originated in the twentiest century and are fast expanding in the digital world with intelligent
decision systems. Applications proliferate in health care (medical decision-making), logistics, transportation,
industrial and public services facilitated through enhanced tools involving artificial intelligence (AI),
machine learning, human-machine interactions, and machine-to-machine cooperations (Internet of Things).
Within economics the behavioral foundations emerged from game theory with links to
competition theory and policy, competitiveness, organizations and teams up to managerial economics
with decision analysis of multiple objectives, risk and uncertainty. New subdisciplines have emerged such
as information economics, computational economics, behavioral and experimental economics.The latter
got recent prominence through Nobel Prizes in economics for D.Kahneman (2002) and R. Thaler (2017).
The collection of selected essays to follow emphasizes some limited foundational, theme related key issues
subsumed under the title. We proceed partly in chronological order which also moves from more theoretical,
conceptual themes to further application. All are categorized in three parts. At the end a brief bibliography
points to relevant related literature.
1. Preferences, Information and Decisions
1.1. Über die Existenz einer stetigen, reellen Nutzenfunktion (On the Existence of a continuous,
real-valued utility function)
The article pursues a simple representation of binary relations , preference-indifference or strict preference,
on a bundle of objects X (commodity bundles) by a numerical function (utility) on the real line. For its
representation it only uses ordering properties compatible for continuous functions on the real line. This
distinguishes itself from G. Debreu’s representation theorems (Debreu [1]) as he uses
ordered topological spaces and structural topological properties later extended to continuity properties of
Paretian utility (Debreu [2]). The reason behind is that basic rational preferences can be shown for “ordinal
utility functions“ in deterministic settings (or consumer choice theory) without taking recourse to more
aadvanced topological tools. The latter lead to more elegant representations but less intuitive economic
interpretations.
1.2. Methodologische Entwicklungen in der Messtheorie (Methodological Developments in
Measurement Theory)
This piece serves as a limited survey on measurement theory following a comprehensive , seminal treatment
by Pfanzagl [3]. It complements issues of measurement of utility theory as used in economic and psychology
research. We show the similarity in the structure of measurement theory to that of utility theory.
It lends itself to (a) algebraic metric operations , (b) axiomatic models, (c) order relations linking various
entities, (d) topology on ordered sets and (e) transformations of empirical relational systems on numerical
scales.
1.3 Existence of a Utility on a Topological Semigroup
Here we go beyond ordinal utility of Sec. 1.1. and explore the connection between cardinal and expected
utility theory. Again the work of G. Debreu [4]
has been seminal. To prove existence for an additive utility representation we need specific algebraic
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HANS W. GOTTINGER
PREFACE AND INTRODUCTION
assumptions in addition to those of the order topology commonly found in an orderd to topological semigroup
(tsg). The use of an order topology on a semigroup suggests a wide variety of embeddings of preference
orderings into real numbers through dimensional transformations. That is, a tsg would allow a collection
of metrics (beyond additivity) to be transformed into real numbers to “cardinalize“ utilities. Utilities on
tsgs would fit as one category of several algebraic-topological constructs to clasif diverse preference orders
and utilities (Vind [5]).
1.4 Conditional Utility
Here I consider a situation where the utility of a risky/uncertain prospect in a Von Neumann-Morgenstern
utility context is affected by an “extraneous chance mechanism“, sort of stochastic shock through changes
of states of nature which additionally affects its utility valuation. Putting it in Savage’s system [6] of
decision acts would yield the difference between prior utility (non conditionalized) and posterior utility
(conditionalized) as a revealed measure of the value of information (VI) provided one would know about
the extraneous chance mechanism.
1.5 Foundations of Lexicographic Utility
A common preference order on the choice of sure or random prospects would be open to tradeoff or
compensatory choices reflected simply in microeconomic standard indifference diagrams. Lexicographic
utility can no longer be represented as a real-valued function but is multidimensional on a vector space.
In between we could think of mixed preferences, lexicographic or compensatory, or lexicographic subject
to 2nd, ... , nth order fixed constraints making a feasible preference set. Also stochastic preferences over
lexicographic choices allow lexicographic tradeoff structures.
1.6 Decision Problems under Uncertainty based on Entropy Functionals (Theory and Decision,
1990)
In this paper it is shown how various criteria of optimal decisions under uncertainty relate to the entropy
function known from classical information theory.
