Sincere favorite criterion

The sincere favorite or no favorite-betrayal criterion is a property of some voting systems, that says voters should have no incentive to vote for someone else over their favorite. It protects voters from having to engage in a kind of strategy called lesser evil voting or decapitation (i.e. removing the "head" off a ballot).

Most rated voting systems, including score voting, satisfy the criterion. By contrast, instant-runoff, traditional runoffs, plurality, and most other variants of ranked-choice voting (including all strictly-Condorcet-compliant methods) fail this criterion.

Duverger's law says that systems vulnerable to this strategy will typically (though not always) develop two party-systems, as voters will abandon minor-party candidates to support stronger major-party candidates.

Instant-runoff voting fails the favorite-betrayal criterion whenever it fails to elect the Condorcet winner, a situation referred to as center-squeeze.

Definition
The favorite betrayal criterion is defined as follows:


 * A voting system satisfies the favorite betrayal criterion if there cannot exist a situation where a voter is forced to insincerely list another candidate ahead of their sincere favorite in order obtain a more preferred outcome in the election overall (i.e. the election of a candidate that they prefer to the current winner).

Arguments for
The Center for Election Science argues systems that violate the favorite betrayal criterion strongly incentivize voters to cast dishonest ballots, which can make voters feel unsatisfied or frustrated with the results even after having the opportunity to participate in the election.

Other commentators have argued that failing the favorite-betrayal criterion can increase the effectiveness of misinformation campaigns, by allowing major-party candidates to sow doubt as to whether voting honestly for one's favorite is actually the best strategy.

Rated voting
Because rated voting methods are not affected by Arrow's theorem, they can be both spoilerproof (satisfy IIA) and ensure positive vote weights at the same time. Taken together, these properties imply that increasing the rating of a favorite candidate can never change the result, except by causing the favorite candidate to win; therefore, giving a favorite candidate the maximum level of support is always the optimal strategy.

Examples of systems that are both spoilerproof and monotonic include score voting, approval voting, and highest medians.

Anti-plurality voting
Interpreted as a ranked voting method where every candidate but the last ranked gets one point, Anti-plurality voting passes the sincere favorite criterion. Because there is no incentive to rank one's favorite last, and the method otherwise does not care where the favorite is ranked, the method passes.

Anti-plurality voting thus shows that the sincere favorite criterion is distinct from independence of irrelevant alternatives, and that ranked voting methods do not necessarily fail the criterion.

Instant-runoff voting
This example shows that instant-runoff voting violates the favorite betrayal criterion. Assume there are four candidates: Amy, Bert, Cindy, and Dan. This election has 41 voters with the following preferences:

Sincere voting
Assuming all voters vote in a sincere way, Cindy is awarded only 5 first place votes and is eliminated first. Her votes are transferred to Bert. In the second round, Amy is eliminated with only 10 votes. Her votes are transferred to Bert as well. Finally, Bert has 21 votes and wins against Dan, who has 20 votes.

Result: Bert wins against Dan, after Cindy and Amy were eliminated.

Favorite betrayal
Now assume two of the voters who favor Amy (marked bold) realize the situation and insincerely vote for Cindy instead of Amy:

In this scenario, Cindy has 7 first place votes and so Bert is eliminated first with only 6 first place votes. His votes are transferred to Amy. In the second round, Cindy is eliminated with only 10 votes. Her votes are transferred to Amy as well. Finally, Amy has 21 votes and wins against Dan, who has 20 votes.

Result: Amy wins against Dan, after Bert and Cindy has been eliminated.

By listing Cindy ahead of their true favorite, Amy, the two insincere voters obtained a more preferred outcome (causing their favorite candidate to win). There was no way to achieve this without raising another candidate ahead of their sincere favorite. Thus, instant-runoff voting fails the favorite betrayal criterion.

Condorcet methods
 Commentary from old page on lesser of two evils

Lesser Evil Voting
Noam Chomsky wrote that "voting should not be viewed as a form of personal self-expression or moral judgement directed in retaliation towards major party candidates who fail to reflect our values, or of a corrupt system designed to limit choices to those acceptable to corporate elites" rather as an opportunity to reduce harm or loss.

In 2012, Huffington Post columnist Sanford Jay Rosen stated that the idea became common practice for left-leaning voters in the United States due to their overwhelming disapproval of the United States government's support for the Vietnam War. Rosen stated: "Beginning with the 1968 presidential election, I often have heard from liberals that they could not vote for the lesser of two evils. Some said they would not vote; some said they would vote for a third-party candidate. That mantra delivered us to Richard Nixon in 1972 until Watergate did him in. And it delivered us to George W. Bush and Dick Cheney in 2000 until they were termed out in 2009".

In the 2016 United States presidential election, both major-party candidates (Hillary Clinton and Donald Trump) had disapproval ratings close to 60% by August 2016. Green Party candidate Jill Stein invoked the idea in her campaign stating, "Don't vote for the lesser evil, fight for the greater good". Green Party votes hurt Democratic chances in 2000 and 2016. Accordingly, the lesser evil principle should be applied to two front-runners among many choices, after eliminating from consideration "minor party candidates (who) can be spoilers in elections by taking away enough votes from a major party candidate to influence the outcome without winning."

In elections between only two candidates where one is mildly unpopular and the other immensely unpopular, opponents of both candidates frequently support the mildly unpopular candidate. For example, in the second round of the 2002 French presidential election graffiti in Paris, told people to "vote for the crook, not the fascist". The "crook" in those scribbled public messages was Jacques Chirac of Rally for the Republic and the "fascist" was Jean-Marie Le Pen of the National Front. Chirac eventually won the second round having garnered 82% of the vote.

Lesser-evil voting is commonly referenced in the context of United States presidential elections, where the use of first-past-the-post and instant-runoff balloting often forces voters to choose between two candidates they dislike, rather than supporting a candidate they do like. 