class svvamp.GeneratorProfileGaussianWell(n_v, n_c, sigma, shift=None, sort_voters=False)

Profile generator using the ‘Gaussian well’ model.

Parameters:

• n_v (int) – Number of voters.

• n_c (int) – Number of candidates.

• sigma (list or ndarray) – 1d array of numbers. The variance of the gaussian distribution along each dimension.

• shift (list or ndarray) – 1d array of numbers, same dimension as sigma. Shift for the mean position of the candidates.

• sort_voters (bool) – This argument is passed to Profile.

Notes

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 distribution 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.

Remark: if n_dim = 1, the population is single-peaked.

Examples

>>> generator = GeneratorProfileGaussianWell(n_v=10, n_c=3, sigma=[1], shift=[10])
>>> profile = generator()
>>> profile.preferences_rk.shape
(10, 3)