טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentZakai Matan
SubjectThe Robustness of Scoring Rules to Noisy Preferences
DepartmentDepartment of Industrial Engineering and Management
Supervisor Dr. Eyal Baharad
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The intellectual discussion over the definition of the optimal social choice mechanism has started long ago and involves various disciplines such as economics, political science, psychology, mathematics, and statistics. The issue of personal decision making and social choice is becoming more relevant as the human society is growing and developing and new questions are raised.

This study deals with social decision making under the assumption that the process of personal decision making suffers from deviations as shown by Kahneman & Tversky (1974).

The main objective of this paper is to find the social choice mechanism which is least vulnerable to such deviations in personal decision making.

Following the work of Baharad & Nitzan, this paper examines the majority decisiveness criterion and the possibility of finding the compromise between the majority's will on one hand and the prevention of a majority tyranny on the other. 

Finally, the issues of noisy preferences and strategic manipulative voting are taken into account. This paper aims to evaluate the different scoring rules according to their vulnerability to these noises. Following the model they developed, the vulnerability of several social choice mechanisms (scoring rules such as Plurality, Inverse Plurality, Borda, Vote for t) is calculated. This criterion is used to find the least vulnerable social choice mechanism to individual decision deviations.

Baharad & Nitzan (2002) prove that under strategic coordinated voting at a level denoted by d, there exists a sufficient condition to assure that a scoring rule is vulnerable to majority decisiveness at the level of  α, ½<α<1.

The analysis of d under the different scoring rules enables us to test their vulnerability to noisy preferences using the model designed to evaluate their sensitivity to majority decisiveness.

I find that under a majority decisiveness scale of α,  ½<α<1, the least vulnerable social choice mechanism to individual decision deviations is the Inverse Plurality rule and, furthermore, under this criterion the mechanism which enables the maximum score allocation to the set of alternatives will be the least vulnerable to deviations. The Inverse Plurality rule that fulfils this demand is a mechanism by which each voter rules out one candidate and leaves the rest with the maximum score possible and with no inner group ranking.

The prospect of finding the optimal social choice mechanism is still far away and involves the implicit definition of the set of criteria.