Editing Negative responsiveness (section)

== Frequency of violations ==
The frequency of negative response will depend on the electoral method, the candidates, and the distribution of outcomes.
===Empirical analysis===
In the US, a 2021 analysis of [[Instant-runoff voting|instant-runoff]] elections in California between 2008 and 2016, as well as the [[2009 Burlington, Vermont mayoral election]], found an upward monotonicity anomaly rate of 0.74% (1/135) in all elections, 2.71% (1/37) when limited to elections going to a second round of counting and 7.7% (1/13) of elections with three competitive candidates.<ref>{{cite journal |last1=Graham-Squire |first1=Adam |last2=Zayatz |first2=N. |title=Lack of Monotonicity Anomalies in Empirical Data of Instant-runoff Elections |journal=Representation |date=2 October 2021 |volume=57 |issue=4 |pages=565–573 |doi=10.1080/00344893.2020.1785536}}</ref><ref name="McCune"/> A more comprehensive 2023 survey of 182 American IRV elections where no candidate was ranked first by a majority of voters found seven total examples of non-monotonicity (3.8%), broken down into 2.2% (4/182) examples of upward monotonicity, 1.6% (3/182) of downward montonicity and 0.5% (1/182) of no-show or truncation (one example was both an upward and downward monotonicity failure).<ref name=":522" /><ref name="McCune">{{cite journal |last1=McCune |first1=David |last2=Graham-Squire |first2=Adam |title=Monotonicity anomalies in Scottish local government elections |journal=Social Choice and Welfare |date=August 2024 |volume=63 |issue=1 |pages=69–101 |doi=10.1007/s00355-024-01522-5 |doi-access=free|arxiv=2305.17741 }}</ref> Two of those elections are also noted as specific examples below.

====Semi-empirical====
Some empirical research do not have access to full ballot preference data, and thus make probabilistic estimates of transfer patterns. A 2013 survey of Irish elections using IRV and [[PR-STV]] found plausible non-monotonicity in 20 out of 1326 elections between 1922 and 2011.<ref name="Gallagher">{{Cite conference |last=Gallagher |first=Michael |date=September 2013 |title=Monotonicity and non-monotonicity at PR-STV elections |url=https://www.lancaster.ac.uk/fass/events/epop2013/docs/MGallagherMonotonicityEPOP13.pdf |conference=Annual conference of the elections, public opinion and parties (EPOP) specialist group, University of Lancaster |volume=13}}</ref>

Data from the five UK general elections between 1992 and 2010 showed 2642 three candidate elections in English constituencies. With second preferences imputed from survey data, 1.7% of all elections appeared vulnerable to monotonicity anomalies (1.4% upward, 0.3% downward), significantly lower than simulated datasets from the same paper. However, when limited to the 4.2% of elections considered three-way competitive<!--This should be the 111 elections where PL support >25% but might need to check that, also probably get consensus that it's correct per CALC-->, 40.2% appeared vulnerable (33% upward, 7.1% downward), and further increasing with closer competition, a result closer to the simulations.<ref name=":3">{{Cite journal |last=Miller |first=Nicholas R. |date=October 2017 |title=Closeness matters: monotonicity failure in IRV elections with three candidates |url=https://userpages.umbc.edu/~nmiller/MONFAILURE.R2.NRM.pdf |journal=Public Choice |volume=173 |issue=1–2 |pages=91–108 |doi=10.1007/s11127-017-0465-5 |quote=Impartial Culture Profiles: All, TMF: 15.1% |hdl-access=free |hdl=11603/20938}}</ref>

A 2022 analysis out of the 10 French presidential elections (conducted under the [[two-round system]]) 2 had results where monotonicity violations were not mathematically possible, another 6 where violations were unlikely given the evidence, leaving 2 elections ([[2002 French presidential election|2002]] and [[2007 French presidential election|2007]]) where an upward monotonicity violation was probable and likely respectively.<ref name=":4">{{cite journal |last1=Keskin |first1=Umut |last2=Sanver |first2=M. Remzi |last3=Tosunlu |first3=H. Berkay |url=https://hal.science/hal-03413280/document |title=Monotonicity violations under plurality with a runoff: the case of French presidential elections |journal=Social Choice and Welfare |date=August 2022 |volume=59 |issue=2 |pages=305–333 |doi=10.1007/s00355-022-01397-4}}</ref>

=== Theoretical models===
Results using the [[impartial culture]] model estimate about 15% of elections with 3 candidates;<ref>{{Cite web |last=Miller |first=Nicholas R. |date=2016 |title=Monotonicity Failure in IRV Elections with Three Candidates: Closeness Matters |url=https://userpages.umbc.edu/~nmiller/MONFAILURE.R2.NRM.pdf |access-date=2020-07-26 |website=University of Maryland Baltimore County |at=Table 2 |language=en |quote=Impartial Culture Profiles: All, TMF: 15.1% |edition=2nd}}</ref><ref name="Miller2012"/> however, the true probability may be much higher, especially when restricting observation to close elections.<ref name=":2">{{Cite journal |last=Quas |first=Anthony |date=2004-03-01 |title=Anomalous Outcomes in Preferential Voting |url=https://www.worldscientific.com/doi/abs/10.1142/S0219493704000912 |journal=Stochastics and Dynamics |language=en |volume=04 |issue=1 |pages=95–105 |doi=10.1142/S0219493704000912 |issn=0219-4937|url-access=subscription }}</ref>

A 2013 study using a two-dimensional [[spatial model of voting]] estimated at least 15% of IRV elections would be nonmonotonic in the best-case scenario (with only three equally-competitive candidates). The researchers concluded that "three-way competitive races will exhibit unacceptably frequent monotonicity failures" and "In light of these results, those seeking to implement a fairer multi-candidate election system should be wary of adopting IRV."<ref name="Ornstein" />

=== Specific examples ===
==== 2022 in Alaska ====
[[2022 Alaska's at-large congressional district special election|Alaska's first-ever instant-runoff election]] resulted in a victory for [[Democratic Party (United States)|Democrat]] [[Mary Peltola]], but had many voters for [[Republican Party (United States)|Republican]] [[Sarah Palin]] instead ranked Peltola first, Peltola would have lost.<ref>{{Cite journal |last1=Graham-Squire |first1=Adam |last2=McCune |first2=David |date=2024-01-02 |title=Ranked Choice Wackiness in Alaska |url=https://www.tandfonline.com/doi/full/10.1080/10724117.2023.2224675 |journal=Math Horizons |language=en |volume=31 |issue=1 |pages=24–27 |doi=10.1080/10724117.2023.2224675 |issn=1072-4117|url-access=subscription }}</ref>

==== Burlington, Vermont ====
In [[2009 Burlington, Vermont mayoral election|Burlington's second IRV election]], incumbent [[Bob Kiss]] was re-elected, despite losing in a head-to-head matchup with Democrat Andy Montroll (the [[Condorcet winner]]). However, if Kiss had gained more support from Wright voters, Kiss would have lost.<ref name=":522" />

==== 2005 German election in Dresden ====
In the [[2005 German federal election]], [[Christian Democratic Union of Germany|CDU]] supporters in [[Dresden]] were instructed to vote for the [[Free Democratic Party (Germany)|FDP]], a strategy that allowed the CDU to win an additional seat.<ref name=":4222" /> This led the [[Federal Constitutional Court]] to rule that negative responsiveness violates the [[Basic Law for the Federal Republic of Germany|German constitution]]'s guarantee of [[One man, one vote|equal and direct suffrage]].<ref name=":0322"/>