Monotonicity: Difference between revisions
Add: monotonicity isn't participation, and no DPC methods have been proven monotone. Do some cleanup. Remove part with citation needed from 2011.
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(Add: monotonicity isn't participation, and no DPC methods have been proven monotone. Do some cleanup. Remove part with citation needed from 2011.) |
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<ref name="Austen-Smith Banks 2014 pp. 531–537">{{cite journal | last=Austen-Smith | first=David | last2=Banks | first2=Jeffrey | title=Monotonicity in Electoral Systems - American Political Science Review | journal=American Political Science Review | volume=85 | issue=2 | date=2014-08-01 | issn=1537-5943 | doi=10.2307/1963173 | pages=531–537 | url=http://www.jstor.org/stable/1963173 | access-date=2020-02-03}}</ref>
Of the single-winner ranked voting systems, [[Borda count|Borda]], [[Schulze method|Schulze]], [[Ranked Pairs]], [[Maximize Affirmed Majorities]], [[Descending Solid Coalitions]], and [[Descending Acquiescing Coalitions]]<ref name="Woodall-Monotonicity" /> are monotone, while [[Coombs' method]], [[runoff voting]], and [[instant-runoff voting]] (IRV) are not.
Most variants of the [[single transferable vote]] (STV) [[proportional representation]]
All [[plurality voting system]]s are monotone if the ballots are treated as rankings where using ''more than two ranks is forbidden''. In this setting [[first past the post]] and [[approval voting]] as well as the multiple-winner systems [[single non-transferable vote]], [[plurality-at-large voting]] (multiple non-transferable vote, bloc voting) and [[cumulative voting]] are monotonic. [[Party-list proportional representation]] using [[D'Hondt method|D'Hondt]], [[Sainte-Laguë method|Sainte-Laguë]] or the [[largest remainder method]] is monotone in the same sense.
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Using an example that applies to [[instant-runoff voting]] (IRV) and to the [[two-round system]], it is shown that these voting systems violate the mono-raise criterion.
Suppose a
Suppose the votes are cast as follows:
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===Estimated likelihood of IRV lacking monotonicity===
Crispin Allard argued, based on a mathematical model that the probability of monotonicity failure actually changing the result of an election for any given [[
Another probability model, the "impartial culture", yields about 15% probability. In elections with more than 3 candidates, these probabilities tend to increase eventually toward 100% (in some models this limit has been proven, in others it is only conjectured).
==Real-life monotonicity violations==
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