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.[1] 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).[2]
Most rated voting systems, including score voting, satisfy the criterion.[3] [4] [5] By contrast, most variants of ranked voting fail this criterion.[6] [7] Lesser-evil-voting is particularly prevalent in plurality-based voting systems like ranked choice voting (RCV),[8] [9] traditional runoffs, and first-past-the-post. Such pathologies are typically associated with center-squeeze.
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.[10]
The no favorite betrayal criterion is defined as follows:
A voting system satisfies the no 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 to obtain a more preferred outcome in the election overall (i.e. the election of a candidate that they prefer to the current winner).
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 despite having the opportunity to participate in the election.[11] [12] [13] [14]
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.[15]
See main article: article and 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.
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.
See also: 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:
| Preferences | |
|---|---|---|
| 10 | Amy > Bert > Cindy > Dan | |
| 6 | Bert > Amy > Cindy > Dan | |
| 5 | Cindy > Bert > Amy > Dan | |
| 20 | Dan > Amy > Cindy > Bert |
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.
| Votes in round/ Candidate | 1st | 2nd | 3rd | |
|---|---|---|---|---|
| Amy | 10 | 10 | – | |
| Bert | 6 | 11 | 21 | |
| Cindy | 5 | – | – | |
| Dan | 20 | 20 | 20 |
Result: Bert wins against Dan, after Cindy and Amy were eliminated.
Now assume two of the voters who favor Amy (marked bold) realize the situation and insincerely vote for Cindy instead of Amy:
| Ballots | |
|---|---|---|
| 2 | Cindy > Amy > Bert > Dan | |
| 8 | Amy > Bert > Cindy > Dan | |
| 6 | Bert > Amy > Cindy > Dan | |
| 5 | Cindy > Bert > Amy > Dan | |
| 20 | Dan > Amy > Cindy > Bert |
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.
| Votes in round/ Candidate | 1st | 2nd | 3rd | |
|---|---|---|---|---|
| Amy | 8 | 14 | 21 | |
| Bert | 6 | – | – | |
| Cindy | 7 | 7 | – | |
| Dan | 20 | 20 | 20 |
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.