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{{merge|Preferential voting|date=August 2022|target=Ranked voting}}
{{Wikipedia|Ranked voting}}
 
:''This article is about voting systems that use ranked ballots, which can also include voting systems that use <nowiki>[[w:Level of measurement#Interval scale|interval scale]]</nowiki> ballots, i.e. [[cardinal voting systems]]''
 
[[Image:Preferential ballot.svg|thumb|Sample ballot of ranked voting using written numbers]]
 
'''Ranked voting''' is any election [[voting system]] in which voters use a '''ranked (or preferential) ballot''' to [[ranking|rank]] choices in a sequence on the [[Level of measurement#Ordinal scale|ordinal scale]]: 1st, 2nd, 3rd, etc. There are multiple ways in which the rankings can be counted to determine which candidate (or candidates) is (or are) elected (and different methods may choose different winners from the same set of ballots). The other major branch of voting systems is [[cardinal voting]], where candidates are independently rated, rather than ranked.<ref>{{Cite book|title=Liberalism against populism: a confrontation between the theory of democracy and the theory of social choice|last=Riker|first=William Harrison|date=1982|publisher=Waveland Pr|isbn=0881333670|location=|pages=29–30|oclc=316034736|quote=''Ordinal utility'' is a measure of preferences in terms of rank orders—that is, first, second, etc. ... ''Cardinal utility'' is a measure of preferences on a scale of cardinal numbers, such as the scale from zero to one or the scale from one to ten.}}</ref>
 
The similar term "Ranked Choice Voting" (RCV) is used by the US organization [[FairVote]] to refer to the use of ranked ballots with specific counting methods: either [[instant-runoff voting]] for single-winner elections or [[single transferable vote]] for multi-winner elections. In some locations, the term "preferential voting" is used to refer to this combination of ballot type and counting method, while in other locations this term has various more-specialized meanings.<ref name=":02"/>
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There are many types of ranked voting, with several used in governmental elections. [[Instant-runoff voting]] is used in Australian state and federal elections, in Ireland for its presidential elections, and by [[Ranked-choice voting in the United States|some jurisdictions in the United States]], United Kingdom, and New Zealand. A type and classification of ranked voting is called the [[single transferable vote]], which is used for national elections in Ireland and Malta, the Australian Senate, for regional and local elections in Northern Ireland, for all local elections in Scotland, and for some local elections in New Zealand and the United States. [[Borda count]] is used in [[Slovenia]]<ref>{{Cite journal|last=Toplak|first=Jurij|title=The parliamentary election in Slovenia, October 2004|journal=Electoral Studies|volume=25|issue=4|pages=825–831|doi=10.1016/j.electstud.2005.12.006|year=2006}}</ref> and [[Nauru]]. [[Contingent vote]] and [[Supplementary vote]] are also used in a few locations. [[Condorcet method]]s are used by [[Schulze method#Users|private organizations and minor parties]], but currently are not used in governmental elections.
 
[[Arrow's impossibility theorem]] and [[Gibbard's theorem]] prove that all voting systems must make trade-offs between desirable properties, such as the preference between two candidates being unaffected by the popularity of a third candidate.<ref name=Mankiw>{{cite book | title=Principles of Microeconomics | publisher=South-Western Cengage Learning | first=Gregory |last=Mankiw | edition=6th| year=2012 | isbn=978-0538453042 |pages=475–479| author-link=Gregory Mankiw}}</ref><ref name=":0">{{cite web|url=https://electology.org/podcasts/2012-10-06_kenneth_arrow|title=Interview with Dr. Kenneth Arrow|last= Hamlin|first=Aaron|date=October 6, 2012|website=The Center for Election Science|publisher=Center for Election Science|access-date=|quote=''CES:'' you mention that your theorem applies to preferential systems or ranking systems. ... But the system that you're just referring to, Approval Voting, falls within a class called cardinal systems. ... ''Dr. Arrow:'' And as I said, that in effect implies more information. ... I’m a little inclined to think that [[score voting|score systems]] where you categorize in maybe three or four classes probably (in spite of what I said about manipulation) is probably the best.}}</ref> Accordingly there is no consensus among academics or public servants as to the "best" electoral system.<ref name="eupaper">{{cite web | url=http://www.stevendroper.com/elect_system.html | title=Electoral Systems in Europe: An Overview | publisher=European Centre for Parliamentary Research and Documentation | location=Brussels | date=October 2000 | accessdate=November 7, 2019}}</ref>
 
