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The no favorite-betrayal or sincere favorite criterion is a property of some voting systems that protects voters from having to engage in "lesser evil voting". The criterion says voters should have no incentive to vote for someone else over their favorite.[1][2]

Most rated voting systems, including score, satisfy the criterion.[3][4][5] By contrast, Instant-runoff, traditional runoffs, plurality, and most other variants of ranked-choice voting (including strictly-Condorcet-compliant methods) fail this criterion.[4][6] [7]

Instances of instant-runoff voting failing the criterion usually occur in combination with other election pathologies in the context of a 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).

The criterion permits the strategy of insincerely ranking another candidate equal to one's favorite.[1]

Public Opinion

Proponents of cardinal systems argue that the favorite betrayal criterion is of high importance because it enables voters to give their true favorite maximum support without need for worry. Arguments against the criteria posit that other, mutually exclusive criteria are more important.

Equal Vote, a major proponent of STAR voting, argues that a voting system must reward voter honesty, both on the individual level and in the aggregate. They consider the favorite betrayal criterion to be of high importance.[8] The Center for Election Science claims that failure of the favorite betrayal criterion incentivizes voters to cast dishonest ballots and results in lower voter satisfaction.[9][10] Democracy Chronicles, an online publication whose mission is to strengthen democracy worldwide, argues that the favorite betrayal criterion is paramount, since failure can open the door for misinformation campaigns to push voters to cast insincere ballots. They argue that the current media landscape and public perception of election systems requires that giving one's preferred candidate maximum support must always be the best strategy, so that no one can be convinced to do otherwise for any reason.[11]

The Sightline Institute, an organization dedicated to making Cascadia "a global model of sustainability," argues that the criteria's importance depends on a voter's relative perceived value between it and later-no-harm, a mutually-exclusive criterion which states that it must always be safe to give second-favorite candidates support after a top favorite.[12][13][14] According to Sightline, if voters feel strongly that their favorite should win but still want to express opinions about other candidates, they should be more drawn towards systems which satisfy later-no-harm. If they feel that any of their preferred candidates winning would provide sufficient satisfaction, then later-no-harm is not as necessary, and the favorite betrayal criterion is helpful to ensure that showing support for their true favorite cannot backfire. Voters of the first variety may choose to bullet vote under systems which pass the favorite betrayal criterion, not wanting to accidentally cause a less preferred candidate to beat their favorite. However, under a system which fails the favorite betrayal criterion, any voter may choose to strategically betray their favorite candidate to secure a more favorable result.[5]

Example evaluations

Score voting

Main article: score voting

The following will provide an example and explain how score voting satisfies the favorite betrayal criterion. Score voting functions as follows:

  1. Voters give each candidate a score to indicate support. Scores are numerical values from 0 to a maximum value, usually 5, 7, 10 or 100.
  2. Candidates left unassigned are automatically given a score of 0.
  3. The candidate with the highest cumulative score wins.

Assume there are three candidates: Agnew, BillyJoe, and Cletus. The voters may give scores up to 5. The vote totals appear as follows:

Candidate Total score
Agnew 35
BillyJoe 39
Cletus 22

Assume there is one final voter who has yet to cast their vote, and they know the results as they currently stand. This voter could have any of the following six preferences among the candidates:

  1. Agnew > BillyJoe > Cletus
  2. Agnew > Cletus > BillyJoe
  3. BillyJoe > Cletus > Agnew
  4. BillyJoe > Agnew > Cletus
  5. Cletus > Agnew > BillyJoe
  6. Cletus > BillyJoe > Agnew

If Agnew or BillyJoe is the voter's true favorite, as in scenarios 1-4, the best strategy is to give their true favorite 5 points. This would cause their favorite to win and so no better outcome is possible.

If the voter's true favorite is Cletus, it is safe to give Cletus 5 points. Doing so would not change the scores or relative standing of Agnew and BillyJoe. If the voter wishes to control the outcome of the election, they must also award points to both Agnew and BillyJoe. In this scenario, the voter must give Agnew 5 points if they wish for them to win, but doing so merely places Agnew at the same level of support as Cletus. Since the voter has no incentive to lower their support for Cletus, score voting passes the favorite betrayal criterion.