Of particular interest is the “Expected Utility of Perfect Information“(EUPI) being closely linked to Shannon’s
information measure. This gives rise to other decision theoretic notions such as expected opportunity loss,
payoff relevant information emerging from statistical decision analysis . They are conceptually applied
to optimality at equilibrium in many person games as well as to specific types of economic organizations
such as teams.
1.7 Choice and Complexity
Here we relate human choice processes to computation and machines. We move from the notions of
effective computability, effective algorithms to computational complexity with respect to computable
relations identified as preference relations generating choice processes. In the center of observations will
be a basic model of a social choice machine (SCM). The basic features from a SCM would be threefold:
(i) characterizing computational rationality as a sort of bounded or limited human/machine rationality. (ii)
computational rationality being bound by the computational complexity of the choice process, (iii) rational
choice processes being restricted by the computational difficulty of effectively realizing rational choice
functions. Exploring recursive computational functions in recursive topological spaces yield a description
of effective computability and corresponding complexity. They end up being “simulated“ by sequential
finite state machines as Turing machines. The complexity number of a Turing machine simulating a choice
function is the minimal length of the program which simulates this machine.
1.8 Computational Costs and Bounded Rationality
The bound will be achieved by the fact that computations are not costless, that is they use procedures that
require the use of scarce resources . In such situations decision may use simple heuristics or “rules of
thumb“ to reduce the cost of computation. A device to measure computational bounds could be finite state
sequential machines or Turing machines. Some applications relate to the construction of aggregation of a
consumer price index up to decentralized resource allocation in the theory of the firm.
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HANS W. GOTTINGER
1.9 Krohn-Rhodes Complexity on Decision Rules
This is designed as an updated review of algebraic complexity of Krohn-Rhodes [7] and its connection to
bounded rationality properties of H. Simon [8], its intrinsic application to chess-playing programs, heuristics
and problem solving with interface issues of economics to computer and management science.
1.10 An Information-Theoretic Approach to Large Organizations
Here we look at the interaction of decision , information and performance in large economic organizations
and challenges that would arise from issues of bounded rationality treated in previous sections. Decision
theoretic and computable models of organizations have been advanced by March and Simon [9] and
Marschak and Radner [10]. I build processing tasks in terms of a “machine model“ that face payoff relevant
information and complexity limits.
1.11 Some Measures of Information arising in Statistical Games
Payoff relevant information with respect to an expected utility/loss function arises from statistical decision
functions embedded in game theory (Blackwell and Girshick [11]). They serve as value of information
(VI) provided by experiments. In a best sense VI, positive or negative, is the amount that payoff-relevant
information adds to or reduces from the payoff function associated with a decision in a statistical game. I
propose various measures of information emerging from statistical decision theory that reflect the economic
aspects of usefulness of information (based on some kind of utility or loss function) rather than the original
physical/engineering viewpoint of transmitting and controlling information flows through a large (noisy
or noiseless) communication channel (Shannon and Weaver [12]). Thus it creates an informational metric
for payoff functions in terms of an economic value of information.
1.12 Subjective Qualitative Information Structures based on Orderings
In this essay I reverse the qualitative relation “not more probable than“ as a “primitive“ of probability to
information in review of Savage’s [6] introduction to subjective probability. This is an attempt to axiomatize
subjective information as a conceptual precursor to generating subjective probabilities on corresponding
(information induced) events. The primitive relation “not more informative than“ is constructed on the basis
of order topopologies by the Hungarian mathematician A. Cszaszar called topogenous structures. I then
show that semi-topogeneous information structures (also named experiments) have a natural mapping on
subjective probability structures of the Savage type. With the more recent advance of artificial intelligence,
machine learning and big data potential applications can be foreseen that such qualitative information
structures could be machine-generated in terms of qualitative orderings.
1.13 Qualitative Information and Comparative Informativeness
This essay provides a conceptual qualification , refinement and expansion of the previous Section 1.12 and
a diversification into various directions.
1.14 On a Problem of Optimal Search
A simple search as a classical opertaions research (OR) problem (Stone [13]) is treated as a sequential
statistical decision problem and involves some optimal stopping. Given a sequential decision problem, in
order to find the best decision (policy) now is whether to stop and make a decision or to go on and take
another observation it is desirable to know the best decision in the future., Consequently, the search for an
optimal decision should not proceed according to chronological time but in reverse order to work backwards
in time since the present optimum involves the future optimum. This is incorporated in the principle of
dynamic programming (Bellman [14]). In a grid type search, with T [(pk, N] formally denoting the minimum
average number of comparisons of cells per successful search, given N cells and prior distribution (pk) on
k trials. Then the search procedure starts with the selection of a cell for the first comparison . T [(pk, N] is
subject to the formalism of dynamic programming.
