This paper extends the work of Gehrlein and Fishburn (1976) and Gehrlein (1982) by providing a general theorem relating to the analytical representation of the probability of an event in a given space of profiles. It applies to any event characterized by a set of linear inequalities regardless...

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,...

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 show that Arrow's condition of independence of irrelevant alternatives is logically related to conditions of consistency of choice (in particular, to Arrow's choice axiom). The relation, however, is indirect. The link is provided by an independence condition due to Hansson (Synthese, 1969)...