Recently, an increasing number of authors, including [[David Farrell (political scientist)|David Farrell]], [[Ian McAllister (political scientist)|Ian McAllister]] and [[Jurij Toplak]], see preferentiality as one of the characteristics by which electoral systems can be evaluated.<ref name=":02">{{Cite journal|last=Toplak|first=Jurij|date=2017|title=Preferential Voting: Definition and Classification|journal=Lex Localis – Journal of Local Self-Government|volume=15|issue=4|pages=737–761|doi=10.4335/15.4.737-761(2017)}}</ref><ref>{{Cite journal|last1=Farrell|first1=David M.|first2=Ian|last2=McAllister|date=2004-02-20|title=Voter Satisfaction and Electoral Systems: Does Preferential Voting in Candidate-Centered Systems Make A Difference|url=http://repositories.cdlib.org/csd/04-04|language=en}}</ref> According to this view, all electoral methods are preferential, but to different degrees and may even be classified according to their preferentiality.<ref name=":02" /> By this logic, [[cardinal voting]] methods such as [[Score voting]] or [[STAR voting]] are also "preferential".
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== Majority rule as an approximation of utilitarianism ==
 
It is important to emphasize that majoritarianism and cardinal utilitarianism are not necessarily opposing principles. From a utilitarian perspective, majoritarianism can be considered an [[Majority_criterion#Majority_rule_as_an_approximation_of_utilitarianism|approximation of utilitarian principles]] under certain conservative assumptions. This is analogous to how most systems of ethics can be cast as varieties of utilitarianism with constraints on the utilities being used, even systems that are not utilitarian ''as such''.
Within a theoretical framework using strictly ranked preferences, as in many models in modern neoclassical economics, all one can hope to achieve from a collection of social preferences is what is referred to as a ''[https://en.wikipedia.org/wiki/Pareto_efficiency Pareto equilibrium]'': a situation where no individual can be better off without making at least one individual worse off. This concept is used, for example, to establish the Pareto equilibrium within free markets and their usage of available resources. For a given set of individual preferences many such Pareto equilibria may exist, forming what it is called a ''Pareto frontier''.
 
However, Pareto equilibria can be arbitrarily anti-democratic. As an extreme example, an authoritarian dictatorship where the dictator holds all the power and wealth, and the rest of the population has none, is a perfectly legitimate Pareto equilibrium. In order to improve the lot of everyone else (with the exception of the dictator), the social choice function has to violate the preferences of the dictator to remain in power. That is, the social choice function must necessarily use some additional criterion to navigate the Pareto frontier in order to reach an equilibrium that is perceived as "better".
 
This is what majority rule is doing. It is used to justify the violation of preferences of a minority (like the sole dictator) in order to pursue a "better" equilibrium (the majority of the population).
 
However, the notion of "counting" preferences does not exist under a strict ranked preference mathematical framework. "Counting", be it with integers or real numbers, is inherently a cardinal procedure.
 
In order to invoke majority rule an assumption must be made that is inherently cardinally utilitarian: that satisfying each individual's preference has the same ''cardinal utility'' gain for every person, and that these utilities can be aggregated and totals compared. This is fundamentally a cardinal utility counting procedure, and in the case of two options immediately produces majority rule as a result of maximization of utility.
 
Therefore, all ranked systems can be seen as approximations of cardinal utilitarianism to various extents, and operate under the same core assumption of democracy as cardinal voting methods: that every individual has some fundamentally commensurable value that may be counted.
 
Condorcet voting systems, by applying majority rule to all pairwise comparisons, are effectively looking for the most consistently approximately utilitarian candidate. This intuitively explains the better utilitarian performance of Condorcet systems under various numerical simulations.
 
== Discussion ==
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<references/>
 
[[Category:Ballot types]]
== Notes ==
 
:''The above text was copied from https://en.wikipedia.org/w/index.php?title=Ranked_voting&oldid=946352148 ''
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