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Mathematical function
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
Choice_function
Function that ranks states of society according to their desirability
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
Social_welfare_function
Axiom of set theory
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:
Axiom_of_choice
Study of rational collective decision-making
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
Social_choice_theory
Standard system of axiomatic set theory
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
Zermelo–Fraenkel_set_theory
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
Monotonicity (mechanism design)
Monotonicity_(mechanism_design)
Mathematical function such that every output has at least one input
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
Surjective_function
Possible axiom for set theory
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
Axiom_of_determinacy
Deciding between multiple options
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
Choice
Concept in mathematics
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
Axiom_of_countable_choice
Axiom in set theory
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)
Axiom_of_global_choice
Association of one output to each input
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
Function_(mathematics)
Theorem in mathematical logic
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
Diaconescu's_theorem
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Field of economics and game theory
defines what should happen under full information. Define a social choice function f ( θ ) {\displaystyle f(\theta )} mapping the (true) type profile
Mechanism_design
Method of making choices that maximises utility
words, our social-choice function is utilitarian. The VCG family is a family of mechanisms that implements the utilitarian welfare function. A typical mechanism
Vickrey–Clarke–Groves mechanism
Vickrey–Clarke–Groves_mechanism
Theorem that every set can be well-ordered
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
Well-ordering_theorem
Game theory concept
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
Game_form
German logician and mathematician (1871–1953)
pairing Axiom of union Axiom schema of specification Boltzmann brain Choice function Cumulative hierarchy Pairwise comparison Von Neumann universe 14990
Ernst_Zermelo
Mathematical relation assigning a probability event to a cost
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
Loss_function
Topics referred to by the same term
arising from the way that the data are collected A selection, or choice function, a function that selects an element from a set Divine selection, selection
Selection
Counterintuitive mathematical object
historical examples of this are: Ranked-choice voting is commonly described as a pathological social choice function, because of its tendency to eliminate
Pathological_(mathematics)
Paradox in social choice
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
Liberal_paradox
Social choice theorem on superiority of majority voting
social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function between
May's_theorem
Proof all ranked voting rules have spoilers
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
Arrow's_impossibility_theorem
Principle in economics and game theory
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
Revelation_principle
Axiomatic set theories based on the principles of mathematical constructivism
range of a function are both sets. Additionally, an Axiom of non-choice asserts the existence of a choice function in cases where the choice is already
Constructive_set_theory
System of mathematical set theory
"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
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Semantic object to which an operator applies
Angelika Kratzer proposed another choice function-based theory, which is similar to Reinhart's except that the choice function variable is left free. Recent
Scope_(formal_semantics)
Topics referred to by the same term
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
Selector
Axiom of set theory
The axiom of non-choice, also called axiom of unique choice, axiom of function choice or function comprehension principle is a function existence postulate
Axiom_of_non-choice
Concept in game theory
The dominant-strategy revelation-principle says that every social-choice function that can be implemented in dominant-strategies can be implemented by
Incentive_compatibility
1951 book by Kenneth Arrow
state(s) from the subset as the social choice set. Less informally, the social choice function is the function mapping each environment S of available
Social Choice and Individual Values
Social_Choice_and_Individual_Values
Index of articles associated with the same name
for social choice functions, and is a condition for Arrow's impossibility theorem. With unrestricted domain, the social welfare function accounts for
Voting_criteria
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
Concept in economics and decision theory
lotteries, which can be any quantified choice. The relationship between these two kinds of utility functions has been a source of controversy among both
Utility
About mathematical functions
The mathematical concept of a function dates from the 17th century in connection with the development of calculus; for example, the slope d y / d x {\displaystyle
History of the function concept
History_of_the_function_concept
