Math 108 Topics in Mathematics | Laura Barnes |
9.2 Majority Rule and Condorcet's Method - Video

9.2 Majority Rule and Condorcet's Method - Video

Key Ideas

In a dictatorship, all ballots except that of the dictator are ignored.

In imposed rule, candidate X wins regardless of who votes for whom.

When there are only two candidates or alternatives, May’s theorem states that
majority rule is the
only voting method that satisfies three desirable properties, given an odd number of voters and no ties.

Condorcet’s method declares a candidate is a winner if he or she can defeat every other candidate in a one-on-one competition using majority rule.

Condorcet’s voting paradox can occur with three or more candidates in an election where Condorcet’s method yields no winners. For example, in a three-candidate race, two-thirds of voters could favor A over B, two-thirds of voters could favor B over C, and two-thirds of voters could favor C over A. This is the example given in the text. With three or more candidates, there are elections in which Condorcet’s method yields no winners.