Editing Negative responsiveness (section)

<noinclude>{{Requested move notice|1=Mono-raise criterion|2=Talk:Negative responsiveness#Requested move 16 April 2025}}
</noinclude>[[Category:Electoral system criteria]]
{{Short description|Property of electoral systems}}{{Electoral systems sidebar|expanded=Paradox}}
[[File:IRV_Yee.svg|alt=A diagram showing who would win an IRV election for different electorates. The win region for each candidate is erratic, with random pixels dotting the image and jagged, star-shaped (convex) regions occupying much of the image. Moving the electorate to the left can cause a right-wing candidate to win, and vice versa.|thumb|300x300px|A 4-candidate Yee diagram under IRV. The diagram shows who would win an IRV election if the electorate is centered at a particular point. Moving the electorate to the left can cause a right-wing candidate to win, and vice versa. Black lines show the [[Voronoi diagram|optimal solution]] (achieved by [[Condorcet method|Condorcet]] or [[Score voting|score]] voting).]]
In [[Social choice theory|social choice]], the '''negative response''',<ref>{{Cite journal |last=May |first=Kenneth O. |date=1952 |title=A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision |url=https://www.jstor.org/stable/1907651 |journal=Econometrica |volume=20 |issue=4 |pages=680–684 |doi=10.2307/1907651 |issn=0012-9682 |jstor=1907651|url-access=subscription }}</ref><ref name=":4222">{{Cite book |last=Pukelsheim |first=Friedrich |url=http://archive.org/details/proportionalrepr0000puke |title=Proportional representation: apportionment methods and their applications |date=2014 |publisher=Cham; New York : Springer |others=Internet Archive |isbn=978-3-319-03855-1}}</ref> '''perversity''',<ref name="jstor.org">{{Cite journal |last1=Doron |first1=Gideon |last2=Kronick |first2=Richard |date=1977 |title=Single Transferrable Vote: An Example of a Perverse Social Choice Function |url=https://www.jstor.org/stable/2110496 |journal=American Journal of Political Science |volume=21 |issue=2 |pages=303–311 |doi=10.2307/2110496 |issn=0092-5853 |jstor=2110496|url-access=subscription }}</ref> or '''additional support paradox'''<ref name=":0">{{Cite web <!--Is this a conference?--> |last=Felsenthal |first=Dan S. |date=April 2010 |title=Review of paradoxes afflicting various voting procedures where one out of m candidates (m ≥ 2) must be elected |url=https://eprints.lse.ac.uk/27685/ |language=en |location=GBR |pages=1–52}}</ref> is a [[Pathological (mathematics)#In voting and social choice|pathological behavior]] of some [[Electoral system|voting rules]] where a candidate loses as a result of having too much support (or wins because of increased opposition). In other words, increasing (decreasing) a candidate's [[Ranked voting|ranking]] or [[Rated voting|rating]] causes that candidate to lose (win), respectively.<ref name=":0" /> Electoral systems that do not exhibit perversity are sometimes said to satisfy the [[Monotonic function|'''monotonicity''']] '''criterion'''.<ref name="Woodall-Monotonicity222">D R Woodall, [http://www.votingmatters.org.uk/ISSUE6/P4.HTM "Monotonicity and Single-Seat Election Rules"], ''[[Voting matters]]'', Issue 6, 1996</ref>

