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{{Short description| |
{{Short description|Criterion that prevents lesser-evil voting}}{{Electoral systems}} |
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{{essay|date=May 2024}} |
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The ''' |
The '''sincere favorite''' or '''no favorite-betrayal criterion''' is a [[voting system criterion|property]] of some voting systems that says voters should have no incentive to vote for someone else over their favorite.<ref name="small">Alex Small, “Geometric construction of voting methods that protect voters’ first choices,” arXiv:1008.4331 (August 22, 2010), http://arxiv.org/abs/1008.4331.</ref> It protects voters from having to engage in [[lesser-evil voting]] or a strategy called "decapitation" (removing the "head" off a ballot).<ref>{{Cite journal |last1=Merrill |first1=Samuel |last2=Nagel |first2=Jack |date=1987-06-01 |title=The Effect of Approval Balloting on Strategic Voting under Alternative Decision Rules |url=https://www.cambridge.org/core/product/identifier/S0003055400194481/type/journal_article |journal=American Political Science Review |language=en |volume=81 |issue=2 |pages=509–524 |doi=10.2307/1961964 |jstor=1961964 |issn=0003-0554}}</ref> |
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Most [[rated voting]] systems, including [[score voting |
Most [[rated voting]] systems, including [[score voting]], satisfy the criterion.<ref>{{Cite journal |last1=Baujard |first1=Antoinette |last2=Gavrel |first2=Frédéric |last3=Igersheim |first3=Herrade |last4=Laslier |first4=Jean-François |last5=Lebon |first5=Isabelle |date=September 2017 |title=How voters use grade scales in evaluative voting |url=https://halshs.archives-ouvertes.fr/halshs-01618039/file/1729.pdf |journal=European Journal of Political Economy |volume=55 |pages=14–28 |doi=10.1016/j.ejpoleco.2017.09.006 |issn=0176-2680 |quote=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.}}</ref><ref name="STAR Analysis2">{{cite journal |last1=Wolk |first1=Sara |last2=Quinn |first2=Jameson |last3=Ogren |first3=Marcus |date=2023-03-20 |title=STAR Voting, equality of voice, and voter satisfaction: considerations for voting method reform |url=https://link.springer.com/article/10.1007/s10602-022-09389-3 |journal=Constitutional Political Economy |type=Journal Article |volume=34 |issue=3 |pages=310–334 |doi=10.1007/s10602-022-09389-3 |access-date=2023-07-16}}</ref><ref name="Sightline2">{{cite web |last=Eberhard |first=Kristin |date=2017-05-09 |title=Glossary of Methods for Electing Executive Officers |url=https://www.sightline.org/2017/05/09/glossary-of-executive-officer-voting-systems/ |access-date=2023-12-31 |website=Sightline Institute}}</ref> |
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</ref> <ref name="STAR Analysis">{{cite journal |url=https://link.springer.com/article/10.1007/s10602-022-09389-3 |title=STAR Voting, equality of voice, and voter satisfaction: considerations for voting method reform |last1=Wolk |first1=Sara |last2=Quinn |first2=Jameson |last3=Ogren |first3=Marcus |date=2023-03-20 |journal=Constitutional Political Economy |volume=34 |issue=3 |pages=310–334 |doi=10.1007/s10602-022-09389-3 |access-date=2023-07-16 |type=Journal Article}}</ref><ref name="Sightline">{{cite web |url=https://www.sightline.org/2017/05/09/glossary-of-executive-officer-voting-systems/ |title=Glossary of Methods for Electing Executive Officers |last=Eberhard |first=Kristin |date=2017-05-09 |website=Sightline Institute |access-date=2023-12-31}}</ref> |
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[[Duverger's law]] says that systems vulnerable to this strategy will typically (though not always) develop [[Two-party system|two-party systems]], as voters will abandon minor-party candidates to support stronger major-party candidates.<ref name=":12">{{Cite book |last=Volić |first=Ismar |url=http://dx.doi.org/10.2307/jj.7492228 |title=Making Democracy Count |date=2024-04-02 |publisher=Princeton University Press |isbn=978-0-691-24882-0 |publication-date=2024-04-02 |at=Ch. 2 |chapter=Duverger's law |doi=10.2307/jj.7492228}}</ref> |
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[[Instant runoff voting|Instant-runoff]], [[two-round system|traditional runoffs]], [[Plurality voting|plurality]], and most other variants of [[ranked voting systems|ranked-choice voting]] (including strictly-[[Condorcet method|Condorcet-compliant methods]]) fail this criterion.<ref name="STAR Analysis" /><ref name="Woodall Monotonicity">{{cite journal |last1=Woodall |first1=Douglas |date=1997-06-27 |title=Monotonicity of single-seat preferential election rules |url=https://doi.org/10.1016/S0166-218X(96)00100-X |journal=Discrete Applied Mathematics |volume=77 |issue=1 |pages=81–98 |doi= 10.1016/S0166-218X(96)00100-X|access-date=2024-05-02}}</ref> <ref name="Fishburn">{{cite journal |last1=Fishburn |first1=Peter |last2=Brams |first2=Steven |date=1983-09-01 |title=Paradoxes of Preferential Voting |url=http://www.jstor.org/stable/2689808 |journal=Mathematics Magazine |volume=56 |issue=4 |pages=207–214 |doi=10.1080/0025570X.1983.11977044 |jstor=2689808 |access-date=2024-05-02}}</ref> |
