StrategyTwelve

class poisson_approval.StrategyTwelve(d_ranking_ballot, d_weak_order_ballot=None, profile=None, voting_rule=None)[source]

A strategy profile for a 12-type profile.

Parameters

d_ranking_ballot (dict) –
Keys are rankings and values are strategies, e.g. 'abc': 'ab'. A strategy can be a valid ballot (e.g. 'a' or 'ab' when the ranking is 'abc'), UTILITY_DEPENDENT or '' if the behavior of these voters is not specified in the strategy. Cf. ProfileTwelve.

In the case of Plurality, the valid ballots for voters 'abc' are 'a' and 'b'. In the case of Anti-plurality, their valid ballots are 'ab' (vote against c) and 'ac' (vote against b).
d_weak_order_ballot (dict) – Key: weak order. Value: strategy. A strategy can be a valid ballot, SPLIT or '' if the behavior of these voters is not specified in the strategy. This is useful in two cases only: for “haters” (e.g. 'a~b>c') in Plurality, and for “lovers” (e.g. 'a>b~c') in Anti-Plurality. In all other cases, voters with a weak order have a dominant strategy and they automatically use it. About 'SPLIT': for example, in Plurality, 'a~b>c': SPLIT means that half of voters with weak order abc cast a ballot for a, and the other half for b.
profile (Profile, optional) – The “context” in which the strategy is used.
voting_rule (str) – The voting rule. Possible values are APPROVAL, PLURALITY and ANTI_PLURALITY. Default: the same voting rule as profile if a profile is specified, APPROVAL otherwise.

Examples

>>> strategy = StrategyTwelve({'abc': 'utility-dependent', 'bac': 'b'})
>>> strategy
StrategyTwelve({'abc': 'utility-dependent', 'bac': 'b'})
>>> print(strategy)
<abc: utility-dependent, bac: b>
>>> strategy.abc
'utility-dependent'
>>> strategy.a_bc
'a'
>>> strategy.ab_c
'ab'

property a_bc

Strategy of voters with type a_bc.

Type: str

property a_cb

Strategy of voters with type a_cb.

Type: str

property ab_c

Strategy of voters with type ab_c.

Type: str

property abc

Strategy of voters with ranking abc.

Type: str

property ac_b

Strategy of voters with type ac_b.

Type: str

property acb

Strategy of voters with ranking acb.

Type: str

property b_ac

Strategy of voters with type b_ac.

Type: str

property b_ca

Strategy of voters with type b_ca.

Type: str

property ba_c

Strategy of voters with type ba_c.

Type: str

property bac

Strategy of voters with ranking bac.

Type: str

property bc_a

Strategy of voters with type bc_a.

Type: str

property bca

Strategy of voters with ranking bca.

Type: str

property c_ab

Strategy of voters with type c_ab.

Type: str

property c_ba

Strategy of voters with type c_ba.

Type: str

property ca_b

Strategy of voters with type ca_b.

Type: str

property cab

Strategy of voters with ranking cab.

Type: str

property cb_a

Strategy of voters with type cb_a.

Type: str

property cba

Strategy of voters with ranking cba.

Type: str

property d_ranking_best_response: Defined when a profile is given. Cf. TauVector.d_ranking_best_response.

deepcopy_with_attached_profile(profile)

Deep copy with an attached profile.

Parameters: profile (Profile) – The new attached profile.
Returns: A deep copy of this strategy, with profile attached to it.
Return type: Strategy

property duo_ab: Defined when a profile is given. Cf. TauVector.duo_ab.

property duo_ac: Defined when a profile is given. Cf. TauVector.duo_ac.

property duo_ba: Defined when a profile is given. Cf. TauVector.duo_ba.

property duo_bc: Defined when a profile is given. Cf. TauVector.duo_bc.

property duo_ca: Defined when a profile is given. Cf. TauVector.duo_ca.

property duo_cb: Defined when a profile is given. Cf. TauVector.duo_cb.

property is_equilibrium

Whether this strategy is an equilibrium (in the context of the given profile). Cf. Profile.is_equilibrium().

