NAME
   Statistics::RankOrder - Algorithms for determining overall rankings from
   a panel of judges

VERSION
   version 0.13

SYNOPSIS
     use Statistics::RankOrder;

     my $r = Statistics::RankOrder->new();

     $r->add_judge( [qw( A B C )] );
     $r->add_judge( [qw( A C B )] );
     $r->add_judge( [qw( B A C )] );

     my %ranks = $r->mean_rank;
     my %ranks = $r->trimmed_mean_rank(1);
     my %ranks = $r->median_rank;
     my %ranks = $r->best_majority_rank;

DESCRIPTION
   This module offers algorithms for combining the rank-ordering of
   candidates by a panel of judges. For the purpose of this module, the
   term "candidates" means candidates in an election, brands in a
   taste-test, competitors in a sporting event, and so on. "Judges" means
   those rank-ordering the candidates, whether these are event judges,
   voters, etc. Unlike "voting" algorithms (e.g. majority-rule or
   single-transferable-vote), these algorithms require judges to rank-order
   all candidates. (Ties may be permissible for some algorithms).

   Algorithms included are:

   *   Lowest-Mean

   *   Trimmed-Lowest-Mean

   *   Median-Rank

   *   Best-of-Majority

   In this alpha version, there is minimal error checking. Future versions
   will have more robust error checking and may have additional ranking
   methods such as pair-ranking methods.

METHODS
 new
    $r = Statistics::RankOrder->new();

   Creates a new object with no judges on the panel (i.e. no data);

 "add_judge"
    $r->add_judge( [qw( A B C D E )] );

   Adds a judge to the panel. The single argument is an array-reference
   with the names of candidates ordered from best to worst.

 "best_majority_rank"
    my %ranks = $r->best_majority_rank;

   Ranks candidates according to the "Best-of-Majority" algorithm. The
   median rank is found for each candidate. If there are an even number of
   judges, the worst of the two median ranks is used. The idea behind this
   method is that the result for a candidate represents the worst rank such
   that a majority of judges support that rank or better. Ties in the
   median ranks are broken by the following comparisons, in order, until
   the tie is broken:

   *   larger "Size of Majority" (SOM) -- number of judges ranking at
       median rank or better

   *   lower "Total Ordinals of Majority" (TOM) -- sum of ordinal rankings
       of judges ranking at median rank or better

   *   lower "Total Ordinals" (TO) -- sum of all ordinals from all judges

   If a tie still exists after these comparisons, then the tie stands. (In
   practice, this is generally rare.) When a tie occurs, the next rank
   assigned after the tie is calculated as if the tie had not occurred.
   E.g., 1st, 2nd, 2nd, 4th, 5th.

   Returns a hash where the keys are the names of the candidates and the
   values are their rankings, with 1 being best and higher numbers worse.

 "candidates"
    my %candidates = $r->candidates;

   Returns a hash with keys being the names of candidates and the values
   being array references containing the rankings from all judges for each
   candidate.

 "judges"
    my @judges = $r->judges;

   Returns a list of array-references representing the rank-orderings of
   each judge.

 "mean_rank"
    my %ranks = $r->mean_rank;

   Ranks candidates according to the "Lowest Mean Rank" algorithm. The
   average rank is computed for each candidate. The candidate with the
   lowest mean rank is placed 1st, the second lowest mean rank is 2nd, and
   so on. If the mean ranks are the same, the candidates tie for that
   position. When a tie occurs, the next rank assigned after the tie is
   calculated as if the tie had not occurred. E.g., 1st, 2nd, 2nd, 4th,
   5th.

   Returns a hash where the keys are the names of the candidates and the
   values are their rankings, with 1 being best and higher numbers worse.

 "median_rank"
    my %ranks = $r->median_rank;

   Ranks candidates according to the "Median Rank" algorithm. The median
   rank is found for each candidate. If there are an even number of judges,
   the worst of the two median ranks is used. The idea behind this method
   is that the result for a candidate represents the lowest rank such that
   a majority of judges support that rank or better. The candidate with the
   lowest median rank is placed 1st, the second lowest median rank is 2nd,
   and so on. If the median ranks are the same, the candidates tie for that
   position. When a tie occurs, the next rank assigned after the tie is
   calculated as if the tie had not occurred. E.g., 1st, 2nd, 2nd, 4th,
   5th.

   Returns a hash where the keys are the names of the candidates and the
   values are their rankings, with 1 being best and higher numbers worse.

 "trimmed_mean_rank"
    my %ranks = $r->trimmed_mean_rank( N );

   Ranks candidates according to the "Trimmed Lowest Mean Rank" algorithm.
   The average rank is computed for each candidate after dropping the N
   lowest and N highest scores. E.g. trimmed_mean_rank(2) will drop the 2
   lowest and highest scores. The candidate with the lowest mean rank is
   placed 1st, the second lowest mean rank is 2nd, and so on. If the mean
   ranks are the same, the candidates tie for that position. When a tie
   occurs, the next rank assigned after the tie is calculated as if the tie
   had not occurred. E.g., 1st, 2nd, 2nd, 4th, 5th.

   Returns a hash where the keys are the names of the candidates and the
   values are their rankings, with 1 being best and higher numbers worse.

SEE ALSO
   *   Lingua::EN::Number::Ordinate -- for converting "1" to "1st", etc.

   For further details on various ranking methods, in particular, the "Best
   of Majority" method, see the following articles:

   *   "Rating Skating", Gilbert W. Basset and Joseph Persky, Journal of
       the American Statistical Association, volume 89, Issue 427 (Sept
       1994), pp. 1075-1079

   *   "The Canadians Should Have Won!?", Maureen T. Carroll, Elyn K.
       Rykken, and Jody M. Sorensen.
       <http://mathcs.muhlenberg.edu/~rykken/skating-full.pdf>

SUPPORT
 Bugs / Feature Requests
   Please report any bugs or feature requests through the issue tracker at
   <https://github.com/dagolden/Statistics-RankOrder/issues>. You will be
   notified automatically of any progress on your issue.

 Source Code
   This is open source software. The code repository is available for
   public review and contribution under the terms of the license.

   <https://github.com/dagolden/Statistics-RankOrder>

     git clone https://github.com/dagolden/Statistics-RankOrder.git

AUTHOR
   David Golden <[email protected]>

COPYRIGHT AND LICENSE
   This software is Copyright (c) 2005 by David A Golden.

   This is free software, licensed under:

     The Apache License, Version 2.0, January 2004

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