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== US Presidential elections == |
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Instances of [[instant-runoff voting]] failing the criterion usually occur in combination with other [[List of pathological elections|election pathologies]] in the context of a [[center-squeeze]]. |
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The "sincere favorite criterion" suggests that a voter should always rank their sincere favorite candidate as their top choice, without strategizing based on the likely outcomes. However, in certain voting systems, this strategy can lead to suboptimal results, which makes the criterion less applicable. |
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== Definition == |
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The favorite betrayal criterion is defined as follows: |
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The U.S. presidential election is a prime example where voters might avoid using a sincere favorite criterion. This is due to the Electoral College system, which is structured as a "[[first-past-the-post voting|first-past-the-post]]" (FPTP) election within each state. Here, if a voter's sincere favorite has no realistic chance of winning, it may be rational for them to vote for a more viable candidate to prevent a less preferred option from winning. This is known as "tactical voting." |
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: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). |
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Several sources discuss how the FPTP system (like the one used in U.S. presidential elections) can disincentivize the use of sincere voting strategies: |
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The criterion permits the strategy of insincerely ranking another candidate equal to one's favorite.<ref name="small">Alex Small, “Geometric construction of voting methods that protect voters’ first choices,” arXiv:1008.4331 (August 22, 2010), http://arxiv.org/abs/1008.4331.</ref> |
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1. Gary Cox's "Making Votes Count: Strategic Coordination in the World’s Electoral Systems" explores strategic voting in FPTP systems and how they encourage tactical voting. |
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== Public Opinion == |
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2. Steven Brams and Peter Fishburn's "Approval Voting" touches on how non-ranking systems like approval voting can mitigate the issues with sincere voting in FPTP contexts. |
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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. |
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3. William H. Riker's "Liberalism against Populism" provides an analysis of the implications of various voting systems on strategic behaviors, including in U.S. elections. |
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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.<ref>{{cite web |url=https://www.equal.vote/gaming_the_vote |title=Voting Method Gameability |author=<!--Not stated--> |website=Equal Vote |publisher=The Equal Vote Coalition |access-date=2023-07-17}}</ref> The [[The Center for Election Science|Center for Election Science]] claims that failure of the favorite betrayal criterion incentivizes voters to cast dishonest ballots and results in lower voter satisfaction.<ref>{{cite web |url=https://electionscience.org/voting-methods/spoiler-effect-top-5-ways-plurality-voting-fails/ |title=Top 5 Ways Plurality Voting Fails |last=Hamlin |first=Aaron |date=2015-05-30 |website=Election Science |publisher=The Center for Election Science |access-date=2023-07-17}}</ref><ref>{{cite web |url=https://electionscience.org/voting-methods/runoff-election-the-limits-of-ranked-choice-voting/ |title=The Limits of Ranked-Choice Voting |last=Hamlin |first=Aaron |date=2019-02-07 |website=Election Science |publisher=The Center for Election Science |access-date=2023-07-17}}</ref> 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.<ref>{{cite web |url=https://democracychronicles.org/schulze-questioning-a-popular-ranked-voting-system/ |title=Schulze: Questioning a Popular Ranked Voting System |last=Ossipoff |first=Michael |date=2013-05-20 |website=Democracy Chronicles |access-date=2024-01-01}}</ref> |
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These references can provide a deeper theoretical grounding on why the sincere favorite criterion is frequently not practical in FPTP and U.S. presidential elections. |
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The Sightline Institute, an organization dedicated to making [[Pacific Northwest|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.<ref>{{cite web |url=https://www.sightline.org/about/ |title=About Us |author=<!--Not stated--> |website=Sightline |publisher=Sightline Institute |access-date=2024-01-01}}</ref><ref name="Hamlin">{{cite journal |last1=Hamlin |first1=Aaron |last2=Hua |first2=Whitney |date=2022-12-19 |title=The case for approval voting |url=https://link.springer.com/article/10.1007/s10602-022-09381-x |journal=Constitutional Political Economy |volume=34 |issue=3 |pages=335–345 |doi=10.1007/s10602-022-09381-x |access-date=2024-05-02}}</ref><ref>{{cite book |last=Sullivan |first=Brendan |date=2022 |title=An Introduction to the Math of Voting Methods |location= |publisher=619 Wreath |isbn=9781958469033}}</ref> 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.<ref name = "Sightline"/> |