Type: EquilibriumStatus

property pivot_strict_ab: Defined when a profile is given. Cf. TauVector.pivot_strict_ab.

property pivot_strict_ac: Defined when a profile is given. Cf. TauVector.pivot_strict_ac.

property pivot_strict_ba: Defined when a profile is given. Cf. TauVector.pivot_strict_ba.

property pivot_strict_bc: Defined when a profile is given. Cf. TauVector.pivot_strict_bc.

property pivot_strict_ca: Defined when a profile is given. Cf. TauVector.pivot_strict_ca.

property pivot_strict_cb: Defined when a profile is given. Cf. TauVector.pivot_strict_cb.

property pivot_tij_abc: Defined when a profile is given. Cf. TauVector.pivot_tij_abc.

property pivot_tij_acb: Defined when a profile is given. Cf. TauVector.pivot_tij_acb.

property pivot_tij_bac: Defined when a profile is given. Cf. TauVector.pivot_tij_bac.

property pivot_tij_bca: Defined when a profile is given. Cf. TauVector.pivot_tij_bca.

property pivot_tij_cab: Defined when a profile is given. Cf. TauVector.pivot_tij_cab.

property pivot_tij_cba: Defined when a profile is given. Cf. TauVector.pivot_tij_cba.

property pivot_tjk_abc: Defined when a profile is given. Cf. TauVector.pivot_tjk_abc.

property pivot_tjk_acb: Defined when a profile is given. Cf. TauVector.pivot_tjk_acb.

property pivot_tjk_bac: Defined when a profile is given. Cf. TauVector.pivot_tjk_bac.

property pivot_tjk_bca: Defined when a profile is given. Cf. TauVector.pivot_tjk_bca.

property pivot_tjk_cab: Defined when a profile is given. Cf. TauVector.pivot_tjk_cab.

property pivot_tjk_cba: Defined when a profile is given. Cf. TauVector.pivot_tjk_cba.

property pivot_weak_ab: Defined when a profile is given. Cf. TauVector.pivot_weak_ab.

property pivot_weak_ac: Defined when a profile is given. Cf. TauVector.pivot_weak_ac.

property pivot_weak_ba: Defined when a profile is given. Cf. TauVector.pivot_weak_ba.

property pivot_weak_bc: Defined when a profile is given. Cf. TauVector.pivot_weak_bc.

property pivot_weak_ca: Defined when a profile is given. Cf. TauVector.pivot_weak_ca.

property pivot_weak_cb: Defined when a profile is given. Cf. TauVector.pivot_weak_cb.

print_all_pivots(): Defined when a profile is given. Cf. TauVector.print_all_pivots().

print_weak_pivots(): Defined when a profile is given. Cf. TauVector.print_weak_pivots().

property scores: Defined when a profile is given. Cf. TauVector.scores.

property share_double_votes: Defined when a profile is given. Cf. TauVector.share_double_votes.

property share_sincere

Share of voters that happen to cast a sincere ballot (in the context of the given profile).

Cf. ProfileCardinal.share_sincere(). This is defined only for a ProfileCardinal.

Type: Number

property share_sincere_among_strategic_voters

Share of strategic voters that happen to cast a sincere ballot (in the context of the given profile).

Cf. ProfileCardinal.share_sincere_among_strategic_voters(). This is defined only for a ProfileCardinal.

Type: Number

property share_single_votes: Defined when a profile is given. Cf. TauVector.share_single_votes.

property tau

The tau-vector associated to this strategy (in the context of the given profile). Cf. Profile.tau().

Type: TauVector

property trio: Defined when a profile is given. Cf. TauVector.trio.

property trio_1t_a: Defined when a profile is given. Cf. TauVector.trio_1t_a.

property trio_1t_b: Defined when a profile is given. Cf. TauVector.trio_1t_b.

property trio_1t_c: Defined when a profile is given. Cf. TauVector.trio_1t_c.

property trio_2t_ab: Defined when a profile is given. Cf. TauVector.trio_2t_ab.

property trio_2t_ac: Defined when a profile is given. Cf. TauVector.trio_2t_ac.

property trio_2t_ba: Defined when a profile is given. Cf. TauVector.trio_2t_ba.

property trio_2t_bc: Defined when a profile is given. Cf. TauVector.trio_2t_bc.

property trio_2t_ca: Defined when a profile is given. Cf. TauVector.trio_2t_ca.

property trio_2t_cb: Defined when a profile is given. Cf. TauVector.trio_2t_cb.

property winners: Defined when a profile is given. Cf. TauVector.winners.

property τ

The tau-vector (alternate notation). Cf. Profile.τ().

Type: TauVector