Hotelling-Downs plurality competition on a line

Each voter supports the nearest candidate (ties split equally); candidates maximise their vote share (Hotelling 1929, Downs 1957). With a finite electorate a candidate's share, as its position y varies, changes only where it becomes equidistant with a rival for some voter (\(y = c_k\) or \(y = 2v - c_k\)); the best response is found exactly by evaluating those breakpoints and the midpoints between them. The configuration is a Nash equilibrium when no candidate can raise its share. Without positions the two-candidate equilibrium is returned: both candidates at the median.

Usage

PluralityCompetition(voters, positions = NULL, weights = NULL)

Arguments

voters

Voter ideal points.

positions

Candidate positions; NULL for the two-candidate Downsian equilibrium.

weights

Voter weights (default 1).

Value

List with shares, positions, best_response (location and share per candidate), gain, is_equilibrium and median_interval.

References

Hotelling, H. (1929). Stability in competition. Economic Journal 39, 41-57.

Eaton, B. C. and Lipsey, R. G. (1975). The principle of minimum differentiation reconsidered. Review of Economic Studies 42, 27-49.

Examples

PluralityCompetition(c(0, 1, 2, 7, 9), c(1, 2))$gain
#> [1] 0.1 0.0