Tutorial 4: Population models¶
Note
In this tutorial, we present the probabilistic models that can be used in
SVVAMP to generate a population. It is also possible to enter
a population manually (Population) or to import a
population from a file (PopulationFromFile).
Plot a population¶
Create a population of 100 voters with preferences over 5 candidates, using the Von-Mises Fisher model, which represents a polarized culture:
import svvamp
pop = svvamp.PopulationVMFHypersphere(V=100, C=5, vmf_concentration=10)
pop.labels_candidates = ['Alice', 'Bob', 'Catherine', 'Dave', 'Ellen']
Plot the restriction of the population to 3 candidates, for example [0, 2, 3] (Alice, Catherine and Dave), in the utility space:
pop.plot3(indexes=[0, 2, 3])
Cf. plot3() for more information about this
representation.
Plot the restriction of the population to 4 candidates, for example [0, 1, 2, 4] (Alice, Bob, Catherine and Ellen), in the utility space:
pop.plot4(indexes=[0, 1, 2, 4])
Cf. plot4() for more information about this
representation.
Impartial culture¶
The Spheroid model is an extension of the Impartial Culture to utilities:
pop = svvamp.PopulationSpheroid(V=100, C=5)
pop.plot3()
pop.plot4()
The Cubic Uniform model is another one:
pop = svvamp.PopulationCubicUniform(V=5000, C=3)
pop.plot3(normalize=False)
pop = svvamp.PopulationCubicUniform(V=5000, C=4)
pop.plot4(normalize=False)
Neutral culture with weak orders¶
The Ladder model is also neutral (it treats all candidates equally) and voters are also independent, like in Impartial Culture, but weak orders are possible.
pop = svvamp.PopulationLadder(V=1000, C=3, n_rungs=5)
pop.plot3(normalize=False)
pop = svvamp.PopulationLadder(V=1000, C=4, n_rungs=5)
pop.plot4(normalize=False)
Cf. PopulationLadder.
Polarized cultures¶
In the beginning of this tutorial, we have already met the Von-Mises Fisher model on the hypersphere. A variant is the VMF model on the hypercircle.
Political spectrum¶
In these models, voters and candidates draw independent positions in a
Euclidean space (the ‘political spectrum’). The utility of a voter v for a
candidate c is a decreasing function of the distance between their
positions. If the dimension of the political spectrum is 1,
then the population is necessarily single-peaked (cf. ‘The theory of
committees and elections’, Duncan Black, 1958).
Gaussian Well model:
pop = svvamp.PopulationGaussianWell(V=1000, C=4, sigma=[1], shift=[0])
pop.plot3()
pop.plot4()
Euclidean Box model:
pop = svvamp.PopulationEuclideanBox(V=1000, C=4, box_dimensions=[1])
pop.plot3()
pop.plot4()