Sincere favorite criterion
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Electoral systems |
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The sincere favorite or no favorite-betrayal criterion is a
Most
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.[8]
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]
Arguments for
The
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.[12]
Compliant methods
Rated voting
Because
Examples of systems that are both spoilerproof and monotonic include score voting, approval voting, and highest medians.
Non-compliant methods
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:
# 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.
Condorcet methods
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See also
- Comparison of electoral systems
- Electoral systems
- Vote splitting
- Independence of irrelevant alternatives
- Strategic voting
External links
- 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
- [13]
- [14]
References
- ^ 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.
- JSTOR 1961964.
- 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.
- ^ . Retrieved 2023-07-16.
- ^ Eberhard, Kristin (2017-05-09). "Glossary of Methods for Electing Executive Officers". Sightline Institute. Retrieved 2023-12-31.
- . Retrieved 2024-05-02.
- JSTOR 2689808. Retrieved 2024-05-02.
- 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.
- .
- ISBN 9781958469033.