Coalition games in the spatial model

MedianLines: median lines of a weighted voting game in the plane. WeightedGameCore: core parties (no open half-plane through the position holds a winning coalition). SpatialHeart: the polygon bounded by the median lines (or the core point). QuotaSolution: quota of a weighted majority game. MinimalRangeCoalition: minimal-range winning coalition. RoemerPune: Roemer's party-unanimity Nash equilibrium with factional bargaining. Identical to the Python arm morie.fn.coalgame.

Usage

MedianLines(positions, weights, quota)

WeightedGameCore(positions, weights, quota)

SpatialHeart(positions, weights, quota)

QuotaSolution(weights, quota)

MinimalRangeCoalition(positions, weights, quota)

RoemerPune(a, b, mu, sigma, alpha_a, alpha_b, iters = 200L)

Arguments

positions

Two-column matrix of party positions (vector for MinimalRangeCoalition).

weights

Party weights (seats).

quota

Winning threshold.

a, b

Party ideal points (a < b).

mu, sigma

Mean and standard deviation of the median voter.

alpha_a, alpha_b

Opportunist bargaining weights.

iters

Best-response iterations.

Value

List (matrix of index pairs for MedianLines).

References

Schofield, N. (1999). The heart and the uncovered set. Journal of Economics, Supplement 8, 79-113.

Shapley, L. S. (1953). Quota solutions of n-person games. Contributions to the Theory of Games II, 343-359.

de Swaan, A. (1973). Coalition Theories and Cabinet Formations. Elsevier.

Roemer, J. E. (2001). Political Competition: Theory and Applications. Harvard University Press.

Examples

MedianLines(rbind(c(0, 0), c(1, 0), c(0, 1)), c(1, 1, 1), 2)
#>      [,1] [,2]
#> [1,]    0    1
#> [2,]    0    2
#> [3,]    1    2
QuotaSolution(c(1, 1, 1), 2)$quota
#> [1] 0.5 0.5 0.5