A disturbing phenomenon in voting, which causes most of the problems as well as the interest in the field, is that election outcomes (for fixed preferences) can change with the way the ballots are tallied. This causes difficulties because with each possible choice, some set of voters can be...

Tournaments are complete and asymmetric binary relations. This type of binary relation rules out the possibility of ties or indifferences which are quite common in other contexts. In this work we generalize, from a normative point of view, some important tournament solutions to the context in...

Voting paradoxes are unpleasant surprises encountered in elections. They pertain to such phenomena as additional support being detrimental for candidates and not voting leading to better outcomes than voting for some voters. No voting system is immune to all paradoxes and, therefore voting...

McKelvey [4] proved that for strong simple preference aggregation rules applied to multidimensional sets of alternatives, the typical situation is that either the core is nonempty or the top-cycle set includes all available alternatives. But the requirement that the rule be strong excludes,...

This paper analyzes the concept of envy-freeness in the framework of Arrovian social choice theory. We define various no-envy conditions and study their relationships with Arrow's condition of independence of irrelevant alternatives. We also propose a new condition, called Minimal Equity, that...

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...

Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T; a Copeland winner of T is a vertex with a maximum out-degree. In this paper, we show that 13 is the minimum number of vertices that a tournament must have so...