IteratedBucklin¶

class svvamp.IteratedBucklin(population, **kwargs)[source]¶

Iterated Bucklin method.

Inherits functions and optional parameters from superclasses ElectionResult and Election.

Example:

>>> import svvamp
>>> pop = svvamp.PopulationSpheroid(V=100, C=5)
>>> election = svvamp.IteratedBucklin(pop)

The candidate with least adjusted median Borda score (cf. below) is eliminated. Then the new Borda scores are computed. Etc. Ties are broken in favor of lower-index candidates: in case of a tie, the candidate with highest index is eliminated.

Adjusted median Borda score:

Let med_c be the median Borda score for candidate c. Let x_c the number of voters who put a lower Borda score to c. Then c‘s adjusted median is med_c - x_c / (V + 1).

If med_c > med_d, then it is also true for the adjusted median. If med_c = med_d, then c has a better adjusted median iff x_c < x_d, i.e. if more voters give to c the Borda score med_c or higher.

So, the best candidate by adjusted median is the Bucklin winner. Here, at each round, we eliminate the candidate with lowest adjusted median Borda score, which justifies the name of “Iterated Bucklin method”.

Unlike Baldwin method (= Iterated Borda), Iterated Bucklin does not meet the Condorcet criterion. Indeed, a Condorcet winner may have the (strictly) worst median ranking.

CM(): Non-polynomial or non-exact algorithms from superclass Election.

ICM(): The algorithm from superclass Election is polynomial and has a window of error of 1 manipulator.

IM(): Non-polynomial or non-exact algorithms from superclass Election.

not_IIA(): Non-polynomial or non-exact algorithms from superclass Election.

TM(): Exact in polynomial time.

UM(): Non-polynomial or non-exact algorithms from superclass Election.

candidates_by_scores_best_to_worst¶

1d array of integers. Candidates are sorted according to their order of elimination.

By definition / convention, candidates_by_scores_best_to_worst[0] = w.

scores¶: 2d array of integers. scores[r, c] is the adjusted median Borda score of candidate c at elimination round r.

w¶: Integer (winning candidate).