Sincere favorite criterion
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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][2] 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).[3]
Most rated voting systems, including score voting, satisfy the criterion.[4][5][6] By contrast, instant-runoff, traditional runoffs, plurality, and most other variants of ranked-choice voting (including all strictly-Condorcet-compliant methods) fail this criterion.[5][7][8]
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.[9]
Instant-runoff voting fails the favorite-betrayal criterion whenever it fails to elect the Condorcet winner, a situation referred to as center-squeeze.
Definition[edit]
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]
Arguments for[edit]
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.[10][11][12]
Other commentators have argued that even systems that fail favorite-betrayal only rarely 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.[13]
Compliant methods[edit]
Rated voting[edit]
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.[14]
Examples of systems that are both spoilerproof and include score voting and highest medians.
Non-compliant methods[edit]
Instant-runoff voting[edit]
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:
| # 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[edit]
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[edit]
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.
Condorcet methods[edit]
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In popular culture[edit]
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.[15]
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.[16] 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".[16]
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.[17] Green Party candidate Jill Stein invoked the idea in her campaign stating, "Don't vote for the lesser evil, fight for the greater good".[18] Green Party votes hurt Democratic chances in 2000 and 2016.[19][20][21] 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."[22]
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.[23]
The principle of "the lesser of two evils" is sometimes jokingly changed to "the evil of two lessers", such as in the titles of these articles about the US presidential elections of 1988[24] and 2016.[25]
See also[edit]
- Comparison of electoral systems
- Electoral systems
- Vote splitting
- Independence of irrelevant alternatives
- Strategic voting
External links[edit]
- Collective Decisions and Voting: The Potential for Public Choice
- Chaotic Elections!: A Mathematician Looks at Voting
- Decisions and Elections: Explaining the Unexpected
- Election Methods
- Survey of methods satisfying FBC
- FBC in relation to duopoly
- FBC used in mathematical proofs
- Commentary on FBC in relation to other voting methods
- [26]
- [27]
References[edit]
- ^ 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.
- ^ 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) - ^ Merrill, Samuel; Nagel, Jack (1987-06-01). "The Effect of Approval Balloting on Strategic Voting under Alternative Decision Rules". American Political Science Review. 81 (2): 509–524. doi:10.2307/1961964. ISSN 0003-0554.
- ^ 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.
- ^ 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.
- ^ Eberhard, Kristin (2017-05-09). "Glossary of Methods for Electing Executive Officers". Sightline Institute. Retrieved 2023-12-31.
- ^ 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.
- ^ 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.
- ^ Volić, Ismar (2024-04-02). "Duverger's law". Making Democracy Count. Princeton University Press. Ch. 2. doi:10.2307/jj.7492228. ISBN 978-0-691-24882-0.
- ^ Hamlin, Aaron (2015-05-30). "Top 5 Ways Plurality Voting Fails". Election Science. The Center for Election Science. Retrieved 2023-07-17.
- ^ Hamlin, Aaron (2019-02-07). "The Limits of Ranked-Choice Voting". Election Science. The Center for Election Science. Retrieved 2023-07-17.
- ^ "Voting Method Gameability". Equal Vote. The Equal Vote Coalition. Retrieved 2023-07-17.
- ^ Ossipoff, Michael (2013-05-20). "Schulze: Questioning a Popular Ranked Voting System". Democracy Chronicles. Retrieved 2024-01-01.
- ^ "RangeVoting.org - Favorite betrayal (executive summary)". rangevoting.org. Retrieved 2020-05-14.
We've come a long way since the days when range and approval voting were the only known methods in which betraying your favorite is strategically avoidable. Now many other methods also are known with that "FBC property." [...] However, it appears Range and Approval satisfy FBC in a stronger and more obvious sense than these other methods. Specifically, with Range and Approval, betraying your favorite simply never is useful. With the other methods it can be strategically useful (cause X to win instead of Y, where the betrayers prefer X) but if so there is always a way to get the same effect (i.e. make X win) by some other dishonest vote not involving favorite betrayal.
{{cite web}}: CS1 maint: url-status (link) - ^ Noam Chomsky and John Halle, "An Eight Point Brief for LEV (Lesser Evil Voting)," New Politics, June 15, 2016.
- ^ a b Stanford Jay Rosen (2012-09-25). "Don't Get Fooled Again: Why Liberals and Progressives Should Vote Enthusiastically for President Obama". Huffington Post. Retrieved 2013-03-23.
- ^ Aaron Blake (2016-08-31). "A record number of Americans now dislike Hillary Clinton". Washington Post. Retrieved 2016-08-31.
- ^ "Meet Jill Stein, the Other Anti-Establishment Progressive Running for President". 26 May 2016.
- ^ "Did Ralph Nader Spoil Al Gore's Presidential Bid? A Ballot-Level Study of Green and Reform Party Voters in the 2000 Presidential Election". Retrieved 30 March 2023.
- ^ "Jill Stein cost Hillary dearly in 2016. Democrats are still writing off her successor". Politico.
- ^ "Green Party candidate Jill Stein got more votes than Trump's victory margin in 3 key states". December 2016.
- ^ "10.6 Minor Parties," American Government and Politics in the Information Age, University of Minnesota, 2011.
- ^ "Chirac's new challenge". The Economist. 2002-05-06. Retrieved 2011-04-15.
- ^ Schneider, William (18 September 1988). "THE EVIL OF TWO LESSERS". Los Angeles Times. Retrieved 12 September 2020.
- ^ Keinon, Herb (6 November 2016). "Clinton vs. Trump: 'The evil of two lessers'". Jerusalem Post. Retrieved 12 September 2020.
- ^ 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.
- ^ Sullivan, Brendan (2022). An Introduction to the Math of Voting Methods. 619 Wreath. ISBN 9781958469033.