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== |
== Definition == |
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A voting rule satisfies the sincere favorite criterion if there is never a need to "betray" a perfect candidate—i.e. if a voter will never achieve a worse result by honestly ranking their favorite candidate first.<ref name="small" /> |
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== Arguments for == |
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The [[The Center for Election Science|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.<ref>{{cite web |url=https://electionscience.org/voting-methods/spoiler-effect-top-5-ways-plurality-voting-fails/ |title=Top 5 Ways Plurality Voting Fails |last=Hamlin |first=Aaron |date=2015-05-30 |website=Election Science |publisher=The Center for Election Science |access-date=2023-07-17}}</ref><ref>{{cite web |url=https://electionscience.org/voting-methods/runoff-election-the-limits-of-ranked-choice-voting/ |title=The Limits of Ranked-Choice Voting |last=Hamlin |first=Aaron |date=2019-02-07 |website=Election Science |publisher=The Center for Election Science |access-date=2023-07-17}}</ref><ref>{{cite web |url=https://www.equal.vote/gaming_the_vote |title=Voting Method Gameability |author=<!--Not stated--> |website=Equal Vote |publisher=The Equal Vote Coalition |access-date=2023-07-17}}</ref><ref name="Hamlin">{{cite journal |last1=Hamlin |first1=Aaron |last2=Hua |first2=Whitney |date=2022-12-19 |title=The case for approval voting |journal=Constitutional Political Economy |volume=34 |issue=3 |pages=335–345 |doi=10.1007/s10602-022-09381-x |doi-access=free}}</ref> |
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Other commentators have argued that failing the favorite-betrayal criterion can increase the effectiveness of [[Misinformation|misinformation campaigns]], by allowing major-party candidates to sow doubt as to whether voting honestly for one's favorite is actually the best strategy.<ref>{{cite web |url=https://democracychronicles.org/schulze-questioning-a-popular-ranked-voting-system/ |title=Schulze: Questioning a Popular Ranked Voting System |last=Ossipoff |first=Michael |date=2013-05-20 |website=Democracy Chronicles |access-date=2024-01-01}}</ref> |
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The following will provide an example and explain how score voting satisfies the favorite betrayal criterion. Score voting functions as follows: |
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== Compliant methods == |
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# 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. |
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# Candidates left unassigned are automatically given a score of 0. |
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# The candidate with the highest cumulative score wins. |
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=== Rated voting === |
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Assume there are three candidates: Agnew, BillyJoe, and Cletus. The voters may give scores up to 5. The vote totals appear as follows: |
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Because [[rated voting]] methods are not affected by [[Arrow's impossibility theorem|Arrow's theorem]], they can be both [[spoilerproof]] (satisfy [[Independence of irrelevant alternatives|IIA]]) and ensure [[Positive response|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. |
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{| class="wikitable" |
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! Candidate |
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! Total score |
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| Agnew |
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| 35 |
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| BillyJoe |
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| 39 |
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| Cletus |
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| 22 |
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Examples of systems that are both spoilerproof and monotonic include [[score voting]], [[approval voting]], and [[Highest median voting rules|highest medians]]. |
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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: |
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=== Anti-plurality voting === |
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# Agnew > BillyJoe > Cletus |
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# Agnew > Cletus > BillyJoe |
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# BillyJoe > Cletus > Agnew |
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# BillyJoe > Agnew > Cletus |
