NAME
Vote::Count::Matrix
VERSION 0.009
Win-Loss Matrix
Condorcet Pairwise Methods require a Win-Loss Matrix. This object takes an RCV BallotSet with an optional Active list and returns the Matrix as an Object. The Ojbect is capable of Scoring itself, Calculating a Smith Set, and identifying Condorcet Winners and Losers.
SYNOPSIS
my $Matrix =
Vote::Count::Matrix->new(
'BallotSet' => $myVoteCount->BallotSet() );
my $Scores = $Matrix->ScoreMatrix();
my %DominantSet = $Matrix->SmithSet()->%*;
my $CondorcetWinner = $Matrix->CondorcetWinner();new
Parameters:
BallotSet (required)
A Ballot Set reference as generated by ReadBallots, which can be retrieved from a Vote::Count object via the ->BallotSet() method.
BallotSetType (future use)
Defaults to rcv. Currently rcv is the only type supported. In the future the Matrix may be able to deal directly with Range Ballots.
Active (optional)
A hash reference with active choices as the keys. The default value is all of the choices defined in the BallotSet.
Methods
MatrixTable
Returns a MarkDown formatted table with the wins losses and ties for each Active Choice as text.
GetPairResult ( $A, $B )
Returns the results of the pairing of two choices as a hashref.
Example where $A and $B are "STRAWBERRY" and "FUDGESWIRL":
{
'FUDGESWIRL' => 6,
'loser' => "STRAWBERRY",
'margin' => 2,
'STRAWBERRY' => 4,
'tie' => 0,
'winner' => "FUDGESWIRL"
}GetPairWinner ( $A, $B )
Returns the winner of the pairing of two choices. If there is no Winner it returns a false value (empty string).
ScoreMatrix
Returns a HashRef of the choices and their Matrix Scores. The scoring is 1 for each win, 0 for losses and ties. In the event a choice has ties but no wins their score will be .001. Where N is the number of choices, a Condorcet Winner will have a score of N-1, a Condorcet Loser will have a score of 0. Since a choice with at least one tie but no wins is not defeated by all other choices they are not a Condorcet Loser, and thus those cases are scored with a near to zero value instead of 0. Methods that wish to treat no wins but tie case as a Condorcet Loser may test for a score less than 1.
LeastWins
Returns an array of the choice or choices with the fewest wins.
CondorcetLoser
Eliminates all Condorcet Losers from the Matrix Object's Active list. Returns a hashref:
{
verbose => 'verbose message',
terse => 'terse message',
eliminated => [ eliminated choices ],
eliminations => number of eliminated choices,
};CondorcetWinner
Returns either the Condorcet Winner or an empty string if there is none.
SmithSet
Finds the innermost Smith Set (Dominant Set). [ assistance in finding proof of the algorithm used would be appreciated so it could be correctly referenced in this documentation ]. A Dominant Set is a set which defeats all choices outside of that set. The inner Smith Set is the smallest possible Dominant Set.
Returns a hashref with the keys as the choices of the Smith Set.