Aristotle must be turning over in his grave. The theory of democracy can never be the same (actually, it never was!) since Arrow. " (Samuelson, 1973) The following analysis proposes that the Voting Paradox is not a paradox, but rather a question of the candidates' aims.
Collective choice theorists develop a solemn quiver in their voices when they come face to face with the problem labeled as the Voting Paradox, also known as the Cyclical Majority Problem. It arises, for instance, when candidates X and Y have to deal with a voting population A, B, and C whose members have the preference orderings concerning the propositions U, u, and w given in the following Preference Matrix:
A, B, and C can be considered as individual voters or as groups of voters whose individual members have identical preference orderings and therefore vote as a bloc. Cyclical majorities arise as none of the voters or voting blocs is considered to be numerous enough to fulfill the numerical condition of a given decision rule. This assumption means that no voter or voting group represents more than 50% of the votes. It also implies that no two voters (or no two voting groups) have the same preference orderings if the decision rule is fulfilled by the agreement of two voters on the one proposition.
From this and the above matrix, we see that any proposition out of the set zl, u, and w, offered to the voting community A, B and C, can be defeated by a second proposition. In the case where candidate X presents 21 and candidate Y offers w, X will