Kind of mathematical function
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
Measurable_function
Mathematical proposition equivalent to the axiom of choice
\square } If we assume the axiom of choice, or, more specifically, if we assume the existence of a choice function for a given poset P {\displaystyle P}
Zorn's_lemma
Special functions of several complex variables
quadratic forms, and solitons. Theta functions in two dimensions are functions of two complex arguments. In one choice of parameter, for example, z {\displaystyle
Theta_function
Decision rule of maximizing utility
{R} } be a utility function, describing the amount of happiness an individual i derives from each possible state. A social choice rule is a mechanism
Utilitarian_rule
elaborated in the page on Budget-proposal aggregation. A random social choice function (RSCF) takes as input the set of voters' preference relations. It returns
Fractional_social_choice
Sigmoid shape special function
mathematics, the error function (also called the Gauss error function), often denoted by e r f {\displaystyle \mathbf {erf} } , is the function erf ( z ) = 2
Error_function
Instantaneous rate of change (mathematics)
original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent
Derivative
Free choice in which only one option is actually offered
A Hobson's choice is a free choice in which only one thing is actually offered. The term is often used to describe an illusion that choices are available
Hobson's_choice
Size of a set in mathematics
does not tell you which set you have constructed, just that such a choice function exists, leaving the constructed set implicit. It is hardly controversial
Cardinality
Fixed-point theorem
maximal element. Let g be a choice function on P ( X ) − { ∅ } . {\displaystyle P(X)-\{\varnothing \}.} Define a function f : X → X {\displaystyle f:X\to
Bourbaki–Witt_theorem
social choice theory, the binary relation typically represents the pairwise majority comparison between alternatives. A tournament solution is a function f
Tournament_solution
1100 AD. Bhaskara was the first known person to find the generalised choice function, although Brahmagupta may have known earlier. Hemacandra asked how
History_of_combinatorics
Function in statistics
interpretations. For each choice of base, the logit function takes values between negative and positive infinity. The “logistic” function of any number α {\displaystyle
Logit
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Single-winner ranked-choice electoral system
(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
Instant-runoff_voting
Topics referred to by the same term
ordering. Monotonicity (mechanism design), a property of a social choice function. Monotonicity criterion, a property of a voting system. Resource monotonicity
Monotone
Smooth approximation of one-hot arg max
The softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution
Softmax_function
Infinite cardinal number
elements do.) Beth number Gimel function Regular cardinal Infinity Transfinite number Ordinal number Given the axiom of choice, every infinite set has a cardinality
Aleph_number
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Hypergeometric function in mathematics
The general hypergeometric function is a function that is (more or less) defined on a Grassmannian, and depends on a choice of some complex numbers and
General hypergeometric function
General_hypergeometric_function
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
Mapping arbitrary data to fixed-size values
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support
Hash_function
Inferential psychometric model
brightness, weight etc., and forced-choice responses of a human or animal test subject. The psychometric function therefore is a specific application
Psychometric_function
v − i ) {\displaystyle v\equiv (v_{i},v_{-i})} . A social choice function is a function that takes as input the value-vector v {\displaystyle v} and
Single-parameter_utility
Electoral system property
number of voters increases toward infinity. A non-resolvable social choice function is often only considered to be a partial electoral method, sometimes
Resoluteness_criterion
Analytic function in mathematics
The Riemann zeta function or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a mathematical function of a complex variable
Riemann_zeta_function
input is a set. Set-valued function: whose values are sets. Choice function called also selector or uniformizing function: assigns to each set one of
List_of_types_of_functions
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability
Likelihood_function
Mathematical result on infinite trees
finite sets has a choice function, that is to say, the axiom of countable choice for finite sets. This form of the axiom of choice (and hence of Kőnig's
Kőnig's_lemma
In social choice theory, unrestricted domain, or universality, is a property of social welfare functions in which all preferences of all voters (but no
Unrestricted_domain
Method for analyzing revealed preferences
In essence, choice modelling assumes that the utility (benefit, or value) that an individual derives from item A over item B is a function of the frequency
Choice_modelling
System of mathematical set theory
a choice function if c is a function and c ( x ) ∈ x {\displaystyle c(x)\in x} for each member x of domain c. Choice: There exists a choice function c
Morse–Kelley_set_theory
Negative of a convex function
atmosphere involve concave functions. In expected utility theory for choice under uncertainty, cardinal utility functions of risk averse decision makers
