RP Condorcet

Introduction

What is the RP Condorcet method?

The ranked pairs (RP) Condorcet method is a voting system that, given a set of preferences ballots, produces a sorted list of winners. It guarantees that each winner is the candidate that was prefered, in a pair-confrontation, to all those ranked lower. This method has been created by Nicolaus Tideman in 1987.

"If there is a candidate who is preferred over the other candidates, when compared in turn with each of the others, RP guarantees that candidate will win." [1]

Compared to the basic Condorcet method, RP always produces an answer because it is not paralysed by the tricky case known as the voting paradox [2].

What is this script?

Given a file (formatted as described below), this script computes the RP Condorcet method on the corresponding vote and produces a sorted list of the winners of this vote. Ties are supported.

The script was created and tested using [3], and it follows perfectly its behavior with all the examples, simple to complex, that were tested.

Usage

Script call

The script displays its usage when called without any argument.

To compute the result of a vote with the RP Condorcet method, just give a file name as an argument to the script:

$> ./rpcondorcet.pl FILENAME

You can enable the verbose mode by adding the -v option:

$> ./rpcondorcet.pl -v FILENAME

File format

Here is an example of a file used by the script:

# A := Albert
# J := John

40: A > J > S
S=J>A
35:J>S>A
# S := Seiko
25:S > A = J

The file describing a vote which we want to evaluate with this script must follow this rule: each of its line must be of one of the following types:

EMPTY LINE: this line is only composed of blanks (possibly spaces and tabulations, and a end-of-line character).
BALLOT LINE: [<NUM>:] <ID> {<SEP> <ID>}*, where:
- [X] means that X is optionnal,
- {X}* means that X can be repeated zero or more times,
- <NUM> represents the number of ballots of the described kind,
- <ID> is an identifier, that is a sequence of one or more characters delimited by spaces, tabulations, end-of-line or <SEP>,
- <SEP> is a separator and is either ">" or "=". For instance, "X > Y" means that X is prefered to Y, and "X = Y" means that X and Y are equally evaluated by the voter.
ALIAS LINE: # <ID> := <SENTENCE>, where <ID> is the name used in the ballot lines and <SENTENCE> is any sequence of characters ended by a end-of-line character.

An alias line is used by the script when displaying the result of the vote: it replace the <ID> by the <SENTENCE> everywhere it has to be printed. This way, one can easily write a ballot file with simple, short <ID>s, and get back a comfortable, complete display of the result. If more than one alias line exists for the same <ID>, only the last one will be used.

The blank characters are mainly ignored, except in a <SENTENCE>, so that you can write your vote file in a clear, human-readable way.

thilp / condorcet