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Social choice theory is the study of theoretical and practical methods to aggregate or combine individual preferences into a collective social welfare function. The field generally assumes that individuals have preferences , and it follows that they can be modeled using utility functions , by the VNM theorem .
Less informally, the social choice function is the function mapping each environment S of available social states (at least two) for any given set of orderings (and corresponding social ordering R) to the social choice set, the set of social states each element of which is top-ranked (by R) for that environment and that set of orderings.
A social scoring function maps each candidate to a number representing their quality. For example, the standard social scoring function for first-preference plurality is the total number of voters who rank a candidate first. Every social ordering can be made into a choice function by considering only the highest-ranked outcome.
Arrow's theorem assumes as background that any non-degenerate social choice rule will satisfy: [15]. Unrestricted domain — the social choice function is a total function over the domain of all possible orderings of outcomes, not just a partial function.
Sociology is the scientific study of human society that focuses on society, human social behavior, patterns of social relationships, social interaction, and aspects of culture associated with everyday life.
Neutrality: The social choice function treats all outcomes the same, i.e. permuting the order of the outcomes does not change the result. Positive responsiveness: If the social choice was indifferent between A and B, but a voter who previously preferred B changes their preference to A, then the social choice is still A.
Émile Durkheim. In sociology, classical theories are defined by a tendency towards biological analogy and notions of social evolutionism: Functionalist thought, from Comte onwards, has looked particularly towards biology as the science providing the closest and most compatible model for social science.
In social choice theory, unrestricted domain, or universality, is a property of social welfare functions in which all preferences of all voters (but no other considerations) are allowed. Intuitively, unrestricted domain is a common requirement for social choice functions, and is a condition for Arrow's impossibility theorem.