PH 456 Exam Definitions Exam
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Anonymity - ANSWER All voters are treated equally in SCF
Neutrality - ANSWER All options are treated equally in SCF
Positive Responsiveness - ANSWER Marginal contributions from voters change SCF
outcome
Universal Domain - ANSWER No restrictions in principle on the combination of votes to
candidates
May's Theorem - ANSWER Majority Rule is the only SCF to satisfy all four
G-B Theorem - ANSWER If a SCF meets three conditions, it is dictatorial
Resoluteness - ANSWER SCF is complete, acyclic, and asymmetric
Strategy Proofness - ANSWER No manipulability in SCF
Manipulation - ANSWER An SCF is manipulable if a voter can misrepresent preferences
to get a better outcome than a true representation
SCF - ANSWER Mapping of preference profiles onto alternatives X such that a binary
relation R is generated, inducing choice function to pick optimal C(A) out of subset of A
in X.
Dictatorial - ANSWER SCF is dictatorial if one person's preferences is always aligned, or
direct implies the overall outcome of SCF
Collective Rationality - ANSWER SCF satisfies completeness and transitivity
Pareto Principle - ANSWER If everyone prefers x to y, then SCF selects x over y
Non-dictatorship - ANSWER No individual always determines (or has preferences
always aligned to) SCF outcome
IIA (Arrow) - ANSWER Ranking of x vs y depends only on individual preferences between
x and y, not on rankings of other options which may be between or to each side of them.
Arrow's Theorem - ANSWER If SCF satisfies CR, PP, UD, and IIA, then doesn't satisfy
ND.
Local decisiveness - ANSWER If everyone in subgroup G prefers x to y, then x is chosen
, over y in the SCF for everyone
Global decisiveness - ANSWER If a group G's preference's can decide SCF outcome for
all options
Field expansion - ANSWER If a subgroup is locally decisive over one pair, it is globally
decisive.
Contraction of decisive sets - ANSWER If a subgroup is globally decisive, a subgroup of
that is also globally decisive.
SWFL - ANSWER A function which assigns complete and transitive relation R on X to
every profile of welfare W in omega.
IIA (SWFL) - ANSWER If for any two pair of options, x is preferred to y and the welfare of
* is identical to -*, then x* is preferred to y* too.
Pareto indifference - ANSWER If the welfare profile resulting from two options is
identical, SWFL ranks them equally.
ONC - ANSWER U_i = e_i(W_i). e_i allows positive Monotonic transformations and there's
no intra or inter comp.
CNC - ANSWER U_i = a_i(W_i) + b_i. a_i > 0. b_i is individual relative real numbers. Can
be positive affine transformed. Can do intra but not inter comps.
OZC - ANSWER U_i = e_i(W_i) and e_i is zero preserving. Can have inter comps on zeros
OLC - ANSWER U_i = e(W_i). Still positive monotonic, but e has to be transformed for
everyone at once. (Zero not always preserved though)
CUC - ANSWER U_i = a(W_i) + b_i. Can do inter but in units and not absolutes. Can be
transformed positive affine but a is constant for everyone.
CFC - ANSWER U_i = a(W_i) + b. Can do full inter comps in levels as everyone has the
same a and b. Can still use positive affine transformations.
RZC, RUC, RFC - ANSWER U_i = a_i(W_i), U_i(x) = W_i(x)=0. U_i = a(W_i). U_i = a(W_i),
U_i(x) = W_i(x)=0. Second part is to zero set the comparison. Take away individual
dependence on a for unit and full comps.
ESS - ANSWER Strategy is evolutionarily stable if it performs strictly better against itself
versus other strategies against it, or if other strategies perform as well against it as
itself but it performs better against other strategies than other strategies on each other.
Nash Solution - ANSWER The game solution ought to maximize the product of individual
utilities. NS = max(u(x)u(y)). So rearrange feasible set equation to solve for y and plug it
into NS equation and max using differentiation.
