No favorite betrayal criterion

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reworked the introduction for wording and strict accuracy

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{{Short description|No lesser evil voting system criterion}}{{Short description|No lesser evil voting system criterion}}
The '''no favorite betrayal criterion''' describes whether a voting system avoids situations in which individuals insincerely rank their candidates to obtain their preferred outcome ("lesser evil voting"), rather than supporting their favorite candidate. Many [[Rated voting|rated]] and [[Condorcet method|Condorcet]] voting methods satisfy the criterion, including [[score voting]], whereas [[instant-runoff voting]], [[Two-round system|two-round systems]], and [[plurality voting]] do not.<ref>{{Cite web|url=https://rangevoting.org/FBCsurvey.html|title=Survey of FBC (Favorite-Betrayal Criterion)|last=Ossipoff|first=Mike|last2=Smith|first2=Warren D.|date=Jan 2007|website=Center for Range Voting|url-status=live|archive-url=|archive-date=|access-date=2020-04-08}}</ref><ref>{{Cite journal|last=Merrill|first=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/prod...0194481/type/journal_article|journal=American Political Science Review|language=en|volume=81|issue=2|pages=509–524|doi=10.2307/1961964|issn=0003-0554}}</ref><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.}}The '''no favorite betrayal criterion''' is a voting system criterion which requires that a voter must not have any incentive to betray their favorite candidate. For a voting method to satisfy the criterion, awarding maximum support to a voter's favorite candidate must always be a part of their optimum voting strategy. Many [[Rated voting|rated]] and [[Condorcet method|Condorcet]] voting methods satisfy the criterion, including [[score voting]] and [[approval voting]], whereas [[ranked voting| ranked voting systems]] such as [[instant-runoff voting]], [[Two-round system|two-round systems]], and [[plurality voting]] do not.<ref>{{Cite web|url=https://rangevoting.org/FBCsurvey.html|title=Survey of FBC (Favorite-Betrayal Criterion)|last=Ossipoff|first=Mike|last2=Smith|first2=Warren D.|date=Jan 2007|website=Center for Range Voting|url-status=live|archive-url=|archive-date=|access-date=2020-04-08}}</ref><ref>{{Cite journal|last=Merrill|first=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/prod...0194481/type/journal_article|journal=American Political Science Review|language=en|volume=81|issue=2|pages=509–524|doi=10.2307/1961964|issn=0003-0554}}</ref><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 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><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> If the criterion is satisfied, voters can instead insincerely rank other candidates as equal to their favorite choice.<ref name="small">{{Citation |last=Small |first=Alex |title=Geometric construction of voting methods that protect voters' first choices |date=2010-08-25 |url=http://arxiv.org/abs/1008.4331 |access-date=2024-05-06 |doi=10.48550/arXiv.1008.4331}}</ref></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><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> The criterion permits voters to insincerely rank other candidates as equal to their favorite choice.<ref name="small">{{Citation |last=Small |first=Alex |title=Geometric construction of voting methods that protect voters' first choices |date=2010-08-25 |url=http://arxiv.org/abs/1008.4331 |access-date=2024-05-06 |doi=10.48550/arXiv.1008.4331}}</ref>
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