On the stability of results for aggregation procedures

Abstract

Some distortions are possible in the process of preference aggregation. For example, one voter who is pivotal for some preference profile may not read instructions properly and accidently submit wrong preference. We study how different voting rules react to these distortions for three, four and five alternatives with computer modelling. One of the results is: contrary to the results for the degree of manipulability estimations the most stable rule is the rule that requires less information from preferences when calculating final results — threshold rule. With more alternatives the difference between this rule and rules that require information about the whole ranking is more visible. So, for the rules that require less information the probability to influence the results goes down when the number of alternatives increases. Another result: the resoluteness (weighted average number of alternatives in the final outcome) is positively correlated with the stability of aggregation procedures. Threshold rule is the best one for the most cases when we consider both stability and resoluteness.