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Social choice studies the behavior of different mathematical procedures (social welfare functions) used to combine individual preferences into a coherent whole. [ 2 ] [ 3 ] [ 4 ] It contrasts with political science in that it is a normative field that studies how a society can make good decisions, whereas political science is a descriptive ...
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.
The social function of communication is to maintain equilibrium in the social system by keeping the different orientations in balance. [103] In Newcomb's words, communication enables "two or more individuals to maintain simultaneous orientation to each other and towards objects of the external environment". [98]
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.
This is an accepted version of this page This is the latest accepted revision, reviewed on 7 March 2025. Transmission of information For other uses, see Communication (disambiguation). "Communicate" redirects here. For other uses, see Communicate (disambiguation). There are many forms of communication, including human linguistic communication using sounds, sign language, and writing as well as ...
Every Pareto efficient social choice function is necessarily a utilitarian choice function, a result known as Harsanyi's utilitarian theorem. Specifically, any Pareto efficient social choice function must be a linear combination of the utility functions of each individual utility function (with strictly positive weights).
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.