PopulationGaussianWell

class svvamp.PopulationGaussianWell(V, C, sigma, shift=None)

Population with ‘Gaussian well’ model.

Parameters:

• V – Integer. Number of voters.
• C – Integer. Number of candidates.
• sigma – 1d array of numbers. The variance of the gaussian law along each dimension.
• shift – 1d array of numbers, same dimension as sigma. Shift for the mean position of the candidates.

Returns:

A Population object.

Let us note n_dim the number of elements in sigma. For voter v (resp. each candidate c) and each axis i in range(n_dim), a position x_i[v] (resp. y_i[c]) is independently drawn according to a normal law of mean 0 and variance sigma[i]. If shift is used, the distribution of positions for candidates is displaced by this vector.

Let d[v, c] denote the Euclidean distance between voter v‘s position x[v] and candidate c‘s position y[c]. Then preferences_ut[v, c] = A - d[v, c], where A is such that the average utility is 0 over the whole population.

If ndim = 1, the population is single-peaked.