Voting rules are known to exhibit various paradoxical or problematic behaviors, typically in the form of their failure to meet the Condorcet criterion or in their vulnerability to strategic voting. Our basic premise is that a decrease in the number of coalitions of voters that exist with similar...

The Condorcet winner in an election is a candidate that could defeat each other candidate in a series of pairwise majority rule elections. The Condorcet efficiency of a voting rule is the conditional probability that the voting rule will elect the Condorcet winner, given that such a winner...

We report in this note some results on the theoretical likelihood of Condorcet's Other Paradox in three alternative elections. This paradox occurs when we have a voting situation such that no Wheighted Scoring Rule (WSR) will select the Pairwise Majority Rule Winner as the WSR winner. We...

A procedure is developed to obtain representations for the probability of election outcomes with the Impartial Anonymous Culture Condition and the Maximal Culture Condition. The procedure is based upon a process of performing arithmetic with integers, while maintaining absolute precision with...

The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise elections. The Condorcet efficiency of a voting procedure is the conditional probability that it will elect the Condorcet winner, given that a Condorcet winner exists....