A note on condorcet sets

Suppose we have a set S2 of possible political platforms and a number N (preferably odd) of voters. The platforms will also be called points. If a platform P is preferred to a platform Q by a majority vote, we write P )bQ. We suppose that between any pair of points P and Q there is a relation either P )bQ or Q > P. In order that this should be realistic, we must assume that the number of points is at most countably infinite, but for simplicity we shall go further and assume that the number is finite. When P )p Q we say also that P preponderates Q or Q is preponderated by P. In this note, the word dominates is reserved for Pareto domination: P dominates Q if it is unanimously preferred to Q.