VII
HANS W. GOTTINGER
PREFACE AND INTRODUCTION
2. Intelligent Decision Systems
2.1 Intelligent Decision Support systems
We describe intelligent decision systems as a prototype of a decision technology that subjects itself to
computerization, therefore opening itself up to computational tools such as artificial intelligence techniques
through expert systems, neural networks and machine learning. The “intelligence“ and computational parts
have increased tremendously though the Internet over the last 30 years (
statistical decision models are still valid and ramifications in application areas are widely perceived.
2.2 Statistical Expert Systems
On the interface of machine generated “Big Data“ and proper statistical treatment an advice giving program
such as an expert system or decision support system suggests a targeted range of statistical tools and expert
judgements for data analysis involving classification and regression analysis, decision trees, variable selection
and econometrics. The fast computational generation of online data could also activate built-in-intelligent
mechanisms of classifying, categorizing, visualizing, aggregating diverse unstructured data types thus
allowing data analytic tools for statistical metrics – useful for statistical inference and decisions.
2.3 Artificial Intelligence and Economic Modelling
Here is one of the early attempts to explore artificial intelligence/expert system techniques for micromacro
economic models. It discusses some methodological issues in implementing those tools connecting
influence diagrams with qualitative reasoning on graphs and data fusion as similar lines of modeling have
been pursued in AI based “qualitative physics“ modeling.
3. Applications
3.1 Assessment of Social Value in the Allocation of CT Scanners in the Munich Metropolitan
Area
This is an illustrative case study of a synthetic benefit/risk/cost analysis of an allocation problem of a medical
technology that calculates the social value as a decision criterion. The empirical inputs are based on this
specific case, the value judgements on “value of life“ as given in the mid 1980s and the medical technology
parameters at that time. The methodology used for this case may be possibly adapted to a comparative case
of resource allocation decision at any time for other “technology assessment“ purposes with appropriate
impacts and overall checked by sensitivity analysis on the major input variables.
3.2 Adoption Decisions and Diffusion (Swiss Journal of Economics and Statistics, 1991)
The article applies the use of decision modelling under risk/uncertainty to describe the decision-making
process of a firm in its drive of technology adoption and the diffusion of innovation. It shows that adoption
decisions are inheretly linked to risk behavior of firms.
3.3 Choosing Regulatory Options when Environmental Costs are Uncertain
This application area is concerned with the potential of public policies against long-term climate change.
A model of optimal statistical decisions is used to determine the value of information (VI) on restricting
greenhouse gas emissions against choosing effective regulatory measures (including carbon taxes) for
implementation of emission control. Since a balancing process evolves over time with collecting of
information the appropriate algorithmic handling is through dynamic programming (as in Secs. 1.11 and
1.14). A crucial parameter in the evaluation of the decision model is the “critical probability“ or threshold
to determine the differential cost of delaying additional emission restrictions when such restrictions will
be necessary in later periods as against the cost of imposing additional restrictions now that later prove
unnecessary. Alternatively, a “critical probability“ could also determine when the costs of stringently
restricting emissions are small in the future relative to the foregone benefits of limiting emissions in the
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HANS W. GOTTINGER
current period. Though composed at a time when climate treaties have only started to be discussed in the
Kyoto Protocol, the method would fit to a scaled-up application of the Paris Climate Accord (PCA,2016).
3.4 Dynamic Portfolio Strategies with Transaction Costs (Journal of Policy Studies, 2005)
Here I explore a portfolio investment choice model , in financial economics, with a mixed single risky/
riskless asset. to maximize the investor’s expected utility at terminal wealth assuming different forms and
size of transaction costs in trading of assets.
The vintage collection of essays over forty years pursues a path from the foundations of decision theory,
its mathematical representations and conceptual ramifications to aspects of information, computation,
complexity and intelligent decision systems.
Special application areas cover policy analysis of health care delivery, technology adoption in innovating
firms and industries, , and when to induce effective and efficient dynamic regulatory control in policies
toward environmental damage containment of climate change processes and optimal investment decisions
with constraints.
