Options#

>>> RuleIRVAverage.print_options_parameters()
cm_option: ['fast', 'slow', 'very_slow', 'exact']. Default: 'fast'.
icm_option: ['lazy']. Default: 'lazy'.
iia_subset_maximum_size: is_number. Default: 2.
im_option: ['lazy', 'exact']. Default: 'lazy'.
tm_option: ['lazy', 'exact']. Default: 'exact'.
um_option: ['lazy', 'exact']. Default: 'lazy'.

Notes

At each round, all candidates with a Plurality score strictly lower than average are simultaneously eliminated. When all remaining candidates have the same Plurality score, the candidate with lowest index is declared the winner.

This method meets MajFav criterion.

is_cm_():
- cm_option = 'fast': Rely on RuleIRV’s fast algorithm. Polynomial heuristic. Can prove CM but unable to decide non-CM (except in rare obvious cases).
- cm_option = 'slow': Rely on RuleExhaustiveBallot’s exact algorithm. Non-polynomial heuristic (\(2^{n_c}\)). Quite efficient to prove CM or non-CM.
- cm_option = 'very_slow': Rely on RuleIRV’s exact algorithm. Non-polynomial heuristic (\(n_c!\)). Very efficient to prove CM or non-CM.
- cm_option = 'exact': Non-polynomial algorithm from superclass Rule.
Each algorithm above exploits the faster ones. For example, if cm_option = 'very_slow', SVVAMP tries the fast algorithm first, then the slow one, then the ‘very slow’ one. As soon as it reaches a decision, computation stops.
is_icm_(): Exact in polynomial time.
is_im_(): Non-polynomial or non-exact algorithms from superclass Rule.
is_iia(): Non-polynomial or non-exact algorithms from superclass Rule.
is_tm_(): Exact in polynomial time.
is_um_(): Non-polynomial or non-exact algorithms from superclass Rule.

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 = RuleIRVAverage()(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.  1.  2.]
 [ 3. inf  2.]
 [ 5. inf inf]]
candidates_by_scores_best_to_worst
[0 2 1]
scores_best_to_worst
[[ 2.  2.  1.]
 [ 3.  2. inf]
 [ 5. inf inf]]
w = 0
score_w = [2. 3. 5.]
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

property candidates_by_scores_best_to_worst_#: 1d array of integers. Candidates are sorted according to their order of elimination. When several candidates are eliminated during the same round, they are sorted by Plurality score at that round (less votes are eliminated first) and, in case of a tie, by their index (highest indexes are eliminated first).

property scores_#: 2d array of integers. scores[r, c] is the Plurality score of candidate c at elimination round r. By convention, if candidate c does not participate to round r, then scores[r, c] = numpy.inf.

property w_#

Integer (winning candidate).

Default behavior: the candidate with highest value in vector scores_ is declared the winner. In case of a tie, the tied candidate with lowest index wins.