Monotonicity: Difference between revisions
Added information about monotonicity/LNH/mutual majority incompatibility.
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In elections via the single-winner methods [[range voting]] and [[majority judgment]] nobody can help a candidate by reducing or removing support for them. The definition of the monotonicity criterion with regard to these methods is disputed. Some voting theorists argue that this means these methods pass the monotonicity criterion; others say that, as these are not ''ranked'' voting systems, they are out of the monotonicity criterion's scope.
=== Implications ===
It's impossible for a method to pass all of monotonicity, [[later-no-harm]], [[later-no-help]], and [[mutual majority]],<ref name="Woodall-Monotonicity"/> but there do exist methods that pass three of the four. [[First past the post]] passes the first three, [[instant-runoff voting]] passes the last three, and [[Descending Acquiescing Coalitions]] and [[Descending Solid Coalitions]] pass one of the later-no-help/harm criteria as well as monotonicity and mutual majority.
== Definition of monotonicity criteria==
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A party-list strategy exploiting something similar (down-ranking CDU '''and''' additionally up-ranking another party, e.g. FDP) happened in the German federal election of 2005, in which conservative voters in Dresden deliberately voted against the CDU, their party of choice, in order to maximize that party's number of seats in the federal parliament. This was possible due to Germany's voting system (mixed member proportional with overhang seats computed independently for each federal state) and the fact that the vote in Dresden took place a week after the rest of the country due to the death of a candidate, enabling voters in Dresden to vote tactically in full knowledge of the results already achieved elsewhere. As a result of this, the German Constitutional Court ruled on July 3 2008 that the German voting system must be reformed to eliminate its non-monotonicity.<ref> See e.g. [http://fruitsandvotes.com/blog/?p=117]</ref>
=== 2009 Burlington, Vermont
{{seealso|[[2009 Burlington mayoral election]]}}
A real-life monotonicity violation was detected in the [[2009 Burlington mayoral election]] (in [[Vermont]]) under instant-runoff voting (IRV), where the necessary information is available. In this election, the winner Bob Kiss could have been defeated by raising him on some of the ballots. For example, if all voters who ranked Kurt Wright over Bob Kiss over Andy Montroll, would have ranked Kiss over Wright over Montroll, and additionally some people who ranked Wright but not Kiss or Montroll, would have ranked Kiss over Wright, then these votes in favor of Kiss would have defeated him.<ref>[http://www.rangevoting.org/Burlington.html Burlington Vermont 2009 IRV mayor election]</ref> The winner in this scenario would have been Andy Montroll, who was also the [[Condorcet winner]] according to the original ballots, i.e. for any other running candidate, a majority ranked Montroll above the competitor.
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[[Douglas Woodall]] defined several variations or types of monotonicity.<ref name="Woodall-Monotonicity" /> In Woodall's definitions, a candidate x should not be harmed if:
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=== Multi-winner monotonicity ===
Monotonicity would be more aptly named ''endorsement monotonicity'' since it is the preservation of monotonicity relative to endorsement. Since it is the most important form of monotonicity is bears the simple naming. There are however two other important forms of monotonicity for multi-winner voting systems, [[Population monotonicity]] and [[House monotonicity criterion |House monotonicity]].
Multi-winner monotonicity could also be considered in a weaker and stronger sense: the weak form is satisfied whenever, if A is one of the winners, ranking A higher does not kick A out of the winning set; whereas the stronger form is satisfied whenever, if A is one of the winners, ranking A higher does not kick ''anyone'' out of the winning set. In a single winner election, these criteria are the same, but the stronger form is harder to satisfy for multi-winner. Woodall's definition of mono-raise corresponds to the weak form.
==Footnotes==
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[[Category:Voting system criteria]]
[[Category:Monotonic electoral systems|*]]
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