BoundedRationality_TheAdaptiveToolbox.pdf

312
WulfAlbers
AGGREGATION OF UTILITY ON ONE DIMENSION
Below we consider individual and interpersonal choice conflicts that can be described
by numerical variables as payoffs of different persons under different
conditions, or opinions of different persons concerning state outlays, or estimates
of different persons of probabilities of events. We only consider the case
that all variables of a given problem are on the same dimension. We present a
collection of rules of boundedly rational aggregation of the utility of such variables.
The key tool is the utility approach of prominence theory. The approach
could meanwhile be successfully applied to a variety of different interpersonal
conflict situations.
Principles of Aggregation
As standard task we consider the decision between two alternatives, A, B. The
decision is performed via a preference function P(A, B\ which measures the
preference of alternative^ over B.A is preferred to B, if P(A,B) > 0, mdBtoA if
P(A, B) < 0; these inequations are denoted as the preference criterion. Sometimes
it makes sense to split the preference criterion up into two terms of which
each aggregates the arguments for one alternative as P(A, B) = F(A) -F(B\
thenP^, B) > 0 is equivalent to F(A) > F(B). In two-person situations it can
also make sense to split the arguments according to the persons ij as P(A,
B) = P"(i) -P"(j). The function P(A, B) is constructed according to:
Principles of Aggregation of Utility on One Dimension
(1) utility is measured according to prominence theory
(2) utility is aggregated in an additive way
(3) the utilitiy of a variable has weight +1, -1, or 0
(4) no variable can be selected twice
(5) P(a, b) can be presented as a sum of differences of utility values
The restriction to additive aggregation is surprising, since the literature offers
criteria of the type (M(JC) - u(a))/(u(y) - u(b)). On the other hand, the combination
of linear and logarithmic elements in the utility function 12 suggests that
subjects do not distinguish relative and absolute differences, and therefore only
use one kind of operator, here the addition.
The restriction of weights to+1, -1, or 0, and the condition that every variable
can be used at most once are formally identical to the conditions of the construe
tion of numerical responses. We assume that every important attribute has nonzero
weight. The dependence of this evaluation on individual judgments could
be confirmed under experimental conditions. In situations where two persons
For example, the step structure 0, 10, 20, 50 indicates linear shape in the range of 0,
+10, +20, and logarithmic shape in the range of+10, +20, +50.