of sets none of which are empty. Then a choice function (selector, selection) on X is a mathematical function f that is defined on X such that f is a...

economics and social choice theory, a social welfare function—also called a social ordering, ranking, utility, or choice function—is a function that ranks a set...

the axiom of choice and are implied by it. One variation avoids the use of choice functions by, in effect, replacing each choice function with its range:...

the transitive property: Attempting to use majority rule as a social choice function creates situations where we have A better than B and B better than...

nonconstructive because it asserts the existence of a choice function but says nothing about how this choice function is to be "constructed". One motivation for...

monotonicity is a property of a social choice function. It is a necessary condition for being able to implement such a function using a strategyproof mechanism...

every non-empty set. The axiom of global choice states that there is a global choice function τ, meaning a function such that for every non-empty set z, τ(z)...

every countable collection of non-empty sets must have a choice function. That is, given a function A {\displaystyle A} with domain N {\displaystyle \mathbb...

A choice is the range of different things from which a being can choose. The arrival at a choice may incorporate motivators and models. Freedom of choice...

frame, ruleset, or outcome function is the set of rules that govern a game and determine its outcome based on each player's choices. A game form differs from...

mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the...

the axiom of choice, in particular granting a choice function on all sets of this form, implies excluded middle for all propositions. Choice is valid in...

if a social choice function can be implemented with some non-honest mechanism—one where players have an incentive to lie—the same function can be implemented...

model L(R) of a set theory, which accepts only a weak form of the axiom of choice (AC) but contains all real and all ordinal numbers. Some consequences of...

In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common...

image of its domain. Every surjective function has a right inverse assuming the axiom of choice, and every function with a right inverse is necessarily...

social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function between...

(1977). "Single Transferrable Vote: An Example of a Perverse Social Choice Function". American Journal of Political Science. 21 (2): 303–311. doi:10.2307/2110496...

optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one...

defines what should happen under full information. Define a social choice function f ( θ ) {\displaystyle f(\theta )} mapping the (true) type profile...

axiom of choice as follows. Let the set we are trying to well-order be A {\displaystyle A} , and let f {\displaystyle f} be a choice function for the family...

there is extensionally only one possible function input to a choice function. So in that situation, a choice function would explicitly have type f : { a }...

"very strong form of the axiom of choice"—namely, the axiom of global choice: There exists a global choice function G {\displaystyle G} defined on the...

historical examples of this are: Ranked-choice voting is commonly described as a pathological social choice function, because of its tendency to eliminate...

By representing the social choice process as a function on Rel(X)N, we are tacitly assuming that the social choice function is defined for any possible...

part of Objective-C programming language The Selector, radio program Choice function on a family of sets The Selecter, a UK ska band Moshe Selecter, Israeli...

that any non-degenerate social choice rule will satisfy: Unrestricted domain – the social choice function is a total function over the domain of all possible...

pairing Axiom of union Axiom schema of specification Boltzmann brain Choice function Cumulative hierarchy Pairwise comparison Von Neumann universe 14990...

words, our social-choice function is utilitarian. The VCG family is a family of mechanisms that implements the utilitarian welfare function. A typical mechanism...

common choice. Some authors define measurable functions as exclusively real-valued ones with respect to the Borel algebra. If the values of the function lie...