RuleSlater#
- class svvamp.RuleSlater(tie_break_rule='lexico', winner_option='exact', **kwargs)[source]#
Slater method.
- Parameters:
winner_option (str) –
- ‘exact’ or ‘lazy’. Default: ‘exact’. If winner_option is ‘exact’, then the winner is computed as usual.
If winner_option is ‘lazy’, then the winner is computed only in the obvious case where there is a Condorcet winner; note that if there is no Condorcet-admissible candidate, it is however possible to decide
is_cm_automatically to True.
tie_break_rule (str) – ‘lexico’ of ‘random’. Default: ‘lexico’. If tie_break_rule is ‘lexico’, then the candidate with the lowest index is selected in case of a tie (usual behavior of SVVAMP for the other voting rules). If tie_break_rule is random, then each time a profile is loaded, a tie-break order over the candidates is drawn at random. This tie-break is used for the result of the sincere election, but also in case of manipulation.
Options
------- –
>>> RuleSlater.print_options_parameters() cm_option: ['lazy', 'exact']. Default: 'lazy'. icm_option: ['exact']. Default: 'exact'. iia_subset_maximum_size: is_number. Default: 2. im_option: ['lazy', 'exact']. Default: 'lazy'. precheck_heuristic: is_bool. Default: True. tie_break_rule: ['lexico', 'random']. Default: 'lexico'. tm_option: ['lazy', 'exact']. Default: 'exact'. um_option: ['lazy', 'exact']. Default: 'lazy'. winner_option: ['exact', 'lazy']. Default: 'exact'.
Notes
The Slater method is defined similarly to the Kemeny method, but relying on the matrix of victories instead of the matrix of duels.
Examples
>>> profile = Profile(preferences_ut=[ ... [ 0. , -0.5, -1. ], ... [ 1. , -1. , 0.5], ... [ 0.5, 0.5, -0.5], ... [ 0.5, 0. , 1. ], ... [-1. , -1. , 1. ], ... ], preferences_rk=[ ... [0, 1, 2], ... [0, 2, 1], ... [1, 0, 2], ... [2, 0, 1], ... [2, 1, 0], ... ]) >>> rule = RuleSlater()(profile) >>> rule.demo_results_(log_depth=0) ************************ * * * Election Results * * * ************************ *************** * Results * *************** profile_.preferences_ut (reminder) = [[ 0. -0.5 -1. ] [ 1. -1. 0.5] [ 0.5 0.5 -0.5] [ 0.5 0. 1. ] [-1. -1. 1. ]] profile_.preferences_rk (reminder) = [[0 1 2] [0 2 1] [1 0 2] [2 0 1] [2 1 0]] ballots = [[0 1 2] [0 2 1] [1 0 2] [2 0 1] [2 1 0]] scores = [2 0 1] candidates_by_scores_best_to_worst [0 2 1] scores_best_to_worst [2 1 0] w = 0 score_w = 2 total_utility_w = 1.0 ********************************* * Condorcet efficiency (rk) * ********************************* w (reminder) = 0 condorcet_winner_rk_ctb = 0 w_is_condorcet_winner_rk_ctb = True w_is_not_condorcet_winner_rk_ctb = False w_missed_condorcet_winner_rk_ctb = False condorcet_winner_rk = 0 w_is_condorcet_winner_rk = True w_is_not_condorcet_winner_rk = False w_missed_condorcet_winner_rk = False *************************************** * Condorcet efficiency (relative) * *************************************** w (reminder) = 0 condorcet_winner_ut_rel_ctb = 0 w_is_condorcet_winner_ut_rel_ctb = True w_is_not_condorcet_winner_ut_rel_ctb = False w_missed_condorcet_winner_ut_rel_ctb = False condorcet_winner_ut_rel = 0 w_is_condorcet_winner_ut_rel = True w_is_not_condorcet_winner_ut_rel = False w_missed_condorcet_winner_ut_rel = False *************************************** * Condorcet efficiency (absolute) * *************************************** w (reminder) = 0 condorcet_admissible_candidates = [ True False False] w_is_condorcet_admissible = True w_is_not_condorcet_admissible = False w_missed_condorcet_admissible = False weak_condorcet_winners = [ True False False] w_is_weak_condorcet_winner = True w_is_not_weak_condorcet_winner = False