TY - JOUR

T1 - Cognitive foundations of probability

AU - Gilboa, Itzhak

AU - Schmeidler, David

PY - 2002/2

Y1 - 2002/2

N2 - Prediction is based on past cases. We assume that a predictor can rank eventualities according to their plausibility given any memory that consists of repetitions of past cases. In a companion paper, we show that under mild consistency requirements, these rankings can be represented by numerical functions, such that the function corresponding to each eventuality is linear in the number of case repetitions. In this paper we extend the analysis to rankings of events. Our main result is that a cancellation condition h la de Finetti implies that these functions are additive with respect to union of disjoint sets. If the set of past cases coincides with the set of possible eventualities, natural conditions are equivalent to ranking events by their empirical frequencies. More generally, our results may describe how individuals form probabilistic beliefs given cases that are only partially pertinent to the prediction problem at hand, and how this subjective measure of pertinence can be derived from likelihood rankings.

AB - Prediction is based on past cases. We assume that a predictor can rank eventualities according to their plausibility given any memory that consists of repetitions of past cases. In a companion paper, we show that under mild consistency requirements, these rankings can be represented by numerical functions, such that the function corresponding to each eventuality is linear in the number of case repetitions. In this paper we extend the analysis to rankings of events. Our main result is that a cancellation condition h la de Finetti implies that these functions are additive with respect to union of disjoint sets. If the set of past cases coincides with the set of possible eventualities, natural conditions are equivalent to ranking events by their empirical frequencies. More generally, our results may describe how individuals form probabilistic beliefs given cases that are only partially pertinent to the prediction problem at hand, and how this subjective measure of pertinence can be derived from likelihood rankings.

KW - Likelihood ranking

KW - Probability

KW - Ranking of events

UR - http://www.scopus.com/inward/record.url?scp=0036473804&partnerID=8YFLogxK

U2 - 10.1287/moor.27.1.65.330

DO - 10.1287/moor.27.1.65.330

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AN - SCOPUS:0036473804

SN - 0364-765X

VL - 27

SP - 65

EP - 81

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

IS - 1

ER -