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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.
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.
In sociology, a social system is the patterned network of relationships constituting a coherent whole that exist between individuals, groups, and institutions. [1] It is the formal structure of role and status that can form in a small, stable group. [ 1 ]
Social theories are analytical frameworks, or paradigms, that are used to study and interpret social phenomena. [1] A tool used by social scientists, social theories relate to historical debates over the validity and reliability of different methodologies (e.g. positivism and antipositivism), the primacy of either structure or agency, as well as the relationship between contingency and necessity.
When agents have general preferences represented by cardinal utility functions, the utilitarian social-choice function (selecting the outcome that maximizes the sum of the agents' valuations) is not strongly-monotonic but it is weakly monotonic. Indeed, it can be implemented by the VCG mechanism, which is a truthful mechanism with money.
Formally, a social choice function is a map : () from the set of functions between N→Rel(X), to the power set of X. (Intuitively, the social choice function represents a societal principle for choosing one or more social outcomes based on individuals' preferences.