Instant-runoff voting

Main article: Instant-runoff voting

This example shows that instant-runoff voting violates the favorite betrayal criterion. Note that the example for the two-round runoff voting system also works as an example for instant-runoff voting. Instant-runoff functions as follows:

  1. Voters rank candidates from most to least preferred.
  2. Candidates are awarded one vote for every ballot in which they are the preferred candidate.
  3. If a candidate is preferred on more than 50% of the ballots which list active candidates, they win. Otherwise, the next step is performed.
  4. The candidate with the fewest votes is eliminated and their votes are transferred to the next preferred candidate on each ballot. The process returns to the previous step.

Assume there are four candidates: Amy, Bert, Cindy, and Dan. This election has 41 voters with the following preferences:

# of voters Preferences
10 Amy > Bert > Cindy > Dan
6 Bert > Amy > Cindy > Dan
5 Cindy > Bert > Amy > Dan
20 Dan > Amy > Cindy > Bert

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.

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.

Favorite betrayal

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

# of voters 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.

See also

References

  1. ^ a b Alex Small, “Geometric construction of voting methods that protect voters’ first choices,” arXiv:1008.4331 (August 22, 2010), http://arxiv.org/abs/1008.4331. Cite error: The named reference "small" was defined multiple times with different content (see the help page).
  2. ^ Ossipoff, Mike; Smith, Warren D. (Jan 2007). "Survey of FBC (Favorite-Betrayal Criterion)". Center for Range Voting. Retrieved 2020-04-08.{{cite web}}: CS1 maint: url-status (link)
  3. ^ Baujard, Antoinette; Gavrel, Frédéric; Igersheim, Herrade; Laslier, Jean-François; Lebon, Isabelle (September 2017). "How voters use grade scales in evaluative voting" (PDF). European Journal of Political Economy. 55: 14–28. doi:10.1016/j.ejpoleco.2017.09.006. ISSN 0176-2680. A key feature of evaluative voting is a form of independence: the voter can evaluate all the candidates in turn ... another feature of evaluative voting ... is that voters can express some degree of preference.
  4. ^ a b Wolk, Sara; Quinn, Jameson; Ogren, Marcus (2023-03-20). "STAR Voting, equality of voice, and voter satisfaction: considerations for voting method reform". Constitutional Political Economy (Journal Article). 34 (3): 310–334. doi:10.1007/s10602-022-09389-3. Retrieved 2023-07-16.
  5. ^ a b Eberhard, Kristin (2017-05-09). "Glossary of Methods for Electing Executive Officers". Sightline Institute. Retrieved 2023-12-31.
  6. ^ Woodall, Douglas (1997-06-27). "Monotonicity of single-seat preferential election rules". Discrete Applied Mathematics. 77 (1): 81–98. doi:10.1016/S0166-218X(96)00100-X. Retrieved 2024-05-02.
  7. ^ Fishburn, Peter; Brams, Steven (1983-09-01). "Paradoxes of Preferential Voting". Mathematics Magazine. 56 (4): 207–214. doi:10.1080/0025570X.1983.11977044. JSTOR 2689808. Retrieved 2024-05-02.
  8. ^ "Voting Method Gameability". Equal Vote. The Equal Vote Coalition. Retrieved 2023-07-17.
  9. ^ Hamlin, Aaron (2015-05-30). "Top 5 Ways Plurality Voting Fails". Election Science. The Center for Election Science. Retrieved 2023-07-17.
  10. ^ Hamlin, Aaron (2019-02-07). "The Limits of Ranked-Choice Voting". Election Science. The Center for Election Science. Retrieved 2023-07-17.
  11. ^ Ossipoff, Michael (2013-05-20). "Schulze: Questioning a Popular Ranked Voting System". Democracy Chronicles. Retrieved 2024-01-01.
  12. ^ "About Us". Sightline. Sightline Institute. Retrieved 2024-01-01.
  13. ^ Hamlin, Aaron; Hua, Whitney (2022-12-19). "The case for approval voting". Constitutional Political Economy. 34 (3): 335–345. doi:10.1007/s10602-022-09381-x. Retrieved 2024-05-02.
  14. ^ Sullivan, Brendan (2022). An Introduction to the Math of Voting Methods. 619 Wreath. ISBN 9781958469033.
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