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# Cletus > Agnew > BillyJoe |
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# Cletus > BillyJoe > Agnew |
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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. |
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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. |
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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. |
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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. |
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== Non-compliant methods == |
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=== Instant-runoff voting === |
=== Instant-runoff voting === |
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{{ |
{{See also|Instant-runoff voting}} |
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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: |
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#Voters rank candidates from most to least preferred. |
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#Candidates are awarded one vote for every ballot in which they are the preferred candidate. |
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#If a candidate is preferred on more than 50% of the ballots which list active candidates, they win. Otherwise, the next step is performed. |
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#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. |
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{| class="wikitable" |
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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 |
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 7 votes. Her votes are transferred to Amy as well. Finally, Amy has 21 votes and wins against Dan, who has 20 votes. |
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{| class="wikitable" |
{| class="wikitable" |
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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. |
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. |
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=== Condorcet methods === |
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Commentary from old page on [[lesser of two evils]] |
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== Lesser Evil Voting== |
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[[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.<ref>[[Noam Chomsky]] and John Halle, "[https://newpol.org/eight-point-brief-lev-lesser-evil-voting/ An Eight Point Brief for LEV (Lesser Evil Voting)]," ''[https://newpol.org/about/ New Politics],'' June 15, 2016.</ref> |
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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]].<ref name="hufevil">{{cite web |author=Stanford Jay Rosen |date=2012-09-25 |title=Don't Get Fooled Again: Why Liberals and Progressives Should Vote Enthusiastically for President Obama |url=https://www.huffingtonpost.com/sanford-jay-rosen/obama-reelection_b_1913745.html |access-date=2013-03-23 |publisher=Huffington Post}}</ref> Rosen stated: "Beginning with the [[1968 United States presidential election|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 United States presidential election|1972]] until Watergate did him in. And it delivered us to [[George W. Bush]] and [[Dick Cheney]] in [[2000 United States presidential election|2000]] until they were termed out in 2009".<ref name="hufevil" /> |
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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.<ref name="washpostdislike">{{cite news |author=Aaron Blake |date=2016-08-31 |title=A record number of Americans now dislike Hillary Clinton |url=https://www.washingtonpost.com/news/the-fix/wp/2016/08/31/a-record-number-of-americans-now-dislike-hillary-clinton/ |access-date=2016-08-31 |newspaper=Washington Post}}</ref> Green Party candidate [[Jill Stein]] invoked the idea in her campaign stating, "Don't vote for the lesser evil, fight for the greater good".<ref>{{cite web |date=26 May 2016 |title=Meet Jill Stein, the Other Anti-Establishment Progressive Running for President |url=https://www.gq.com/story/jill-stein-green-party-interview}}</ref> Green Party votes hurt Democratic chances in 2000 and 2016.<ref>{{Cite web |title=Did Ralph Nader Spoil Al Gore's Presidential Bid? A Ballot-Level Study of Green and Reform Party Voters in the 2000 Presidential Election |url=https://www.researchgate.net/publication/241583809 |accessdate=30 March 2023}}</ref><ref>{{cite web |title=Jill Stein cost Hillary dearly in 2016. Democrats are still writing off her successor |url=https://www.politico.com/news/2020/06/20/democrats-shrug-off-potential-green-party-spoiler-in-2020-329170 |website=[[Politico]]}}</ref><ref>{{cite web |date=December 2016 |title=Green Party candidate Jill Stein got more votes than Trump's victory margin in 3 key states |url=https://www.vox.com/policy-and-politics/2016/12/1/13811344/jill-stein-clinton-trump-nader-spoiler}}</ref> 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."<ref>"[https://open.lib.umn.edu/americangovernment/chapter/10-6-minor-parties/ 10.6 Minor Parties]," ''American Government and Politics in the Information Age,'' [[University of Minnesota]], 2011.</ref> |
