Participation criterion

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The participation criterion is a voting system criterion for evaluating voting systems and is also known as the No show paradox. It has been defined as follows:

  • Weak participation (Mike Ossipoff): Adding one or more ballots that vote X over Y should never change the winner from X to Y.
  • Strong participation (Douglas Woodall): The addition of a further ballot should not, for any positive whole number k, reduce the probability that at least one candidate is elected out of the first k candidates listed on that ballot.

Plurality voting, approval voting, range voting, and the Borda count all satisfy the participation criterion. All Condorcet methods, Bucklin voting, and IRV fail.

If a voting system fails the participation criterion, then a particularly unusual strategy of not voting can, in at least some circumstances, help a voter's preferred choice win.

The participation criterion for voting systems is one example of a rational participation constraint for social choice mechanisms in general.

Contents

[edit] Quorum requirements

The most common failure of the participation criterion is not in the use of particular voting systems, but in simple yes or no measures that place quorum requirements. A public referendum, for example, that required majority approval and a certain number of voters to participate in order to pass would fail the participation criterion, as a minority of voters preferring the "no" option could cause the measure to fail by simply not voting rather than voting no. A referendum that required a minimum number of yes votes (not counting no's), by contrast, would pass the participation criterion.

[edit] Examples

[edit] Approval voting

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[edit] Borda count

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[edit] Instant-runoff voting

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[edit] Kemeny-Young method

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[edit] Minimax Condorcet

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[edit] Plurality voting system

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[edit] Range voting

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[edit] Ranked Pairs

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[edit] Two-round system

An example of a two-round election that may well have failed the participation criterion is the Louisiana gubernatorial election in 1991. The votes in the first round were as follows:

Edwin W. Edwards 523,096
David Duke 491,342
Buddy Roemer 410,690
Other candidates 124,127

Edwards and Duke advanced to the run-off, which was won by Edwards with 1,057,031 votes to Duke's 671,009.

Now suppose there were 80,653 voters who voted Duke first and preferred Roemer to Edwards, and who were somehow prevented from voting in the first election. Then the first round would have been as follows:

Edwin W. Edwards 523,096
Buddy Roemer 410,690
David Duke 410,689
Other candidates 124,127

And the runoff would have been Roemer v Edwards. Pre-election polls had suggested that in a run-off between those two candidates, Roemer would have won. So our 80,653 voters have achieved a better result by staying at home than they would have by casting an honest vote.

[edit] Schulze method

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[edit] See also

[edit] References

Some parts of this article are derived with permission from text at http://electionmethods.org

[edit] External links