w_missed_weak_condorcet_winner = False condorcet_winner_ut_abs_ctb = 0 w_is_condorcet_winner_ut_abs_ctb = True w_is_not_condorcet_winner_ut_abs_ctb = False w_missed_condorcet_winner_ut_abs_ctb = False condorcet_winner_ut_abs = 0 w_is_condorcet_winner_ut_abs = True w_is_not_condorcet_winner_ut_abs = False w_missed_condorcet_winner_ut_abs = False resistant_condorcet_winner = nan w_is_resistant_condorcet_winner = False w_is_not_resistant_condorcet_winner = True w_missed_resistant_condorcet_winner = False >>> rule.demo_manipulation_(log_depth=0) ***************************** * * * Election Manipulation * * * ***************************** ********************************************* * Basic properties of the voting system * ********************************************* with_two_candidates_reduces_to_plurality = True is_based_on_rk = True is_based_on_ut_minus1_1 = False meets_iia = False **************************************************** * Manipulation properties of the voting system * **************************************************** Condorcet_c_ut_rel_ctb (False) ==> Condorcet_c_ut_rel (False) || || || Condorcet_c_rk_ctb (True) ==> Condorcet_c_rk (True) || || || || || || || V V || || V V Condorcet_c_ut_abs_ctb (True) ==> Condorcet_ut_abs_c (True) || || || || || V V || || maj_fav_c_rk_ctb (True) ==> maj_fav_c_rk (True) || || || || || V V V V majority_favorite_c_ut_ctb (True) ==> majority_favorite_c_ut (True) || || V V IgnMC_c_ctb (True) ==> IgnMC_c (True) || || V V InfMC_c_ctb (True) ==> InfMC_c (True) ***************************************************** * Independence of Irrelevant Alternatives (IIA) * ***************************************************** w (reminder) = 0 is_iia = True log_iia: iia_subset_maximum_size = 2.0 example_winner_iia = nan example_subset_iia = nan ********************** * c-Manipulators * ********************** w (reminder) = 0 preferences_ut (reminder) = [[ 0. -0.5 -1. ] [ 1. -1. 0.5] [ 0.5 0.5 -0.5] [ 0.5 0. 1. ] [-1. -1. 1. ]] v_wants_to_help_c = [[False False False] [False False False] [False False False] [False False True] [False False True]] ************************************ * Individual Manipulation (IM) * ************************************ is_im = nan log_im: im_option = lazy candidates_im = [ 0. 0. nan] ********************************* * Trivial Manipulation (TM) * ********************************* is_tm = False log_tm: tm_option = exact candidates_tm = [0. 0. 0.] ******************************** * Unison Manipulation (UM) * ******************************** is_um = nan log_um: um_option = lazy candidates_um = [ 0. 0. nan] ********************************************* * Ignorant-Coalition Manipulation (ICM) * ********************************************* is_icm = False log_icm: icm_option = exact candidates_icm = [0. 0. 0.] necessary_coalition_size_icm = [0. 6. 4.] sufficient_coalition_size_icm = [0. 6. 4.] *********************************** * Coalition Manipulation (CM) * *********************************** is_cm = False log_cm: cm_option = lazy, um_option = lazy, icm_option = exact, tm_option = exact candidates_cm = [0. 0. 0.] necessary_coalition_size_cm = [0. 1. 3.] sufficient_coalition_size_cm = [0. 2. 3.]
- property candidates_by_scores_best_to_worst_#
1d array of integers. This is an optimal Kemeny order.
In case several orders are optimal, the first one by lexicographic order is given. This implies that if several winners are possible, the one with lowest index is declared the winner.
- property scores_#
1d array of integers. By convention, scores are integers from 1 to
n_c, withn_cfor the winner and 1 for the last candidate in Kemeny optimal order.