We consider a way of generating voting rules based on a random relation, the winners being alternatives that have the highest probability of being supported. We define different notions of support, such as whether an alternative dominates the other alternatives, or whether an alternative is undominated, and we consider structural assumptions on the form of the random relation, such as being acyclic, asymmetric, connex or transitive. We give sufficient conditions on the supporting function for the associated voting rule to satisfy various properties such as Pareto and monotonicity. The random generation scheme involves a parameter p between zero and one. Further voting rules are obtained by tending p to zero, and by tending p to one, and these limiting rules satisfy a homogeneity property, and, in certain cases, Condorcet consistency. We define a language of supporting functions based on eight natural properties, and categorise the different rules that can be generated for the limiting p cases.
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 firstname.lastname@example.org
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 email@example.com