References
[1] Debreu, G., “Representation of a Preference Ordering by a Numerical Function“, in Decision Processes,
R.M. Thrall, C.H. Coombs and R.G. Davis, eds., Wiley: New York 1954, 159-165
[2] Debreu, G., “Continuity Properties of Paretian Utility“, International Economic Review 5, 1964, 285-293
[3] Pfanzagl, J., Theory of Measurement, Physica Verlag: Würzburg-Wien 1968
[4] Debreu, G., “Topological Methods in Cardinal Utility Theory“, in Mathematical Methods in the Social
Sciences, K.J.Arrow, S. Karlin and P. Suppes, eds., Stanford Univ. Press: Stanford,Ca., 1960,16-26
[5] Vind, K., Independence, Additivity and Uncertainty (Studies in Economic Theory),
Springer: New York 2003
[6] Savage, L.J., The Foundations of Statistics, Wiley: New York 1954
[7] Rhodes, J., Application of Automata Theory and Algebra, World Scientific: Singapore 2010
[8] Simon, H., Models of Bounded Rationality, Vol. 2, MIT Press: Cambridge,Ma. 1982
[9] March, J.G. and H. Simon, Organizations, Wiley: New York 1958
[10] Marschak, J. and R. Radner, The Economic Theory of Teams, Yale Univ. Press: New Haven,Cn. 1972
[11] Blackwell, D. and M.A. Girshick, Theory of Games and Statistical Decisions, Wiley: New York 1955
[12] Shannon, C.E. and W. Weaver, The Mathematical Theory of Communication, The Univ. of Illinois
Press: Urbana, Il. 1949
[13] Stone, L.D., Theory of Optimal Search, Academic Press: New York 1975
[14] Bellman, R., Dynamic Programming, Princeton Univ. Press: Princeton,NJ 1957
[15]
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1.
PREFERENCES,
INFOR MATION
AND DECISION
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290 H.-vV.
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
h (y) P x 1 , und das bedeutet lf (y) - f (x) 1 < e. Da x e X und e > 0 willkürlich
gewählt werden können, gewinnen wir die Stetigkeit von f.
Literatur
[l] C. Caratheo dory: Vorlesungen über reelle Funktionen. Leipzig und
Berlin: B. G. Teubner, 1939.
[2] G. De b r e u: Theory of Value. Cowles Foundation for Research in Economics
(Monogr. 17), New York: John Wiley & Sons, 1959.
[3] H. Sonnenschein : The Relationship between Transitive Preference
and the Structure of the Choice Space. Econometrica 33 (1965), S. 624-634.
[4] H. Wold (in Verbindung mit L. Jureen): Demand Analysis.
New York: John Wiley & Sons, 1953.
[5] T. Y ok o y am a: On Uniformity and Continuity Conditions in the
Theory of Consumer's Choice. Osaka Economic Papers 3 (1954), S. 29-35.
Anschrift des Verfassers: Dr.
Department of Economics, University of California, Berkeley, California 94 704,
USA.
Prlnted In A ustrla
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'') Eberhard Fels (1924-1970) zum Gedenken.
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1.3 EXISTENCE OF A UTILITY ON A TOPOLOGICAL SEMIGROUP
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1.4 CONDITIONAL UTILITY
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1.7 CHOICE AND COMPLEXITY
HANS W. GOTTINGER
Mathematical Social Sciences 14 (1987) 1-17
North-Holland
1
CHOICE AND COMPLEXITY
The University of Maastricht (RU), Institute of Management Science, PO Box 591, Maastricht,
The Netherlands
and
Department of Systems Engineering, University of Virginia, Charlol/esville, VA 22901, U.S.A.
Communicated by F.W. Roush
Received 6 May 1986
An attempt is made to propose a concept of limited rationality for choice functions based on
computability theory in computer science.
Starling with the observation that it is possible to construct a machine simulating strategies of
each individual in society, one machine for each individual's preference structure, we identify
internal states of this machine with strategies or strategic preferences. Inputs are possible actions
of other agents in society, thus society is effectively operating as a social choice machine. The
main result states that effective realization of choice functions is bound by the 'complexity of
computing machines'. Given a certain social choice machine, this complexity is simply the length
of the shortest program which simulates this machine.
Key words: Limited rationality; computability; cognitive science; complexity; social choice.
1. Introduction
1
Ever since choice theory has established itself as part of economic theory and
mathematical economics there have been attempts to axiomatize it on the basis
of set theory and topology. To the extent that 'human rationality' and 'human
problem-solving' has been taken as an anchor point for constmcting 'artificial intelligence'
it would be natural to model human choice processes by computational
procedures and by representations of computational theory.
