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The participation criterion, also called vote or population monotonicity, is a voting system criterion that says that a candidate should never lose an election as a result of receiving too many votes in support.^[1] It says that adding a voter who prefers Alice to Bob should not cause Alice to lose the election to Bob.^[2]

Voting systems that fail the participation criterion exhibit the no-show paradox, where a voter is effectively disenfranchised by the electoral system (because turning out to vote would make a bad situation worse). In such a scenario, these voters' ballots are considered "less than worthless", actively harming their interests by reversing an otherwise-favorable outcome.^[3]

Positional and score voting methods satisfy the participation criterion. All methods satisfying paired majority-rule^[4][5] can fail in situations involving four-way cyclic ties, and the highest median methods^[6] can fail in some situations. Most notably, instant-runoff voting—a commonly-used voting rule in the United States and Australia—fails the participation criterion.^[7]

Cause of failure

Instant-runoff elections

The most common cause of participation failures is caused by the use of runoff systems (including instant-runoff voting). In instant-runoff voting, violations of monotonicity can occur even in elections with very few candidates, and occur in 50% of all situations where the results of IRV disagree with those of plurality.^[8]

Incompatibility with the Condorcet criterion

When there are 3 major candidates, Minimax Condorcet and its variants (including Ranked Pairs and Schulze's method) satisfy the participation criterion.^[4] However, with more than 3 candidates, every resolute and deterministic Condorcet method sometimes fail participation.^[4][5] Similar incompatibilities have also been proven for set-valued voting rules.^[5][9][10] However, such results do not apply to maximal lotteries.

However, studies suggest this is empirically rare for modern majority-rule systems, like ranked pairs; one study surveying 306 publicly-available election datasets found no examples of participation failures for methods in the ranked pairs-minimax family.^[11]

Certain conditions weaker than the participation criterion are also incompatible with the Condorcet criterion. For example, weak positive involvement requires that adding a ballot in which candidate A is one of the voter's most-preferred candidates does not change the winner away from A. Similarly, weak negative involvement requires that adding a ballot in which A is one of the voter's least-preferred does not make A the winner if it was not the winner before. Both conditions are incompatible with the Condorcet criterion if one allows ballots to include ties.^[12] If the ballots must express A as their sole favorite, then there exist Condorcet methods that pass.

In fact, an even weaker property can be shown to be incompatible with the Condorcet criterion: it can be better for a voter to submit a completely reversed ballot than to submit a ballot that ranks all candidates honestly.^[13]

Relationship to vote positivity

Negative vote weight (also known as inverse success value) refers to an effect that occurs in certain elections where votes can have the opposite effect of what the voter intended. A vote for a party might result in the loss of seats in parliament, or the party might gain extra seats by not receiving votes. This runs counter to the intuition that an individual voter voting for an option in a democratic election should only increase the chance of that option winning the election overall, compared to not voting (a no-show pathology) or voting against it (monotonicity).

Examples

Copeland

This example shows that Copeland's method violates the participation criterion. Assume four candidates A, B, C and D with 13 potential voters and the following preferences:

The three voters with preferences A > B > C > D are unconfident whether to participate in the election.

Voters not participating

Assume the 3 voters would not show up at the polling place.

The preferences of the remaining 10 voters would be:

The results would be tabulated as follows:

Result: A can defeat two of the three opponents, whereas no other candidate wins against more than one opponent. Thus, A is elected Copeland winner.

Voters participatingedit

Now, consider the three unconfident voters decide to participate:

The results would be tabulated as follows:

Result: B is the Condorcet winner and thus, B is Copeland winner, too.

Conclusionedit

By participating in the election the three voters supporting A would change A from winner to loser. Their first preferences were not sufficient to change the one pairwise defeat A suffers without their support. But, their second preferences for B turned both defeats B would have suffered into wins and made B Condorcet winner and thus, overcoming A.

Hence, Copeland fails the participation criterion. Zdroj:https://en.wikipedia.org?pojem=Participation_criterion
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