choice function वाक्य
उदाहरण वाक्य
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- As for social choice functions, the Gibbard Satterthwaite theorem is well-known, which states that if a social choice function whose range contains at least three alternatives is strategy-proof, then it is dictatorial.
- As for social choice functions, the Gibbard Satterthwaite theorem is well-known, which states that if a social choice function whose range contains at least three alternatives is strategy-proof, then it is dictatorial.
- Alternatively, G�del showed that given the axiom of constructibility one can write down an explicit ( though somewhat complicated ) choice function ? in the language of ZFC, so in some sense the axiom of constructibility implies global choice.
- The axiom of global choice cannot be stated directly in the language of ZFC ( Zermelo Fraenkel set theory with the axiom of choice ), as the choice function ? is a proper class and in ZFC one cannot quantify over classes.
- 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 " '.
- The axiom of global choice states that there is a global choice function ?, meaning a function such that for every non-empty set " z ", ? ( " z " ) is an element of " z ".
- If we try to choose an element from each set, then, because " X " is infinite, our choice procedure will never come to an end, and consequently, we shall never be able to produce a choice function for all of " X ".
- In general proofs involving the axiom of choice do not produce explicit examples of free ultrafilters, though it is possible to find explicit examples in some models of ZFC; for example, Godel showed that this can be done in the constructible universe where one can write down an explicit global choice function.
- Moulin proved that it is possible to define non-dictatorial and non-manipulable social choice functions in the restricted domain of single-peaked preferences, i . e . those in which there is a unique best option, and other options are better as they are closer to the favorite one.
- 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.
- 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 configuration of preference relations; this is sometimes called the Universal Domain assumption .)
- Then our choice function can choose the least element of every set under our unusual ordering . " The problem then becomes that of constructing a well-ordering, which turns out to require the axiom of choice for its existence; every set can be well-ordered if and only if the axiom of choice holds.
- Given a social choice function \ operatorname { Soc }, it is possible to build a social ranking function \ operatorname { Rank }, as follows : in order to decide whether a \ prec b, the \ operatorname { Rank } function creates new preferences in which a and b are moved to the top of all voters'preferences.
- A player i is called a "'dictator "'in a social-choice function \ operatorname { Soc } if \ operatorname { Soc } always selects the outcome that player i prefers over all other outcomes . \ operatorname { Soc } is called a "'dictatorship "'if there is a player i who is a dictator in it.
- It states that if a social choice function can be implemented by an arbitrary mechanism ( i . e . if that mechanism has an equilibrium outcome that corresponds to the outcome of the social choice function ), then the same function can be implemented by an incentive-compatible-direct-mechanism ( i . e . in which players truthfully report type ) with the same equilibrium outcome ( payoffs ).
- It states that if a social choice function can be implemented by an arbitrary mechanism ( i . e . if that mechanism has an equilibrium outcome that corresponds to the outcome of the social choice function ), then the same function can be implemented by an incentive-compatible-direct-mechanism ( i . e . in which players truthfully report type ) with the same equilibrium outcome ( payoffs ).
- :: : Not sure what you mean by a'set of an infinite real number of elements,'but certainly there are infinite sets with definable choice functions : for any ordinal the function'take the least element'is a well-defined choice function . btw, someone who knows how it's done should move this to the maths page Algebraist 15 : 39, 22 February 2007 ( UTC)
- :: : Not sure what you mean by a'set of an infinite real number of elements,'but certainly there are infinite sets with definable choice functions : for any ordinal the function'take the least element'is a well-defined choice function . btw, someone who knows how it's done should move this to the maths page Algebraist 15 : 39, 22 February 2007 ( UTC)
- If the method is applied to an infinite sequence ( " X " " i " : " i " " ? ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.
- If the method is applied to an infinite sequence ( " X " " i " : " i " " ? ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.
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