Perversity is often described by [[Social choice theory|social choice theorists]] as an exceptionally severe kind of [[Pathological (mathematics)#In voting and social choice|electoral pathology]],<ref name="Felsenthal-severe">{{Cite journal |last1=Felsenthal |first1=Dan S. |last2=Tideman |first2=Nicolaus |date=2014-01-01 |title=Interacting double monotonicity failure with direction of impact under five voting methods |url=https://www.sciencedirect.com/science/article/pii/S0165489613000723 |journal=Mathematical Social Sciences |volume=67 |pages=57–66 |doi=10.1016/j.mathsocsci.2013.08.001 |issn=0165-4896 |quote=It is generally agreed among social choice theorists that a voting method that is susceptible to any type of monotonicity failure suffers from a particularly serious defect.|url-access=subscription }}</ref> as such rules can have "backwards" responses to voters' opinions, where popularity causes defeat while unpopularity leads to a win.<ref name=":1">{{Cite book |last=Arrow |first=Kenneth J. |url=http://dx.doi.org/10.12987/9780300186987 |title=Social Choice and Individual Values |date=2017-12-13 |isbn=978-0-300-18698-7 |doi=10.12987/9780300186987 |quote=Since we are trying to describe social welfare and not some sort of illfare, we must assume that the social welfare function is such that the social ordering responds positively to alterations in individual values, or at least not negatively. Hence, if one alternative social state rises or remains still in the ordering of every individual without any other change in those orderings, we expect that it rises, or at least does not fall, in the social ordering.}}</ref> Similar rules treat the well-being of some voters as "less than worthless".<ref name="Arrow">{{Cite book |last=Arrow |first=Kenneth J. |url=http://dx.doi.org/10.12987/9780300186987 |title=Social Choice and Individual Values |date=2017-12-13 |isbn=978-0-300-18698-7 |doi=10.12987/9780300186987 |page=25 |quote=Since we are trying to describe social welfare and not some sort of illfare, we must assume that the social welfare function is such that the social ordering responds positively to alterations in individual values, or at least not negatively. Hence, if one alternative social state rises or remains still in the ordering of every individual without any other change in those orderings, we expect that it rises, or at least does not fall, in the social ordering.}}</ref>  These issues have led to constitutional prohibitions on such systems as violating the right to [[One man, one vote|equal and direct suffrage]].<ref name=":42322">{{Cite book |last=Pukelsheim |first=Friedrich |url=http://archive.org/details/proportionalrepr0000puke |title=Proportional representation : apportionment methods and their applications |date=2014 |publisher=Cham; New York : Springer |others=Internet Archive |isbn=978-3-319-03855-1}}</ref><ref name=":0322">{{Cite news |last=dpa |date=2013-02-22 |title=Bundestag beschließt neues Wahlrecht |url=https://www.zeit.de/politik/deutschland/2013-02/bundestag-wahlrecht-beschluss |access-date=2024-05-02 |work=Die Zeit |language=de-DE |issn=0044-2070}}</ref> Negative response is often cited as an example of a [[perverse incentive]], as rules with negative response can incentivize politicians to take [[Center squeeze|extreme]] or unpopular positions in an attempt to shed excess votes.<ref name=":4" />

Most [[Ranked voting|ranked methods]] (including [[Borda count|Borda]] and all common [[Round-robin voting|round-robin rules]]) satisfy positive response,<ref name="Woodall-Monotonicity222" /> as do all common [[rated voting]] methods (including [[Approval voting|approval]], [[Highest median voting rules|highest medians]], and [[Score voting|score]]).{{NoteTag|Apart from majority judgment, these systems satisfy an even stronger form of positive responsiveness: if there is a tie, any increase in a candidate's rating will break the tie in that candidate's favor.}} 

Negative responsiveness occurs in [[instant-runoff voting]] (IRV),<ref name="Ornstein">{{Cite journal |last1=Ornstein |first1=Joseph T. |last2=Norman |first2=Robert Z. |date=2014-10-01 |title=Frequency of monotonicity failure under Instant Runoff Voting: estimates based on a spatial model of elections |journal=Public Choice |language=en |volume=161 |issue=1–2 |pages=1–9 |doi=10.1007/s11127-013-0118-2 |issn=0048-5829 |s2cid=30833409}}</ref> the [[single transferable vote]],<ref name="jstor.org"/> and the [[two-round system]].<ref name=":4" /> Some [[Quota method|quota-based apportionment methods]] also violate the rule,<ref name=":5" /> as can the [[Maximal lotteries|randomized Condorcet method]] in cases of [[Condorcet cycle|cyclic ties]].

The [[participation criterion]] is closely-related, but different. While positive responsiveness deals with a voter changing their opinion (or vote), participation deals with situations where a voter choosing to cast a ballot at all has a backwards effect on the election.<ref name=":5">{{Cite journal |last=Dančišin |first=Vladimír |date=2017-01-01 |title=No-show paradox in Slovak party-list proportional system |url=https://www.degruyter.com/document/doi/10.1515/humaff-2017-0002/html?lang=en |journal=Human Affairs |language=en |volume=27 |issue=1 |pages=15–21 |doi=10.1515/humaff-2017-0002 |issn=1337-401X|url-access=subscription }}</ref>