Games - CPO-STV

	Games - CPO-STV

CPO-STV, or the Comparison of Pairs of Outcomes by the Single Transferable Vote, is a preference voting system designed to achieve proportional representation. It is a highly sophisticated variant of the Single Transferable Vote (STV) system, designed to overcome some of that system's perceived short-comings. As in other forms of STV, in a CPO-STV election more than one candidate is elected and voters must rank candidates in order of preference. It is a relatively new system and has not yet been used for a public election.

Traditional forms of STV offer voters incentives to vote tactically in certain circumstances and are said to produce outcomes that do not always accurately reflect the preferences of voters. The reason for these problems is that sometimes STV eliminates, at an early stage in the count, a candidate who might have gone on to be elected later had they been allowed to remain in the contest.

CPO-STV was invented by Nicolaus Tideman and aims to overcome these defects by incorporating some of the positive features of Condorcet's method, a voting system designed for single-winner elections, into STV. CPO-STV works by an exhaustive comparison of the various possible outcomes of an election, in accordance with a particular procedure, in order to determine which outcome best matches the preferences of voters. If used for a single winner election CPO-STV becomes the same as Condorcet's method, in the same way that traditional STV becomes Instant Run-off Voting (IRV).

Voting

Each voter ranks the candidates in order of preference. For example:

#Andrea #Carter #Brad #Delilah #Scott

The precise rules for a given CPO-STV election will determine whether or not a voter must rank every single candidate, and whether or not they are permitted to give the same ranking to more than one candidate.

Procedure

Setting the quota

Both the Hare and Droop quotas may be used for a CPO-STV election. However, Tideman recommends a form of the Hagenbach-Bischoff quota. This is the rational number equal to the total number of valid votes cast, divided by the number one greater than the total number of seats to be filled. This can be clearly seen in the formula:

:

\rm votes \over \rm {seats+1}

Finding the winners

CPO-STV compares every possible outcome of an election in order to find the set of winners it considers the best. The winning outcome is determined by means of Condorcet's method. This means that the outcomes are compared one against another in a series of imaginary one-on-one contests. Usually there is an outcome that wins every such contest and it is this set of candidates that are declared elected.

When two outcomes are compared one against another a special method is used to give each a score and so determine which of the two is the winner. When comparing two outcomes the steps are as follows:

# Eliminate candidates in neither outcome: All candidates who are not present in either outcome are excluded and the votes for them are transfered. Any voter who supports an excluded candidate has their vote transfered to their next most preferred candidate who is present in at least one of the two outcomes. # Transfer surpluses of candidates in both outcomes: Where the number of votes for a candidate is greater than the quota, the surplus above the quota is transfered. However, only the surpluses of candidates present in both outcomes are transfered; any other surpluses are ignored. The surplus votes may only be transfered to candidates who are present in at least one of the two outcomes. # Add up the totals: After all necessary exclusions and transfers have occurred, the total number of votes deemed to have been cast for the candidates in a given outcome are added up and the result is considered the score for that outcome. # Declare the winner: The outcome with the higher score is deemed the winner of that particular comparison.

Occasionally, once every possible outcome has been compared against every other outcome, there will be no one outcome that beats all others--that is, no clear 'Condorcet winner'. In such cases a more complicated procedure, known as a Condorcet completion method, must be used to determine the set of winners that are elected. The precise completion method depends on the version of Condorcet's method being used. Versions of Condorcet's method with different, sophisticated completion methods include Ranked Pairs and the Schulze method.

[ Visit the complete Wikipedia entry for CPO-STV ]

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