NiceStatsProfileOrdinal

class poisson_approval.NiceStatsProfileOrdinal(tests_profile=None, tests_strategy=None, tests_strategy_dist=None, tests_strategy_winners=None, conditional_on=None, factory_profiles=None)

Compute nice stats on ordinal profiles.

Parameters

• tests_profile (list) – A list of pairs (test, name), where test is a function ProfileOrdinal -> bool, and name is a string.

• tests_strategy (list) – A list of pairs (test, name), where test is a function StrategyOrdinal -> bool, and name is a string. For these tests, we compute only the probability that a equilibrium meeting the test exists.

• tests_strategy_dist (list) – A list of pairs (test, name), where test is a function StrategyOrdinal -> bool, and name is a string. For these tests, we compute the distribution of numbers of equilibria meeting the test.

• tests_strategy_winners (list) – A list of pairs (test, name), where test is a function StrategyOrdinal -> bool, and name is a string. For these tests, we compute the distribution of numbers of winners in equilibria meeting the test.

• conditional_on (callable) – A function ProfileOrdinal -> bool.

• factory_profiles (callable) – A callable that inputs nothing and outputs a profile. Default: RandProfileOrdinalUniform, with its default parameters.

Notes

The tests in tests_profile concern the profile: what proportion of profiles meet the condition?

The tests in tests_strategy concern the strategies, in the cases where they are equilibrium. For each ordinal profile, we compute the probability (for a uniform distribution of utilities) that at least one strategy is an equilibrium and meets the given condition.

The tests in tests_strategy_dist or tests_strategy_winners concern also the strategies, in the cases where they are equilibrium.

Examples

>>> initialize_random_seeds()
>>> nice_stats = NiceStatsProfileOrdinal(
...     tests_profile=[
...         (lambda profile: any([strategy for strategy in profile.analyzed_strategies_ordinal.equilibria
...                               if strategy.profile.condorcet_winners == strategy.winners]),
...          'There exists a true equilibrium electing the CW'),
...     ],
...     tests_strategy=[
...         (lambda strategy: strategy.profile.condorcet_winners == strategy.winners,
...          'There exists an equilibrium that elects the CW')
...     ],
...     tests_strategy_dist=[
...         (lambda strategy: strategy.profile.condorcet_winners == strategy.winners,
...          'There exists an equilibrium that elects the CW')
...     ],
...     tests_strategy_winners = [
...         (lambda sigma: True, 'Number of possible winners')
...     ],
...     conditional_on=lambda profile: profile.is_profile_condorcet == 1.
... )
>>> nice_stats.run(n_samples=10)

In order to display an overview of all the results, you can use display_results().

Plot a test_strategy and insert a cutoff according to a test_profile:

>>> nice_stats.plot_test_strategy(test='There exists an equilibrium that elects the CW')
>>> nice_stats.plot_cutoff(test='There exists a true equilibrium electing the CW')

Find a particular example or counter-example:

>>> profile = nice_stats.find_example('There exists a true equilibrium electing the CW', False)
>>> print(profile)
<abc: 0.4236547993389047, acb: 0.12122838365799216, bac: 0.0039303209304278885, bca: 0.05394987214431912, cab: 0.1124259903007756, cba: 0.2848106336275805> (Condorcet winner: a)

display_results()

Display the results.

find_example(test, value=True)

Find an example profile.

Parameters

• test (str or int) – Name or index of a test in tests_profile.

• value (bool) – Whether we want an example (True) or a counter-example (False).

Returns

A profile for which the test returned value in the simulation.

Return type

ProfileOrdinal

plot_cutoff(test, left='', right='', style='')

Plot the cutoff of a test on the profile.

Parameters

• test (str or int) – Name or index of a test in tests_profile.

• left (str) – Text to be written on the left.

• right (str) – Text to be written on the right.

• style (str) – Cf. the function plot of matplotlib.

plot_test_strategy(test, ylabel=True, legend=False, replacement_name=None, style='')

Plot a test on strategy.

Parameters

• test (str or int) – Name or index of a test in tests_strategy.

• ylabel (bool) – If True, the name is used in the y-label. Otherwise, the label is P (probability).

• legend (bool) – If True, the legend is displayed.

• replacement_name (str, optional) – If specified, it will be used instead of the test name in the plot.

• style (str) – Cf. the function plot of matplotlib.

run(n_samples)

Run the simulations and store the results.

Parameters

n_samples (int) – Number of profiles meeting the precondition conditional_on.