Hotelling-Downs competition of n candidates over uniform voters

Voters are n_voters Philox uniforms; each votes for the nearest candidate. For a uniform electorate the pure-strategy equilibria of vote-share maximisers are: two candidates at the median; none for three; for four or more, the outer candidates paired at a and 1 - a with the others evenly spaced at 3a, 5a, and so on, a = 1 / (2n - 4) (Eaton and Lipsey 1975; unique for n = 4, 5). The fractions are mapped to sample quantiles and PluralityCompetition gives the largest finite-electorate deviation gain. Identical to the Python arm morie.fn.hotlg.hotelling_model.

Usage

HotellingModel(n_voters = 100, n_candidates = 2, seed = 42)

Arguments

n_voters: Number of voters.
n_candidates: Number of candidates.
seed: Philox seed.

Value

List: value (voter median), equilibrium_positions (NULL for three candidates), fractions, has_pure_equilibrium, shares, max_gain, voter_median, n_voters, n_candidates.

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.

Shaked, A. (1975). Non-existence of equilibrium for the two-dimensional three-firms location problem. Review of Economic Studies 42, 51-55.

Examples

HotellingModel(n_voters = 9, n_candidates = 2, seed = 1)$equilibrium_positions
#> [1] 0.6719983 0.6719983
HotellingModel(n_candidates = 5)$fractions
#> [1] 0.1666667 0.1666667 0.5000000 0.8333333 0.8333333