CondorcetSumDefeats

class svvamp.CondorcetSumDefeats(population, **kwargs)

Condorcet with sum of defeats.

Inherits functions and optional parameters from superclasses ElectionResult and Election.

Example:

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

An elementary move consists of reversing a voter’s preference about a pair of candidate (c, d) (without demanding that her whole relation of preference stays transitive). The score for candidate c is minus the number of elementary moves needed so that c becomes a Condorcet winner.

It is the same principle as Dodgson’s method, but without looking for a transitive profile.

In practice:

\[\texttt{scores}[c] = - \sum_{c \text{ does not beat } d}\left( \left\lfloor\frac{V}{2}\right\rfloor + 1 - \texttt{matrix_duels_rk}[c, d] \right)\]

In particular, for V odd:

\[\texttt{scores}[c] = - \sum_{c \text{ does not beat } d}\left( \left\lceil\frac{V}{2}\right\rceil - \texttt{matrix_duels_rk}[c, d] \right)\]

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

ICM(): Algorithm from superclass Election. It 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. If IIA_subset_maximum_size = 2, it runs in polynomial time and is exact up to ties (which can occur only if V is even).

TM(): Exact in polynomial time.

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

scores

1d array of integers.

\[\texttt{scores}[c] = - \sum_{c \text{ does not beat } d}\left( \left\lfloor\frac{V}{2}\right\rfloor + 1 - \texttt{matrix_duels_rk}[c, d] \right)\]

w

Integer (winning candidate).

Default behavior in superclass ElectionResult:

The candidate with highest value in vector scores is declared the winner. In case of a tie, the tied candidate with lowest index wins.