There is no consistently fair way to choose the winner of an election. A voting method that is democratic and always fair is a mathematical impossibility. Arrow's Impossibility Theorem Kenneth Arrow 1952 Fairness Criteria The Fairness Criteria are things that should always be true according to common sense, but aren't always true in reality. Majority Criterion Book : If there is a choice that has a majority of the first-place votes in an election, then that choice should be the winner of the election. Translation : If someone gets the majority of the votes, then they should win. Condorcet Criterion Book : If there is a choice that in a head-to-head comparison is preferred by the voters over every other choice, then that choice should be the winner of the election. Translation : If Bob is preferred over Jon in a one-on-one comparison and Bob is preferred over Stacey and Bob is preferred over Shelley, then Bob should win the election. Monotonicity Criterion Book : If choice X is a winner of an election and, in a reelection, the only changes in the ballots are changes that only favor X, then X should remain a winner of the election. Translation : Bob wins an election. For some reason there is a reelection. Some people change their minds and rank Bob higher in their preference ballots. Bob should still win the election. Independence of Irrelevant Alternatives Criterion Book : If candidate or alternative X is a winner of an election and one (or more) of the other candidates or alternatives is removed and the ballots recounted, then X should still be a winner of the election. Translation : Bob wins an election. Jon decides to remove himself from the election after the ballots are counted. Shelley calls for a recount because Jon is no longer a candidate. Since Bob won initially, he should still win. Voting Methods Plurality Process : Most first-place votes wins. Weaknesses : Doesn't take into account preferences other than first. Is susceptible to insincere or strategic voting. Fairness : May violate the Condorcet Criterion. Borda Count Process : Places on a ballot are assigned points. Generally, the candidate with the most points wins the election. Weaknesses : Produces a winner that is a compromise candidate (may or may not be a bad thing). Fairness : May violate the Majority Criterion and the Condorcet Criterion. Plurality-with-Elimination Process : Eliminate the least favorite candidate, based on the number of first-place votes, until there is a winner. Weaknesses : Is susceptible to insincere or strategic voting. Fairness : May violate the Monotonicity Criterion and the Condorcet Criterion. Comment : Local elections are a variation of plurality-with-elimination called plurality with a runoff; all candidates except the top two are eliminated in the first round. Pairwise Comparisons Process : The candidate winning the most "matchups" (pairwise comparisons) wins the election. Weaknesses : May produce an election in which everyone wins. Fairness : May violate the Independence of Irrelevant Alternatives Criterion. Ranking Methods Extended Rankings Natural extension of the voting methods. Recursive Rankings Apply the voting method, determine the winner. Eliminate the winner. Apply the voting method again. The new winner is actually the second-place finisher. Eliminate second-place. Apply the voting method again. The new winner is actually the third-place finisher. Etcetera, etcetera, etcetera until all candidates are ranked. Approval Voting Under approval voting , each voter is allowed to give one vote to as many of the candidates as he or she finds acceptable. No limit is set on the number of candidates for whom an individual can vote. Voters show disapproval of other candidates simply by not voting for them. The winner under approval voting is the candidate who receives the largest number of approval votes. This approach is also appropriate in situations where more than one candidate can win, for example, in electing new members to an exclusive society as the National Academy of Sciences or the Baseball Hall of Fame. Cumulative Voting Under cumulative voting, each voter is allowed a number of votes equal to the number of available positions. These votes may be distributed equally among candidates, spread around in unequal distributions, or all be given to a single candidate. The winners under cumulative voting are the candidates who receive the most number of votes, the second-most number of votes, etc. until the positions are filled. This voting method provides numeric minorities the option to vote as a bloc and elect a candidate of their choice..