Strategy-free criterion

Definitions

A sincere vote is one with no falsified preferences or preferences left unspecified when the election method allows them to be specified (in addition to the preferences already specified).

One candidate is preferred over another candidate if, in a one-on-one competition, more voters prefer the first candidate than prefer the other candidate.

If one candidate is preferred over each of the other candidates, that candidate is called "Condorcet candidate" or "Condorcet winner".

Statement of Criterion

If a Condorcet candidate exists, and if a majority prefers this candidate to another candidate, then the other candidate should not win if that majority votes sincerely and no other voter falsifies any preferences.

In a ranked method, it is nearly equivalent to say: If more than half of the voters rank x above y, and there is no candidate z whom more than half of the voters rank above x, then y must not be elected.

Complying Methods

• Complies: Schulze method (with winning votes as the measure of defeat strength), MDDA, MAMPO
• Fails: Approval voting, Cardinal Ratings, Borda count, Plurality voting, Instant-Runoff Voting

Commentary

The reader may be wondering how the Condorcet candidate, if one exists, could possibly not be preferred by a majority of voters over any other candidate. The key is that some voters may have no preference between a given pair of candidates. Out of 100 voters, for example, 45 could prefer the Condorcet candidate over another particular candidate, and 40 could prefer the opposite, with the other 15 having no preference between the two. In that case, it is not true that a majority of voters prefer the Condorcet candidate over the other candidate, and SFC does not apply.

In order to understand SFC, one must also understand that there are two types of insincere votes: false preferences and truncated preferences. Voters truncate by terminating their rank list before their true preferences are fully specified (note that the last choice is always implied, so leaving it out is not considered truncation). Voters falsify their preferences, on the other hand, by reversing the order of their true preferences or by specifying a preference they don't really have. Suppose, for example, that a voter's true preferences are (A,B,C) with no preference between D and E. The vote (A) or (A,B) would be a truncated vote, and the vote (B,A,C) or (A,C,B) or (A,B,C,D,E) would be a falsified vote.

SFC requires that the majority of voters who prefer the Condorcet candidate to another particular candidate vote sincerely (neither falsify nor truncate their preferences), and it also requires that no other voter falsifies preferences. SFC therefore implies that the minority that does not prefer the Condorcet candidate to the other candidate cannot cause the other candidate to win by truncating their preferences. (In theory, that minority could cause the other candidate to win by falsifying their preferences, but that would be a very risky offensive strategy that is more likely to backfire than to succeed.) The significance of the SFC guarantee is that the majority has no need for defensive strategy, hence the name Strategy-Free Criterion.

Schulze was shown to comply with both the Condorcet and Generalized Condorcet Criteria (CC and GCC) above. Although compliance with CC and GCC are important, those criteria apply only in the theoretically ideal case in which all votes are sincere. The Strategy-Free criterion goes further and shows that, under certain reasonable conditions, a majority of voters have no incentive to vote insincerely. The fact that Schulze also complies with SFC therefore enhances the significance of CC and GCC considerably.

Some parts of this article are derived with permission from text at http://electionmethods.org

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