The same but different: An empirical investigation of the reducibility principle

According to classical utility theory the valuation of any lottery should d epend only on its outcomes and their respective probabilities, and should n ot be affected by the nature, complexity and structure of the chance mechan ism. Previous research has documented systematic violations of this princip le. For example, most subjects prefer lotteries in which the payoffs are co ntingent on the joint occurrence of multiple (high probability) events to s imple lotteries, and lotteries in which the earlier stages offer higher pro babilities than the later stages. We review the various violations of this principle and suggest a classification into two major types associated with misunderstanding of chance mechanisms and attitude towards the chance mech anism and process. In the present study 40 subjects were presented with 30 pairs of binary gambles. In any given pair the lotteries had identical outc omes and equal 'reduced' probabilities (and thus equal expected values). Ho wever, the chance mechanisms varied along a variety of factors such as the size of the sample space, the number of stages, temporal ordering, order of probabilities, their transparency and time constraints. Half the subjects saw lotteries involving gains and the other half considered only losses. Af ter choosing one lottery in each pair, the subjects were asked to explain a nd justify their choices. The findings revealed systematic violations of th e reducibility principle: subjects displayed a preference for lotteries wit h larger sample spaces, and for lotteries that allow quicker resolutions in the earlier stages. A clear distinction between some patterns of preferenc es in the gains and loss domains was revealed. In gambles involving gains s ubjects preferred to have the highest probability on the first stage (and t he lowest probability on the last stage), but displayed the opposite prefer ences for losses. A content analysis of the subjects' stated reasons for th eir choices identified eight major categories. The most frequently invoked were hope, fun, simplicity, stress and time. Copyright (C) 2001 John Wiley & Sons, Ltd.