Conditions of Fairness in Voting

These criteria represent conditions of fairness in voting. We use these criteria to determine, in a sense, how fair a method of voting is, and to compare methods. Unfortunately, while these conditions are quite reasonable, we find there can never be any method of voting that will satisfy all of these criteria.

Notice how all criteria can be written in the form of an “If/Then” statement. This is why they can be called conditions. We say the condition is “If A happens, then B should happen”. We find that each condition, while completely reasonable and natural, in each case something we might like to be true, each is nevertheless violated by at least one method of voting we have studied.

1. If a candidate receives a majority of first place votes, that candidate should be the winner. (Majority Criterion)

2. If a candidate beats all other candidates in one-on-one comparisons, that candidate should be the winner. (Condorcet Winner Criterion)

3. If a re-election is held and the only change is that some non-winning candidate drops out, the previous winner should still win the election. (Independence of Irrelevant Alternatives criterion)

4. If there is at least one candidate (A) that every voter prefers to another (B) then it should be impossible for B to win. (Pareto Criterion)

5. If a re-election is held and the only changes are ones that are favorable to the previous winner, that candidate should still win. (Monotonicity Criterion)

Slightly shorter versions of these criteria (easier to remember?)

1. MC – If a candidate has a majority of first place votes, then that candidate should win.

2. CWC – If a candidate beats all others head-to-head, then that candidate should win.

3. IIA – If a re-election is held and non-winning candidates drop out, then the previous winner should still win.

4. Pareto – It should be impossible for a candidate to win if there is at least one other candidate which every voter prefers.

5. Monotonicity – It should be impossible for a winning candidate to lose in a re-election if all vote changes were favorable to that candidate.