|M.Sc Student||Avichai Peretz|
|Subject||Strategic Voting and Partial Efficiency|
|Department||Department of Industrial Engineering and Management||Supervisor||Dr. Eyal Baharad|
|Full Thesis text - in Hebrew|
Many studies in social choice theory discuss a situation where a group of individuals is facing a decision problem, the outcome of which is relevant to its members. The decision problem might be choosing a restaurant, selecting a parliament, approving a company's budget or even deciding whether a defendant is liable. Allowing for preference heterogeneity, many scholars have suggested a voting rule that aggregates the individuals' ranking and yields the group's preferences (note, however, that when a single alternative is to be selected, the complete social ranking is irrelevant).
A common example for such an aggregation is the majority criterion, according to which the selected alternative is the one that is most preferred by a majority of the individuals. The current study focuses on a different class of voting rules, which are usually referred to as "scoring rules". Under these rules, every individual assigns S1 points to his most preferred alternative, S2 to the second best and so on till SK to his less preferred one (S1>SK). A scoring rule selects the alternative that receives the maximal total score.
It is widely known that most voting rules are vulnerable to strategic manipulation in the sense that there exists a preference profile under which at least one voter would benefit from preferences misrepresentation. A-priori, one should distinguish between two types of manipulations; in the first case, the manipulation affects only resource distribution, while in the second, it might reduce social welfare. Put differently, in some cases, a manipulation might result in a selection of a Pareto-dominated alternative (henceforth - inefficient manipulation), which provides an economic-based argument against a strategic manipulation.
In this paper, I focus my attention on this type of manipulation.
An alternative is said to be Pareto-dominated, if there exists another alternative preferred by every individual. Baharad and Neeman (2007) showed that some voting rules are immune to inefficient manipulations; under these rules, none of the individuals could benefit from preference misrepresentation that results in the selection of a Pareto-dominated alternative.
The use of Pareto criterion in economics was intensively criticized, mainly due to the demanding requirement, according to which an allocation a is considered as a Pareto improvement over allocation b if there is no individual whose welfare is reduced, and their exists at least one individual that prefers a over b (an allocation is said to be Pareto-efficient if there is no other allocation which is a Pareto improvement over it). Hence, if a voting rule allows a manipulation that results in the selection of an alternative that is dominated according to the preferences of 95% of the individuals, the voting rule is considered as robustto inefficient manipulation according to the framework suggested by Baharad and Neeman.
In order to handle this difficulty, I have extended the definition of efficiency. Under the new definition, the classical Pareto efficiency becomes a special case: alternative b is referred to as a -dominated by alternative a if there exists an a -majority of the individuals, a Î (0.5,1] , that prefers a to b. An a -dominated alternative is considered as an a - inefficient alternative.
In this study, I have conducted a profound analysis of the sensitivity to a -inefficient manipulation of some major scoring rules (plurality rule, inverse plurality rule and Borda method of count). For every such rule I found the highest a value that allows a strategic manipulation (that enables the selection of an alternative that is preferred by the manipulative coalition) as a function of the electorate size and the number of alternatives. I have thus identified the maximal proportion of the individuals that might prefer a different alternative than the selected one. In addition, I showed that every scoring rule, except the inverseplurality rule, is vulnerable to an a -inefficient manipulation when the number of alternatives is three.