Individual rationality and Pareto optimality - ANSWER Solution must be weakly better
Latest Update
Anonymity - ANSWER All voters are treated equally in SCF
Neutrality - ANSWER All options are treated equally in SCF
Positive Responsiveness - ANSWER Marginal contributions from voters change SCF
outcome
Universal Domain - ANSWER No restrictions in principle on the combination of votes to
candidates
May's Theorem - ANSWER Majority Rule is the only SCF to satisfy all four
G-B Theorem - ANSWER If a SCF meets three conditions, it is dictatorial
Resoluteness - ANSWER SCF is complete, acyclic, and asymmetric
Strategy Proofness - ANSWER No manipulability in SCF
Manipulation - ANSWER An SCF is manipulable if a voter can misrepresent preferences
to get a better outcome than a true representation
SCF - ANSWER Mapping of preference profiles onto alternatives X such that a binary
relation R is generated, inducing choice function to pick optimal C(A) out of subset of A
in X.
Dictatorial - ANSWER SCF is dictatorial if one person's preferences is always aligned, or
direct implies the overall outcome of SCF
Collective Rationality - ANSWER SCF satisfies completeness and transitivity
Pareto Principle - ANSWER If everyone prefers x to y, then SCF selects x over y
Non-dictatorship - ANSWER No individual always determines (or has preferences
always aligned to) SCF outcome
IIA (Arrow) - ANSWER Ranking of x vs y depends only on individual preferences between
x and y, not on rankings of other options which may be between or to each side of them.
Arrow's Theorem - ANSWER If SCF satisfies CR, PP, UD, and IIA, then doesn't satisfy
ND.
Local decisiveness - ANSWER If everyone in subgroup G prefers x to y, then x is chosen
, over y in the SCF for everyone
Global decisiveness - ANSWER If a group G's preference's can decide SCF outcome for
all options
Field expansion - ANSWER If a subgroup is locally decisive over one pair, it is globally
decisive.
Contraction of decisive sets - ANSWER If a subgroup is globally decisive, a subgroup of
that is also globally decisive.
SWFL - ANSWER A function which assigns complete and transitive relation R on X to
every profile of welfare W in omega.
IIA (SWFL) - ANSWER If for any two pair of options, x is preferred to y and the welfare of
* is identical to -*, then x* is preferred to y* too.
Pareto indifference - ANSWER If the welfare profile resulting from two options is
identical, SWFL ranks them equally.
ONC - ANSWER U_i = e_i(W_i). e_i allows positive Monotonic transformations and there's
no intra or inter comp.
CNC - ANSWER U_i = a_i(W_i) + b_i. a_i > 0. b_i is individual relative real numbers. Can
be positive affine transformed. Can do intra but not inter comps.
OZC - ANSWER U_i = e_i(W_i) and e_i is zero preserving. Can have inter comps on zeros
OLC - ANSWER U_i = e(W_i). Still positive monotonic, but e has to be transformed for
everyone at once. (Zero not always preserved though)
CUC - ANSWER U_i = a(W_i) + b_i. Can do inter but in units and not absolutes. Can be
transformed positive affine but a is constant for everyone.
CFC - ANSWER U_i = a(W_i) + b. Can do full inter comps in levels as everyone has the
same a and b. Can still use positive affine transformations.
RZC, RUC, RFC - ANSWER U_i = a_i(W_i), U_i(x) = W_i(x)=0. U_i = a(W_i). U_i = a(W_i),
U_i(x) = W_i(x)=0. Second part is to zero set the comparison. Take away individual
dependence on a for unit and full comps.
ESS - ANSWER Strategy is evolutionarily stable if it performs strictly better against itself
versus other strategies against it, or if other strategies perform as well against it as
itself but it performs better against other strategies than other strategies on each other.
Nash Solution - ANSWER The game solution ought to maximize the product of individual
utilities. NS = max(u(x)u(y)). So rearrange feasible set equation to solve for y and plug it
into NS equation and max using differentiation.
Individual rationality and Pareto optimality - ANSWER Solution must be weakly better
