Informed majority coalition criterion: Difference between revisions
m (Whoops, Durand states that Coombs passes InfMC. Fixed.) |
(Changed language to be a little more precise.) |
||
| (4 intermediate revisions by 2 users not shown) | |||
| Line 3: | Line 3: | ||
{{definition|A group comprising a majority of voters is always able to cast their votes so as to elect any candidate they wish, provided that the votes of the remaining minority are known to them and don't change.}} |
{{definition|A group comprising a majority of voters is always able to cast their votes so as to elect any candidate they wish, provided that the votes of the remaining minority are known to them and don't change.}} |
||
It was independently defined by James Green-Armytage<ref name="Green-Armytage Tideman Cosman 2015 pp. 183–212">{{cite journal | last=Green-Armytage | first=James | last2=Tideman | first2=T. Nicolaus | last3=Cosman | first3=Rafael | title=Statistical evaluation of voting rules | journal=Social Choice and Welfare | publisher=Springer Science and Business Media LLC | volume=46 | issue=1 | date=2015-08-11 | issn=0176-1714 | doi=10.1007/s00355-015-0909-0 | pages=183–212 | url=https://jamesgreenarmytage.com/strategy-utility.pdf}}</ref> and Durand ''et al.''<ref name="Durand Mathieu Noirie 2016 j401">{{cite web | last=Durand | first=François | last2=Mathieu | first2=Fabien | last3=Noirie | first3=Ludovic | title=Can a Condorcet Rule Have a Low Coalitional Manipulability? | website=Archive ouverte HAL | volume=285 | date=2016-08-29 | url=https://hal.science/hal-01369877 | access-date=2023-06-26}}</ref> Any voting method passing the [[majority criterion]] automatically passes the informed majority coalition criterion, since the majority can all their preferred candidate first to make that candidate win. |
It was independently defined by James Green-Armytage<ref name="Green-Armytage Tideman Cosman 2015 pp. 183–212">{{cite journal | last=Green-Armytage | first=James | last2=Tideman | first2=T. Nicolaus | last3=Cosman | first3=Rafael | title=Statistical evaluation of voting rules | journal=Social Choice and Welfare | publisher=Springer Science and Business Media LLC | volume=46 | issue=1 | date=2015-08-11 | issn=0176-1714 | doi=10.1007/s00355-015-0909-0 | pages=183–212 | url=https://jamesgreenarmytage.com/strategy-utility.pdf}}</ref> and Durand ''et al.''<ref name="Durand Mathieu Noirie 2016 j401">{{cite web | last=Durand | first=François | last2=Mathieu | first2=Fabien | last3=Noirie | first3=Ludovic | title=Can a Condorcet Rule Have a Low Coalitional Manipulability? | website=Archive ouverte HAL | volume=285 | date=2016-08-29 | url=https://hal.science/hal-01369877 | access-date=2023-06-26}}</ref> Any voting method passing the [[majority criterion]] automatically passes the informed majority coalition criterion, since the majority can all vote their preferred candidate first to make that candidate win. |
||
[[Range voting]] and the [[Borda count]] also pass the informed majority coalition criterion, even though they fail the [[majority criterion]]. [[Anti-plurality voting]] fails. |
[[Range voting]] and the [[Borda count]] also pass the informed majority coalition criterion, even though they fail the [[majority criterion]]. [[Anti-plurality voting]] fails. |
||
== Relationship to Condorcification == |
|||
The informed majority coalition criterion is of importance when considering the implications of modifying a method to always elect an absolute majority-strength Condorcet winner if one exists. Such a modification can never make a method susceptible to strategic manipulation in more elections than it was before being modified. However, such a modification can change what strategy it's vulnerable to in those elections where it's manipulable. |
|||
The informed majority coalition criterion is important to [[Condorcification]]. Specifically, Condorcifying any method that passes InfMC will ''never'' increase that method's susceptibility to strategic voting; there is no set of preferences where the base method was originally strategy-resistant, while the new method is not. In most cases, Condorcification outright reduces a method's manipulability.<ref name="Durand Mathieu Noirie 2016 j401" /> The argument behind this is simple: a majority under an InfMC system can always elect a Condorcet winner, if they exist, by voting strategically. This makes Condorcification a kind of [[declared strategy voting|automatic strategy]]. |
|||
However, such a modification ''can'' change what ''kind'' of strategy voters need to use in order to manipulate a method, in elections where it is manipulable. |
|||
{{stub}} |
{{stub}} |
||
Latest revision as of 16:29, 21 April 2024
The informed majority coalition criterion (InfMC) or conditional majority determination criterion is a voting method criterion that is a weaker form of the majority criterion. It can be stated as follows:
A group comprising a majority of voters is always able to cast their votes so as to elect any candidate they wish, provided that the votes of the remaining minority are known to them and don't change.
It was independently defined by James Green-Armytage[1] and Durand et al.[2] Any voting method passing the majority criterion automatically passes the informed majority coalition criterion, since the majority can all vote their preferred candidate first to make that candidate win.
Range voting and the Borda count also pass the informed majority coalition criterion, even though they fail the majority criterion. Anti-plurality voting fails.
Relationship to Condorcification
The informed majority coalition criterion is important to Condorcification. Specifically, Condorcifying any method that passes InfMC will never increase that method's susceptibility to strategic voting; there is no set of preferences where the base method was originally strategy-resistant, while the new method is not. In most cases, Condorcification outright reduces a method's manipulability.[2] The argument behind this is simple: a majority under an InfMC system can always elect a Condorcet winner, if they exist, by voting strategically. This makes Condorcification a kind of automatic strategy.
However, such a modification can change what kind of strategy voters need to use in order to manipulate a method, in elections where it is manipulable.
This page is a stub - please add to it.
References
- ↑ Green-Armytage, James; Tideman, T. Nicolaus; Cosman, Rafael (2015-08-11). "Statistical evaluation of voting rules" (PDF). Social Choice and Welfare. Springer Science and Business Media LLC. 46 (1): 183–212. doi:10.1007/s00355-015-0909-0. ISSN 0176-1714.
- ↑ a b Durand, François; Mathieu, Fabien; Noirie, Ludovic (2016-08-29). "Can a Condorcet Rule Have a Low Coalitional Manipulability?". Archive ouverte HAL. Retrieved 2023-06-26.