elections

Part three: There exists a dictator Part three: Since voter k is the dictator for B over C, the pivotal voter for B over C must appear among the first k voters. That is, outside of segment two. Likewise, the pivotal voter for C over B must appear among voters k through N. That is, outside of Segment One. In this part of the argument we refer back to the original ordering of voters, and compare the positions of the different pivotal voters (identified by applying parts one and two to the other pairs of candidates). First, the pivotal voter for B over C must appear earlier (or at the same position) in the line than the dictator for B over C: As we consider the argument of part one applied to B and C, successively moving B to the top of voters' ballots, the pivot point where society ranks B above C must come at or before we reach the dictator for B over C. Likewise, reversing the roles of B and C, the pivotal voter for C over B must be at or later in line than the dictator for B over C. In short, if kX/Y denotes the position of the pivotal voter for X over Y (for any two candidates X and Y), then we have shown kB/C ≤ kB/A ≤ kC/B. Now repeating the entire argument above with B and C switched, we also have kC/B ≤ kB/C. Therefore, we have kB/C = kB/A = kC/B and the same argument for other pairs shows that all the pivotal voters (and hence all the dictators) occur at the same position in the list of voters. This voter is the dictator for the whole election.

thomas paine

These are the times that try men's souls: The summer soldier and the sunshine patriot will, in this crisis, shrink from the service of their country; but he that stands it now, deserves the love and thanks of man and woman. Tyranny, like Hell, is not easily conquered; yet we have this consolation with us, that the harder the conflict, the more glorious the triumph. What we obtain too cheap, we esteem too lightly: it is dearness only that gives every thing its value. Heaven knows how to put a proper price upon its goods; and it would be strange indeed if so celestial an article as freedom should not be highly rated.