Theoretical Statistics and Mathematics Unit, ISI Delhi

October 19, 2011 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Souvik Roy,
Indian Statistical Institute

Title:
An Extreme point Characterization of Strategy-proof Probabilistic rules

Abstract of Talk

We consider collective decision problems with a finite number of agents who have single-peaked preferences on the real line. A probabilistic decision scheme assigns a probability distribution over the set of alternatives to every profile of reported preferences. The main result of the paper is a characterization of the class of unanimous and strategy-proof probabilistic schemes with the aid of deterministic rules as defined by H. Moulin (Public Choice 35 (1980), 437-455). Thereby, the work of Moulin (1980) is extended to the probabilistic framework. Here we give an extreme point characterization of the aforesaid class of probabilistic schemes with deterministic rules as extreme points. Thereby, we show that in single-peaked preference domains any strategy-proof probabilistic rule can be expressed as a convex combination of the strategy proof deterministic rules. This characterization helps in solving other problems such as finding the mechanism that maximizes ex-ante total expected utility of all agents. This is because, given this characterization, maximum ex-ante total utility can be obtained over the set of deterministic rules.
Co-authors: Hans Peters, Arunava Sen, and Ton Storcken.