PopulationSpheroid¶

class svvamp.PopulationSpheroid(V, C, stretching=1)[source]¶

Population with ‘Spheroid’ model.

Parameters:	V – Integer. Number of voters. C – Integer. Number of candidates. stretching – Number between 0 and `numpy.inf` (both included).
Returns:	A `Population` object.

The utility vector of each voter is drawn independently and uniformly on a sphere in \(\mathbb{R}^C\). Then, it is sent on the spheroid that is the image of the sphere by a dilatation of factor stretching in direction [1, ..., 1]. Cf. working paper Durand et al. ‘Geometry on the Utility Sphere’.

The ordinal part of this distribution is the Impartial Culture.

The parameter stretching has only influence on voting systems based on utilities, especially Approval voting.

stretching = 0: pure Von Neumann-Morgenstern utility, normalized to \(\sum_c u_v(c) = 0\) (spherical model with C-2 dimensions).

stretching = 1: spherical model with C-1 dimensions.

stretching = inf: axial/cylindrical model with only two possible values, all-approval [1, ..., 1] and all-reject [-1, ..., -1].

N.B.: This model gives the same probability distribution as a Von Mises-Fisher with concentration = 0.