No-show paradox

[9] Ranked-choice voting (RCV) and the two-round system both fail the participation criterion with high frequency in competitive elections, typically as a result of a center squeeze.

For example, under instant-runoff voting, moving a candidate from first-place to last-place on a ballot can cause them to win.

[11] The most common cause of no-show paradoxes is the use of instant-runoff (often called ranked-choice voting in the United States).

[13] When there are at most 3 major candidates, Minimax Condorcet and its variants (such as ranked pairs and Schulze's method) satisfy the participation criterion.

One study surveying 306 publicly-available election datasets found no participation failures for methods in the ranked pairs-minimax family.

[21] Proportional representation systems using largest remainders for apportionment (such as STV or Hamilton's method) allow for no-show paradoxes.

[5][22] In Germany, situations where a voter's ballot has the opposite of its intended effect (e.g. a vote for a party or candidate causes them to lose) are called negatives Stimmgewicht (lit.

An infamous example occurred in the 2005 German federal election, when an article in Der Spiegel laid out how CDU voters in Dresden I would have to vote against their own party if they wished to avoid losing a seat in the Bundestag.

[5] This led to a lawsuit by electoral reform organization Mehr Demokratie [de] and Alliance 90/The Greens, joined by the neo-Nazi NDP of Germany, who argued the election law was undemocratic.

Negative vote weights cannot be accepted as constitutional on the premise that they cannot be predicted or planned, and thus can hardly be influenced by the individual voter.

The participation criterion can also be justified as a weaker form of strategyproofness: while it is impossible for honesty to always be the best strategy (by Gibbard's theorem), the participation criterion guarantees honesty will always be an effective, rather than actively counterproductive, strategy (i.e. a voter can always safely cast a sincere vote).

While no-show paradoxes can be deliberately exploited as a kind of strategic voting, systems that fail the participation criterion are typically considered to be undesirable because they expose the underlying system as logically incoherent or "spiteful" (actively seeking to violate the preferences of some voters).