## Key Ideas

• In plurality voting, the candidate with the most first-place votes on the preference list ballots is the winner. We do not take into account the votersâ€™ preferences for the second, third, etc., places.
• A voting system that satisfies the Condorcet Winner Criterion (CWC) either has no Condorcet winner or the voting produces exactly the same winner as does Condorcetâ€™s method.
• In the Borda count method, points are assigned to each position in the set of preference lists. For example, in a three-person election, first-place votes may be awarded 2 points each, second-place votes receive 1 point each, and third-place votes are given 0 points each. (Other distributions of points may be used to create similar rank methods.)
• A voting system satisfies independence of irrelevant alternatives (IIA) if it is impossible for a candidate B to move from non-winner status to winner status unless at least one voter reverses the order in which he or she had B and the winning candidate ranked. The Borda count fails to satisfy IIA, as shown in the text.
• An agenda is the listing (in some order) of the candidates. Sequential pairwise voting pits the first candidate against the second in a one-on-one contest. The winner goes on to confront the third candidate on the agenda, while the loser is eliminated. The candidate remaining at the end is the winner. The choice of the agenda can affect the result.
• Sequential pairwise voting fails to satisfy the Pareto condition, which states that if everyone prefers one candidate, say X, to another, say Y, then Y cannot be the winner.
• In the Hare system, the winner is determined by repeatedly deleting candidates that are the least preferred, in the sense of being at the top of the fewest preference lists.
• The Hare system does not satisfy monotonicity.
• Plurality runoff is the voting system in which there is a runoff between the two candidates receiving the most first-place votes. In the case of ties between first or second, three candidates participate in the runoff.
• The plurality runoff method does not satisfy monotonicity.