The extended Condorcet condition: A necessary and sufficient condition for the transitivity of majority decision

This paper presents a synthesis of the necessary and sufficient restrictions that insure a transitive group preference if majority rule is the aggregation procedure. We show the equivalence between transitivity and an extension of the condition of Condorcet which states that if an alternative receives a majority over every other, then it should be the social choice. This extension is equivalent to finding a solution to a system of linear inequalities. We use these inequalities to demonstrate that the recent work on restrictions of voter preferences can be derived from this Extended Condorcet Condition.