We investigate the implications of relaxing Arrow's independence of irrelevant alternatives axiom while retaining transitivity and the Pareto condition. Even a small relaxation opens a floodgate of possibilities for nondictatorial and efficient social choice.

Assuming an odd number of voters, E. S. Maskin recently provided a characterization of majority rule based on full transitivity. This paper characterizes majority rule with a set of axioms that includes two of Maskin's, dispenses with another, and contains weak versions of his other two axioms....

A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let <InlineEquation ID="Equ1"> <EquationSource Format="TEX"><![CDATA[${\cal L}_{C}$]]></EquationSource> </InlineEquation> (resp., <InlineEquation ID="Equ2"> <EquationSource Format="TEX"><![CDATA[$\wp_{C})$]]></EquationSource> </InlineEquation> denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet...</equationsource></inlineequation></equationsource></inlineequation>

Suppose that g is a strategy-proof social choice rule on the domain of all profiles of complete and transitive binary relations that have exactly m indifference classes. If $m \ge 3$ and the range of g has three or more members, then g is dictatorial. If m = 2, then for any set X of feasible...

Given a set of outcomes that affect the welfare of the members of a group, K.J. Arrow imposed the following five conditions on the ordering of the outcomes as a function of the preferences of the individual group members, and then proved that the conditions are logically inconsistent:- The...

The Condorcet rule on the domain of profiles at which there exists a unique Condorcet winner is the unique rule satisfying anonymity, neutrality, and strategy-proofness.

X is infinite and social preference is quasitransitive. Subset Y of X is sufficient for {x,y} if x and y can be socially ordered with individual preference information over Y alone. If there is an integer β such that every pair of alternatives has a sufficient set with at most β members then...

With as few as eight individuals and five alternatives, there are 561, 304, 372, 286, 875, 579, 077, 983 strategy-proof social choice rules.