Concave_function
Graph coloring where each vertex has a list of allowed colors
of colors for each vertex v (called a list), a list coloring is a choice function that maps every vertex v to a color in the list L(v). As with graph
List_coloring
American annual awards ceremony show
The Nickelodeon Kids' Choice Awards, also known as the KCAs or Kids' Choice, is an American annual awards ceremony show produced by Nickelodeon. Usually
Nickelodeon Kids' Choice Awards
Nickelodeon_Kids'_Choice_Awards
Economic concept
the issue; completeness is concerned with the input (domain) of the choice functions; while the strong axiom imposes conditions on the output. The Generalised
Revealed_preference
Class of models in the behavioral sciences
Rational choice modeling refers to the use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social
Rational_choice_model
one for each input field F 1 c k {\displaystyle F_{1}^{ck}} , the choice function T j {\displaystyle T_{j}} of each F 2 {\displaystyle F_{2}} node j
Fusion adaptive resonance theory
Fusion_adaptive_resonance_theory
Integral expressing the amount of overlap of one function as it is shifted over another
evaluated for all values of shift, producing the convolution function. The choice of which function is reflected and shifted before the integral does not change
Convolution
Mathematical concept
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists
Inverse_function
American health technology company
Function Health, often stylized as simply Function, is an American company and platform headquartered in Austin, Texas. The venture capital-backed company
Function_Health
Degree of differentiability of a function or map
In mathematical analysis, the smoothness of a function or map describes the extent to which it has derivatives that exist and vary continuously. Given
Smoothness
of quasi-linear utility functions then the mechanism dominant strategy is dominant-strategy implementable. "A social choice rule is dominant strategy
Implementation_theory
Mathematical function that can be computed by a program
Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes
Computable_function
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Function in Boolean algebra
least some amount of choice to prove that infinite parity functions exist. If f {\displaystyle f} is an infinite parity function and we consider the inverse
Parity_function
mean-standard deviation choice function, which depends in form on the density function f. The von Neumann–Morgenstern utility function is assumed to be increasing
Two-moment_decision_model
supremum of the ordinals that are the image of a function from ωω (usually in models where the axiom of choice is not assumed) κ 1. Often used for a cardinal
Glossary_of_set_theory
Mechanism for evolution
Mate choice is one of the primary mechanisms under which evolution can occur. It is characterized by a "selective response by animals to particular stimuli"
Mate_choice
Detailed diagram in the process industry
modifier, 3rd indicates passive/readout function, 4th - active/output function, and the 5th is the function modifier. This is followed by loop number
Piping and instrumentation diagram
Piping_and_instrumentation_diagram
Set of all things that may be the input of a mathematical function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ( f ) {\displaystyle \operatorname
Domain_of_a_function
Choice between two or more discrete alternatives
In economics, discrete choice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives,
Discrete_choice
Formal power series
generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often
Generating_function
generated text. Function words (determiners, for example) are usually chosen during realisation. The simplest type of lexical choice involves mapping
Lexical_choice
Continuous function that is not absolutely continuous
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in
Cantor_function
Mathematical relation consisting of a multi-variable function equal to zero
some function such as a utility function or a profit function is to be maximized with respect to a choice vector x even though the objective function has
Implicit_function
Family of modal logics for agency and choice
i\in Ag} and moment m {\displaystyle m} , a choice function c h o i c e i m {\displaystyle {\mathsf {choice}}_{i}^{m}} that partitions the set of histories
STIT_logic
Function uniquely mapping two numbers into a single number
mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number. Any pairing function can be used in set
Pairing_function
Statistical model for a binary dependent variable
the choice of link function: the logistic model uses the logit function (inverse logistic function), while the probit model uses the probit function (inverse
Logistic_regression
Economic model which weighs rewards based on when they are received
In economics, a discount function is used in economic models to describe the weights placed on rewards received at different points in time. For example
Discount_function
S-shaped curve
function as the activation function to the result; this model can be seen as a "smoothed" variant of the classical threshold neuron. A common choice for
Logistic_function
Electoral pathology or paradox
(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
Non-negative_responsiveness
Mathematical function with no sudden changes
a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies
Continuous_function
CHOICE FUNCTION
CHOICE FUNCTION
Boy/Male
Greek
Unique choice.
