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A social choice function, sometimes called a voting system in the context of politics, is a rule that takes an individual's complete and transitive preferences over a set of outcomes and returns a single chosen outcome (or a set of tied outcomes). We can think of this subset as the winners of an election, and compare different social choice ...
A VCG mechanism implements a utilitarian social-choice function - a function that maximizes a weighted sum of values (also called an affine maximizer). Roberts' theorem proves that, if: The agents' valuation functions are unrestricted (each agent can have as value function any function from to ), and -
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.
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.
A random social choice function (RSCF) takes as input the set of voters' preference relations. It returns as output a "mixture" - a vector p of real numbers in [0,1], one number for each candidate, such that the sum of numbers is 1.
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.
The social penetration theory (SPT) proposes that as relationships develop, interpersonal communication moves from relatively shallow, non-intimate levels to deeper, more intimate ones. [1] The theory was formulated by psychologists Irwin Altman of the University of Utah [ 2 ] and Dalmas Taylor of the University of Delaware [ 3 ] in 1973 to ...
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).