Editing Negative responsiveness (section)

==Definition==
Miller defined two main classes of monotonicity failure in 2012, which have been repeated in later papers:<ref name="Miller2012"><!--Kinda think we should replace this one with the PDF version, but I can't tell if it's too different-->{{Cite book |last=Miller |first=Nicholas R. |url=https://userpages.umbc.edu/~nmiller/RESEARCH/MF&IRV.pptx |title=Monotonicity Failure in IRV Elections With Three Candidates |year=2012 |pages=23 |type=PowerPoint |quote=Impartial Culture Profiles: All, Total MF: 15.0%}}</ref><ref name="Felsenthal-severe"/>
{{bq|
''Upward monotonicity failure'': Given the use of voting method V and a ballot profile B in which candidate X is the winner, X may nevertheless lose in ballot profile B' that differs from B only in that some voters rank X higher in B' than in B{{pb}}
''Downward monotonicity failure'': Given the use of voting method V and a ballot profile B in which candidate X is a loser, X may nevertheless win in ballot profile B' that differs from B only in that some voters rank X lower in B' than in B.
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In simpler terms, an upward failure occurs when a winner loses from more support, and a downward failure occurs when a loser wins with less support.

=== Views ===
Social choice theorists generally agree that negative responsiveness is an especially severe issue for a voting rule.<ref name="Felsenthal-severe"/> Some have argued the mere possibility should be enough to disqualify runoff-based electoral methods, while others argue this is only true if it occurs in "easy" or "common" cases, generally meaning those without a [[Condorcet cycle]].<ref name="Gallagher"/>

[[Michael Gallagher (academic)|Gallagher]] notes some [[political scientist]]s are less concerned about negative response, arguing voters will not notice or understand it, making it appear random from their perspective and preventing exploitation by [[strategic voting|strategic voters]].<ref name="Gallagher"/> By contrast, other researchers have argued voters will predict negative response and respond by strategically down-ranking their preferred candidates, keeping it from affecting the results.<ref>{{cite journal | url=https://doi.org/10.2307/1963173 | doi=10.2307/1963173 | jstor=1963173 | title=Monotonicity in Electoral Systems | last1=Austen-Smith | first1=David | last2=Banks | first2=Jeffrey | journal=The American Political Science Review | date=1991 | volume=85 | issue=2 | pages=531–537 }}</ref>