Boy/Male
Celtic
Choice.
Female
Spanish
Pet form of Portuguese/Spanish Francisca, CHICA means "French."
Female
English
Variant spelling of English Cherise, CHERICE means "cherry."
Female
Greek
(Φοίβη) Greek name PHOIBE means "shining one." In mythology, this is the name of a Titan goddess of bright intellect.
Male
Spanish
 Spanish name CHICO means "small." Compare with another form of Chico.
Female
English
English name derived from the word, chalice, from Latin calix, CHALICE means "cup."
Male
English
English unisex name derived from the vocabulary word, CHANCE means "chance."Â
Female
Japanese
(æµ) Japanese name CHIE means "wisdom."
Boy/Male
Muslim
Selection, Choice
Female
French
French name CADICE means "chief."
Boy/Male
Arabic, Muslim, Sindhi
Selection; Choice
Surname or Lastname
English
English : variant spelling of Joyce. See also Choice.
Surname or Lastname
English
English : probably a variant of Joyce. There is a family tradition among bearers of the name that it means ‘chosen’, from Middle English, Old French chois (of Germanic origin). In the Middle Ages the word was used both for an ‘act of choosing’ and a ‘thing chosen’, and as an adjective with the meaning ‘chosen’, ‘select’, ‘favored’. Perhaps this word gave rise to a nickname, but there is no evidence to support this speculation.
Male
Portuguese
 Pet form of Portuguese/Spanish Francisco, CHICO means "French." Compare with another form of Chico.
Surname or Lastname
English
English : unexplained.A John Choate who emigrated from England in 1643 and settled in Ipswich, MA, was the ancestor of several prominent 19th century Choates, including Rufus Choate (1799–1859), who was one of the organizers of the Whig Party in MA, and Joseph Hodges Choate (1832–1917), U.S. ambassador to Great Britain.
Surname or Lastname
English
English : from Middle English chike ‘young fowl’ (a shortened form of chiken), applied as a metonymic occupational name for someone who bred poultry for the table, or as a nickname from the same word used as a term of endearment.English : variant of Cheek.
Boy/Male
Arabic, Muslim
Choice
Boy/Male
Muslim
Choice
Boy/Male
Celtic
Choice.
CHOICE FUNCTION
CHOICE FUNCTION
Girl/Female
Muslim
Diminutive of Husn, Beauty
Boy/Male
Indian, Malayalam
Style
Girl/Female
Muslim
Eve
Boy/Male
Hindu
Boy/Male
Indian
Splendor or light or glow
Female
English
English jewelry name, derived from the Italian word cammeo, from either Arabic qamaa'il "flower buds" or Persian chumahan, CAMEO means "agate."
Female
English
Elaborated form of English Mary, MARILENA means "obstinacy, rebelliousness" or "their rebellion."
Boy/Male
Indian
Has one tooth.
Girl/Female
Indian
Highborn, Respected, Noble
Boy/Male
Latin
Twin of Hercules.
CHOICE FUNCTION
CHOICE FUNCTION
CHOICE FUNCTION
CHOICE FUNCTION
CHOICE FUNCTION
v. t.
To make choice of; to select; to take by way of preference from two or more objects offered; to elect; as, to choose the least of two evils.
imp.
of Choose
adv.
Entirely; quite; as, chock home; chock aft.
n.
See Chalice.
n.
A sufficient number to choose among.
n.
A choir or chorus.
superl.
Preserving or using with care, as valuable; frugal; -- used with of; as, to be choice of time, or of money.
a.
Happening by chance; casual.
n.
The chick-pea.
n.
Luck; chance; accident.
v. t.
To cheat, trick, defraud; -- followed by of, or out of; as, to chouse one out of his money.
n.
Opinion or choice expressed; judgment; a vote.
n.
Sound uttered by the mouth, especially that uttered by human beings in speech or song; sound thus uttered considered as possessing some special quality or character; as, the human voice; a pleasant voice; a low voice.
n.
See Chine, n., 3.
n.
A possibility; a likelihood; an opportunity; -- with reference to a doubtful result; as, a chance to escape; a chance for life; the chances are all against him.
adv.
By chance; perchance.