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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 (France)|National Front]]. Chirac eventually won the second round having garnered 82% of the vote.<ref>{{cite web |date=2002-05-06 |title=Chirac's new challenge |url=http://www.economist.com/node/1109370 |access-date=2011-04-15 |publisher=The Economist}}</ref> |
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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.<ref name="LAT1988-09-18-01a">{{cite news |last=Schneider |first=William |author-link=Bill Schneider (journalist) |date=18 September 1988 |title=THE EVIL OF TWO LESSERS |url=https://www.latimes.com/archives/la-xpm-1988-09-18-op-3101-story.html |access-date=12 September 2020 |work=[[Los Angeles Times]]}}</ref><ref name="JP2016-11-06-01a">{{cite news |last=Keinon |first=Herb |author-link=Herb Keinon |date=6 November 2016 |title=Clinton vs. Trump: 'The evil of two lessers' |url=https://www.jpost.com/us-elections/clinton-vs-trump-the-evil-of-two-lessers-471799 |access-date=12 September 2020 |publisher=[[Jerusalem Post]]}}</ref> <!--> |
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== See also == |
== See also == |
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== References == |
== References == |
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{{reflist}} |
{{reflist}}{{Voting systems}} |
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[[Category: |
[[Category:Electoral system criteria]] |
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[[Category:Game theory]] |
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[[Category:Political science]] |
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Latest revision as of 05:43, 12 November 2024
| A joint Politics and Economics series |
| Social choice and electoral systems |
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 Mathematics portal |
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 lesser-evil voting or a strategy called "decapitation" (removing the "head" off a ballot).[2]
Most rated voting systems, including score voting, satisfy the criterion.[3][4][5]
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.[6]
US Presidential elections
[edit]The "sincere favorite criterion" suggests that a voter should always rank their sincere favorite candidate as their top choice, without strategizing based on the likely outcomes. However, in certain voting systems, this strategy can lead to suboptimal results, which makes the criterion less applicable.
The U.S. presidential election is a prime example where voters might avoid using a sincere favorite criterion. This is due to the Electoral College system, which is structured as a "first-past-the-post" (FPTP) election within each state. Here, if a voter's sincere favorite has no realistic chance of winning, it may be rational for them to vote for a more viable candidate to prevent a less preferred option from winning. This is known as "tactical voting."
Several sources discuss how the FPTP system (like the one used in U.S. presidential elections) can disincentivize the use of sincere voting strategies:
1. Gary Cox's "Making Votes Count: Strategic Coordination in the World’s Electoral Systems" explores strategic voting in FPTP systems and how they encourage tactical voting.
2. Steven Brams and Peter Fishburn's "Approval Voting" touches on how non-ranking systems like approval voting can mitigate the issues with sincere voting in FPTP contexts.
3. William H. Riker's "Liberalism against Populism" provides an analysis of the implications of various voting systems on strategic behaviors, including in U.S. elections.
These references can provide a deeper theoretical grounding on why the sincere favorite criterion is frequently not practical in FPTP and U.S. presidential elections.
Definition
[edit]A voting rule satisfies the sincere favorite criterion if there is never a need to "betray" a perfect candidate—i.e. if a voter will never achieve a worse result by honestly ranking their favorite candidate first.[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 despite having the opportunity to participate in the election.[7][8][9][10]
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.[11]
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.
Examples of systems that are both spoilerproof and monotonic include score voting, approval voting, and highest medians.
Anti-plurality voting
[edit]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.
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 7 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
[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
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.
- ^ 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. JSTOR 1961964.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ Ossipoff, Michael (2013-05-20). "Schulze: Questioning a Popular Ranked Voting System". Democracy Chronicles. Retrieved 2024-01-01.