Majority criterion: Difference between revisions
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The majority criterion implies failure of the [[Independence of irrelevant alternatives]] criterion; see the [[Condorcet paradox]] for an example.
[[Category:Voting theory]]▼
== Majority rule as an approximation of utilitarianism ==
It is important to emphasize that majoritarianism and cardinal utilitarianism are not opposing principles. Majoritarianism can be understood as an approximation of utilitarian principles under certain conservative assumptions.
Within a theoretical framework using strictly ranked preferences (ordinal utilities), 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 by themselves 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 the dictator has to remain wealthy and in power. That is, the social choice function must necessarily use some additional criterion to navigate the Pareto frontier (violating at least one individual's preferences) in order to reach an equilibrium that is perceived as "socially better". Under strict ordinal utilities there is no way to distinguish between any equilibrium in the frontier, all are equally "good", so there is no way to determine a "better" one.
Majority rule is introduced in order to make this additional distinction between social states. 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. Framed differently, every individual's A>B preference can exactly cancel (it's commensurable) to any other individual's B>A preference, that is, every individual has exactly the same right to violate every other individual's preferences.
This is fundamentally a cardinal utility procedure, and in the case of two options immediately produces majority rule as a result of maximization of utility: if between any two options, A and B, one has 60% of people preferring A>B and 40% preferring B>A, then the net utility of A will be 60 - 40 = +20 against the net utility of B, 40 - 60 = -20. So a maximization of social utility chooses A, favoring the majority.
Thus, 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, and that the preferences of one individual can override the preferences of any other. (Whether there are different strengths of preference is irrelevant.)
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.
[[Category:Majority-related concepts]]
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