This page is intended to demonstrate the voting methods described in Chapter 9 of For All Practical Purposes.

As in that book, an election is described by each voter's preference list. This simply lists the candidates in order from most to least preferred. For example, if there are 4 candidates (A,B,C,D), and a voter's preference list is CBAD, then that voter would most like C to be chosen, then B, then A, then D. More specifically, if any two candidates were running (because the others had dropped out of the race), that voter would make his or her choice based on which candidate appears first on his/her preference list.

In any election, we would like the voting method used to have certain properties. Unfortunately, Arrow's impossibility theorem says that (when there are three candidates), there is no voting method that can have all of those desirable properties.

A voting method satisfies the Condorcet Winner Criterion if that method will choose the Condorcet winner (described below) when one exists.

Suppose that every voter ranks candidate A higher than B (that is, in a one-on-one election between the two, A would get all the votes). A voting method satisfies the Pareto condition if a candidate B would not be among the winners.

Suppose that we hold an election in which candidate A is one of the winners, and candidate B is one of the losers. Then one voter (say "X") alters his/her preference list, and we hold the election again. If A is now higher on X's preference list, the voting method satisfies monotonicity (or "is monotone") if it is impossible for A to become one of the losers. If B is moved up ... In other words:

• monotonicity means that a winner cannot become a loser because a voter likes him/her more.
• IIA means that a loser cannot become a winner unless someone likes him/her more than a winner.