Resolving Zeckhauser’s paradox Pawitan, Yudi; Isheden, Gabriel
Theory and decision,
05/2020, Volume:
88, Issue:
4
Journal Article
Peer reviewed
Open access
Zeckhauser’s paradox has puzzled and entertained many rationality enthusiasts for almost half a century. You are forced to play a Russian Roulette with a 6-chamber revolver containing either (A) two ...bullets, or (B) four bullets. Would you pay more to remove the two bullets in (A) than you would to remove one in (B)? Most would say yes, but rational considerations based on the classical utility theory suggest you should not. We discuss a possible solution within the classical framework, by explicitly stating and accounting for more detailed preferences in terms of fewer bullets and smaller debt. To a large extent, the paradox arises due to a surreptitious trespassing of Savage’s Small-World utilities implied by a limited set of preferences to govern a larger world containing potentially conflicting preferences. To avoid logical issues associated with death in the roulette, we also describe a non-fatal game-show version, where you choose one box out of six that could be either empty or contain prize money. Here, the paradox arises when you pay from the prize money, but not when you pay from your own money. In summary, the paradox provides a useful lesson about the normative role of the utility function as a rational guide for our decisions and preferences.
The group ranking problem consists of constructing coherent aggregated results from preference data provided by decision makers. Traditionally, the output of a group ranking problem can be classified ...into ranking lists and maximum consensus sequences. In this study, we propose a consensus preference graph approach to represent the coherent aggregated results of users' preferences. The advantages of our approach are that (1) the graph is built based on users' consensuses, (2) the graph can be understood intuitively, and (3) the relationships between items can be easily seen. An algorithm is developed to construct the consensus preference graph from users' total ranking data. Finally, extensive experiments are carried out using synthetic and real data sets. The experimental results indicate that the proposed method is computationally efficient, and can effectively identify consensus graphs.
► This study proposes a new output type of group ranking problem. ► The new output is a consensus preference graph of items. ► The output graph can be understood intuitively and the relationships between items can be easily seen. ► The experimental results show that the proposed method is efficient and effective.
This paper examines an alternative method for analyzing a collection of Likert items in the multi-criteria decision framework. Likert items are compared in pairs and organized in a set of weighted ...digraphs which are aggregated according to the Potential Method rules. In combination with Factor Analysis this approach gives respondents’ preferences on the scale which approximates a measurable value function. As an application of
the proposed methodology, we examine a potential set of incentives and explore the degree to which they would be accepted by the industry. We use Potential Method to elicit firm’s preferences for given incentives and we seek to explain the difference in these preferences by the firm/market factors. Data is collected through a survey of 190 Croatian enterprises performed in 2002.
Mathematical model of a goal-oriented thinking with feedback is described. Basic notions: decision graph, feed-back hierarchy and self-duality are introduced and explained. A source of the conflict ...in our approach is the ignorance about the importance of decision maker's goals. In contrast to Shar, Simonson & Tversky 4 and Deutsch 2 conflict resolution is modeled as a problem of finding a fixed point of a self-assessment operator, i.e. without adding or removing any decision element from decision hierarchy.
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