Violations of coalescing in parametric utility measurement
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Violations of coalescing in parametric utility measurement Andreas Glo¨ckner1,2 • Baiba Renerte3,4 • Ulrich Schmidt5,6,7 Ó The Author(s) 2020
Abstract The majority consensus in the empirical literature is that probability weighting functions are typically inverse-S shaped, that is, people tend to overweight small and underweight large probabilities. A separate stream of literature has reported event-splitting effects (also called violations of coalescing) and shown that they can explain violations of expected utility. This leads to the questions whether (1) the observed shape of weighting functions is a mere consequence of the coalesced presentation and, more generally, whether (2) preference elicitation should rely on presenting lotteries in a canonical split form instead of the commonly used coalesced form. We analyze data from a binary choice experiment where all lottery pairs are presented in both split and coalesced forms. Our results show that the presentation in a split form leads to a better fit of expected utility theory and to probability weighting functions that are closer to linear. We thus provide some evidence that the extent of probability weighting is not an ingrained feature, but rather a result of processing difficulties. Keywords Decision making under uncertainty Cumulative prospect theory Expected utility theory Violations of coalescing Event-splitting effects
1 Introduction Experiments on decision making under risk mostly employ a coalesced presentation of lotteries, i.e., branches which lead to the same consequences are combined and the respective probabilities are added up. However, presenting gamble pairs in a canonical split form makes them easier to compare and process for the decision maker since, in the case of binary choice, both gambles involve the same set of probabilities. For illustration, consider the classic paradox of Allais (1953), also termed common consequence effect, where M$ denotes millions of dollars. Figure 1 presents the Allais paradox in the commonly used coalesced form. Here, subjects Extended author information available on the last page of the article
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tend to choose option A in Choice 1 and option B’ in Choice 2, which constitutes a violation of expected utility. Birnbaum (2004) showed that violations of expected utility (EU) in the common ratio effect can be substantially reduced if the gamble pairs are presented in their canonical split form as depicted in Fig. 2. In the canonical split form, which is a commonly known way of splitting, both lotteries are split such that there are equal probabilities on corresponding ranked branches and the numbers of branches are equal in both gambles and minimal. The presentation in Fig. 2 makes it more transparent that both gambles in each choice have an 89% chance of a common outcome, which should be ignored when determining the preferred option under EU. Also other typical violations of EU, like the common ratio effect or violations of transitivity
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