In economic theory the problem of representation of rational choice or rational
decision mles has obtained primary attention. The realizability of such representation,
however, in terms of computational viability has so far been neglected .. In
economic theory, with the exception of Simon's path-breaking work, the matter of
effective computability of choice and decision mies has essentially been confined to
the problem of costliness of mies. As A. Rubinstein (1985) pointed out, economists
have found it 'difficult to embed the procedural aspects of decision-making in formal
economics models'. As Lewis (1985) has put it: ' .. .if rationality is constrained by
effective computability within the framework of recursive functions ... , the notion
0165-4896/87/$3.50 © 1987, Elsevier Science Publishers B.V. (North-Holland)
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1.8 COMPUTATIONAL COSTS AND BOUNDED RATIONALITY
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1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES
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1.9 KROHN-RHODES COMPLEXITY ON DECISION RULES
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1.10 AN INFORMATION THEORETIC APPROACH TO LARGE ECONOMIC ORGANIZATIONS
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Zh=inf{z;}. Let Z1,=0 and for i-:;:.h Jet z;=z;+(Zhl(n-1)). Then by (b)
f(z1, ... , z) v1. So by minimality f(z1, ... , z) = v1. This is a contradiction since
(z1, ... , Zn ) had a maximum number of zeros among its coordinates. So some Zi are
zero\ By (c) we now apply this same argument to the function Uk(m -1) where
No= {J}. Then we find that at least two of the Zi must be zero. By continuing this
process we find that all but one of the Zi must be zero.
5. The input machine
The input machine collects certain inputs Xj from sources outside or inside the
organiztion, and converts them in a one-to-one fashion into a form that the output
machine can process them. The collection and conversion of Xj will in general
require a certain processing time also, for which the notation tY> was introduced.
(The superscript (i) will henceforth be omitted, for notational simplicity.)
The allowances for the complexity of an input processing task are different from
those of an output machine, in fact, they appear to have no counterpart on the output
machine.
According to a !arge volume of psychometric data, the processing time ('the
reaction time') for an input symbol Xj varies with the probability with which the
symbol arrives. The input machine in other words, somehow quickly accumulates
statistical evidence concerning the relative frequency with which the various Xj are
received and then adapts its processing times accordingly. Symbols that occur rarely
are processed more slowly and those that come up frequently are disposed of
quickly. There are, in fact, indications that the variation of t i with the probability P i
is roughly logarithmic, i.e.
lj = foj - Cj log Pj J (4)
but this observation does not seem to be uniformly acepted by experimental psychologists.
Under these circumstances it may be appropriate to define load dependence for
input machines in a way that is roughly analogous to Definition 1 for output
machines, but includes eq. (4) as a special possibility. In such a case the analogy
should further make plausible allowance for the complexity of alternate and parallel
processing tasks. The size of an input alphabet can be quite !arge. lt may be appropriate
to associate the notion of the complexity of the task of input processing with
the numbers of input symbols, and the probability of their occurrence in roughly the
same way in which this notion was associated with the number of destinations (or of
permutations) for the output machine. The qualitative analogy that suggests itself
here would then be this: an input processing task would be the easier, the smaller the
number n of symbols in the output alphabet, and if n remains the same the task
should become easier if the frequency of the processing is increased.
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1.11 SOME MEASURES OF INFORMATION ARISING IN STATISTICAL GAMES
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1.12 SUBJECTIVE QUALITATIVE INFORMATION – STRUCTURES BASED ON ORDERINGS
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1.13 QUALITATIVE INFORMATION AND COMPARATIVE INFORMATIVENESS
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2.
INTELLIGENT
DECISION
SYSTEMS
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2.2 STATISTICAL EXPERT SYSTEMS
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3.
APPLICATIONS
3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA
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3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA
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3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA
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HANS W. GOTTINGER
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3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA
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3.1 ASSESSMENT OF SOCIAL VALUE IN THE ALLOCATION OF CT SCANNERS IN THE MMA
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3.2 ADOPTION DECISION AND DIFFUSION
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.3 CHOOSING REGUATORY OPTIONS WHEN ENVIRONMENTAL COSTS ARE UNCERTAIN
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3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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HANS W. GOTTINGER
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3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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HANS W. GOTTINGER
3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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HANS W. GOTTINGER
3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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3.4 DYNAMIC PORTFOLIO STRATEGIES WITH TRANSACTION COSTS
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