Binary choice of x over status_quo by a voter at
ideal_point (both default to the origin) with quadratic utility
\(-\beta\|v - z\|^2\) and utility-difference noise: LogitVote,
ProbitVote, CauchyVote give \(F(U(x) - U(s))\).
NormalVote is the NOMINATE Gaussian-utility probit
\(\Phi(\beta e^{-w^2 d_x^2/2} - \beta e^{-w^2 d_s^2/2})\) (Poole and
Rosenthal 1997). BoltzmannVote gives softmax probabilities
\(e^{-d_j^2/T}/\sum_k e^{-d_k^2/T}\) over alternatives (rows of x;
status_quo appended when given or when x is one point).
MixedLogitVote averages the logit probability over
\(\beta_r \sim N(\beta, \sigma^2)\) Philox draws (Train 2009).
ProximityVote is 1, 0.5 or 0 as x is nearer, equidistant or
farther than status_quo in the Minkowski p-norm.
QuadUtility is \(-(x - v)^\top A (x - v)\). MedianVoter2d
is the Plott total-median test: the exact Tukey depth of a point among the
ideal points (rows of x) and whether it is at least \(n/2\).
UtilityMax picks the alternative with the largest quadratic, linear
or Gaussian utility (1-based index). VoteTrading and
VoteTrade2d report the number of Riker-Brams trades
(VoteTradingRikerBrams); WeightedVote returns one
power index of PowerIndices. DiscountUtility is
Grofman's discounting utility \(-\beta\|v - s - \delta(x - s)\|^2\);
MixedUtility the Merrill-Grofman unified utility
\(2(1-\beta)(v-n)\cdot(x-n) - \beta\|v - x\|^2\). Identical to the
Python modules morie.fn.svlgv, svprv, svchy,
svnrm, svblt, svmxl, svpxv, svqud,
svmv2, svutm, svvtr, svvt2, svwvt,
svdsc and svmxu.
Usage
LogitVote(x, ideal_point = NULL, status_quo = NULL, beta = 1)
ProbitVote(x, ideal_point = NULL, status_quo = NULL, beta = 1)
CauchyVote(x, ideal_point = NULL, status_quo = NULL, beta = 1)
NormalVote(x, ideal_point = NULL, status_quo = NULL, beta = 1, w = 1)
BoltzmannVote(x, ideal_point = NULL, status_quo = NULL, temperature = 1)
MixedLogitVote(
x,
ideal_point = NULL,
status_quo = NULL,
beta = 1,
beta_sd = 0.5,
n_draws = 1000L,
seed = 1L
)
ProximityVote(x, ideal_point = NULL, status_quo = NULL, p = 2)
QuadUtility(x, ideal_point = NULL, salience = NULL)
MedianVoter2d(x, ideal_point = NULL)
UtilityMax(x, ideal_point = NULL, utility = "quadratic", scale = 1)
VoteTrading(valuations)
VoteTrade2d(valuations)
WeightedVote(weights, quota = NULL, index = "shapley_shubik")
DiscountUtility(
x,
ideal_point = NULL,
status_quo = NULL,
discount = 0.5,
beta = 1
)
MixedUtility(x, ideal_point = NULL, neutral = NULL, beta = 0.5)Arguments
- x
Alternative (vector), alternatives (matrix rows), or ideal points (
MedianVoter2d).- ideal_point
Voter ideal point (for
MedianVoter2d, the point tested).- status_quo
Status quo (default origin).
- beta
Utility scale, or proximity weight for
MixedUtility.- w
NOMINATE dimension weight.
- temperature
Softmax temperature.
- beta_sd
Standard deviation of the random coefficient.
- n_draws
Simulation draws.
- seed
Philox seed.
- p
Minkowski exponent.
- salience
Vector (diagonal) or matrix of issue saliences.
- utility
"quadratic","linear"or"gaussian".- scale
Gaussian utility scale.
- valuations
Voters x issues signed intensities.
- weights
Player weights.
- quota
Winning quota.
- index
Power index name.
- discount
Fraction of the promised move expected to be enacted.
- neutral
Neutral point for the directional component.
References
Enelow, J. M. and Hinich, M. J. (1984). The Spatial Theory of Voting. Cambridge University Press.
Poole, K. T. and Rosenthal, H. (1997). Congress: A Political-Economic History of Roll Call Voting. Oxford University Press.
Plott, C. R. (1967). A notion of equilibrium and its possibility under majority rule. American Economic Review 57, 787-806.
Grofman, B. (1985). The neglected role of the status quo in models of issue voting. Journal of Politics 47, 230-237.
Merrill, S. and Grofman, B. (1999). A Unified Theory of Voting. Cambridge University Press.