Ranked voting: Difference between revisions
Majority rule as an approximation of utilitarianism
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=== Misordering ===
Most ranked voting methods can incentivize voters to [[Strategic voting|strategically]] vote by ranking candidate Y above X even though the voter preferred X to Y (though the frequency and degree of incentive depend on the method). For this reason, it is claimed that [[Score voting]] is better, because it doesn't incentivize this, and thus may be even better at collecting ranked-preference information than most ranked methods.<ref>{{Cite web|url=https://www.reddit.com/r/EndFPTP/comments/fcexg4/score_but_for_every_pairwise_matchup/fjl1hg3|title=r/EndFPTP - Comment by u/MuaddibMcFly on ”Score but for every pairwise matchup”|website=reddit|language=en-US|access-date=2020-05-14}}</ref>
== Majority rule as an approximation of utilitarianism ==
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.
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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