Participation criterion

The participation criterion is a voting system criterion. It is also known as the "no show paradox". It has been defined^[1] as follows:

• In a deterministic framework, the participation criterion says that the addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing tally of votes should not change the winner from candidate A to candidate B.
• In a probabilistic framework, the participation criterion says that the addition of a ballot, where each candidate of the set X is strictly preferred to each other candidate, to an existing tally of votes should not reduce the probability that the winner is chosen from the set X.

Plurality voting, approval voting, range voting, and the Borda count all satisfy the participation criterion.^{[citation needed]} All Condorcet methods^[2], Bucklin voting^[3], and IRV^[4] fail.

Voting systems that fail the participation criterion allow a particularly unusual strategy of not voting to, in 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.

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.^{[citation needed]} 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. In other words, the addition of a "no" vote may make the measure more likely to pass. A referendum that required a minimum number of yes votes (not counting no's), by contrast, would pass the participation criterion.

Examples

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. If they had stayed home instead of voting, 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

The runoff would have been Roemer vs. Edwards. Pre-election polls had suggested that in a run-off between those two candidates, Roemer would have won, and the 80,653 voters would have got their second-choice rather than their third-choice candidate. Thus, these 80,653 voters would have achieved a more desired result by staying at home than by voting.

See also

• Consistency criterion
• Voting system

References

1. ^ Douglas Woodall (December 1994). "Properties of Preferential Election Rules, Voting matters - Issue 3, December 1994". http://www.votingmatters.org.uk/ISSUE3/P5.HTM. 
2. ^ Herve Moulin (1998-06). "Condorcet's principle implies the no show paradox". http://ideas.repec.org/a/eee/jetheo/v45y1988i1p53-64.html. Retrieved 2011-05-14. 
3. ^ Markus Schulze (1998-06-12). "Regretted Turnout. Insincere = ranking.". http://lists.electorama.com/pipermail/election-methods-electorama.com/1998-June/001727.html. Retrieved 2011-05-14. 
4. ^ Warren D. Smith. "Lecture "Mathematics and Democracy"". http://rangevoting.org/TBlecture.html#partic. Retrieved 2011-05-12. 

Further reading

• Woodall, Douglas R, "Monotonicity and Single-Seat Election Rules" Voting matters, Issue 6, 1996.

External links

• A Strong No Show paradox is a common flaw in Condorcet voting correspondences by Joaquin Perez.