Selected topics in finite mathematics/Condorcet criterion

[Give a very very brief overview of the criteria?]

Objectives

To satisfy the Condorcet criterion, a candidate that is favored to beat ever other candidate in a pairwise race wins. Therefore, if a candidate can defeat every other candidate, then they should win.

Details

[State the definition of the criteria?]

[Rephrase the criteria into if-then form?]

[Give a prose-explanation of the criteria?]

Examples

The Condorcet method satisfies the Condorcet criteria. Indeed, this is its namesake: if a candidate wins all pairwise races, that candidate wins by the Condorcet method.

Sequential pariwise elections also satisfies the Condorcet criterion. In particular, suppose A wins in all pairwise races. Then as soon as A comes up in the agenda, A will win every [pairwise] race until declared the winner.

Nonexamples

Plurality fails to satisfy the Condorcet criterion. Consider the following election. A wins in all pairwise elections, but instead B wins by plurality.

1st choice	A	B	C
2nd choice	B	A	A
3rd choice	C	C	B
Number of votes	2	3	2

Borda count fails to satisfy the Condorcet criterion. Consider the following election. One on one A wins all pairwise races. However, in this election as it is, B wins.

1st choice	B	E	D
2nd choice	C	A	A
3rd choice	F	B	B
4th choice	A	C	E
5th choice	E	D	C
6th choice	D	F	F
Number of votes	1	1	1

Sequential runoffs fail to satisfy the Condorcet Criterion. Consider the following election. Indeed one on one A could defeat either candidate. But in the election as a whole, A is eliminated first.

1st choice	A	B	C
2nd choice	B	A	A
3rd choice	C	C	B
Number of votes	2	3	3

Homework

[Create two elections: one which satisfies the criteria and one which does not?]

Solution

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Solution

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