Perception of probabilities in situations of risk: A case based approach

Abstract

This paper tries to provide a preliminary description of the mental process individuals experience in their attempt to comprehend stated probabilities of simple lotteries.The evaluation of probabilities is based on three main components: lotteries encountered in the past, the realizations of these lotteries, and the similarity between stated probabilities. A probability is evaluated based on the experienced relative frequencies of outcomes that had that stated probability, as well as outcomes of other lotteries, that had similar stated probabilities. This process may result in distortion of probabilities as observed in the literature, in particular overvaluing low probabilities and undervaluing of high probabilities. We also …nd that when the size of the memory grows, the decision maker learns the real value of the stated probabilities.I am indebted to my advisor Itzhak Gilboa for extremely valuable suggestions at all stages of this project, and for his encouragement and advice. I also thank Eddie Dekel, Ady Pauzner, Ariel Rubinstein, Ran Spiegler and Peter Wakker for many helpful suggestions.

Aggregating imprecise or conflicting beliefs: An experimental investigation using modern ambiguity theories

“…2g, gives a curve like these two but more pronounced. This is consistent with the common empirical finding that attitudes towards uncertainty are like those towards risk, but more pronounced (Abdellaoui et al 2005;Fellner 1961 p. 684;Gayer 2010;Hogarth and Einhorn 1990;Kahn and Sarin 1988 p. 270;Kahneman and Tversky 1979 p. 281;Kilka and Weber 2001;Machina 1982 p. 292;Weber 1994 p. 237/238). In other words, the effects of ambiguity (matching probabilities) reinforce those of risk.…”

“…This agrees with the common finding that uncertainty amplifies phenomena found under risk. Several studies have observed a-insensitivity in the gain domain (Abdellaoui et al 2005;Fellner 1961 p. 684;Gayer 2010;Kahn and Sarin 1988 p. 270;Kahneman and Tversky 1975 p. 15 2nd para; Kahneman and Tversky 1979 p. 281 lines −6/−5 and p. 289 l. 5-6; Kilka and Weber 2001;Viscusi 1989;Weber 1994 pp. 237-238).…”

Using a case-based reasoning approach for trading in sports betting markets

“…In this paper, CBR techniques are approached together with probabilistic and fuzzy set-based modeling. Other approaches such as [14], also assess probabilities based on the frequencies of past cases. In [5], authors compare a probabilistic CBR approach with other well-known classification algorithms.…”

Case-based learning with different similarity functions

“…However, since both papers consider a finite set of acts, neither of them addresses the impact of the curvature of the similarity function on behavior. Similarity functions defined on uncountable sets are still largely unstudied, except for Gayer (2003).…”