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An Extreme Point Characterization of Strategy-proof and Unanimous Probabilistic Rules over Binary Restricted Domains

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Working paper
Author/s: 
Hans Peters, Souvik Roy, Soumyarup Sadhukhan, Ton Storcken
Issue number: 
RM/16/012
Series: 
GSBE Research Memoranda
Publisher: 
Maastricht University School of Business and Economics
Year: 
2016
We show that every strategy-proof and unanimous probabilistic rule on a binary restricted domain has binary support, and is a probabilistic mixture of strategy-proof and unanimous deterministic rules. Examples of binary restricted domains include several types of single-dipped domains, the single-peaked domain where peaks are restricted to two adjacent alternatives, and the single-crossing domain with two tops. We also provide some extensions to infinitely many alternatives.
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