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Participation criterion
The participation criterion is a voting system criterion that says candidates should never lose an election as a result of receiving too many votes in support. More formally, it says that adding more voters who prefer Alice to Bob should not cause Alice to lose the election to Bob.
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 could make the result worse for them; such voters are sometimes referred to as having negative vote weights, particularly in the context of German constitutional law, where courts have ruled such a possibility violates the principle of one man, one vote.
Positional methods and score voting satisfy the participation criterion. All deterministic voting rules that satisfy pairwise majority-rule can fail in situations involving four-way cyclic ties, though such scenarios are empirically rare, and the randomized Condorcet rule is not affected by the pathology. The majority judgment rule fails as well. Instant-runoff voting and the two-round system both fail the participation criterion with high frequency in competitive elections, typically as a result of a center squeeze.
The no-show paradox is similar to, but not the same as, the perverse response paradox. Perverse response happens when an existing voter can make a candidate win by decreasing their rating of that candidate (or vice-versa). For example, under instant-runoff voting, moving a candidate from first-place to last-place on a ballot can cause them to win.
The most common cause of no-show paradoxes is the use of instant-runoff (often called ranked-choice voting in the United States). In instant-runoff voting, a no-show paradox can occur even in elections with only three candidates, and occur in 50%-60% of all 3-candidate elections where the results of IRV disagree with those of plurality.
A notable example is given in the 2009 Burlington mayoral election, the United States' second instant-runoff election in the modern era, where Bob Kiss won the election as a result of 750 ballots ranking him in last place.
An example with three parties (Top, Center, Bottom) is shown below. In this scenario, the Center party initially wins. However, say that a group of pro-Top voters joins the election, all of whom cast their ballots with the ranking Top > Center > Bottom:
The participation criterion says that the addition of voters who prefer Center over Bottom should not cause Bottom to win. Yet the increase in support for the Top party allows it to defeat the Center party in the first round. As a result, 15 votes that previously counted toward Center now count toward their second preference, Bottom, which is enough to give Bottom the victory. This makes the election an example of a center-squeeze, a class of elections where instant-runoff and plurality have difficulty electing the majority-preferred candidate.
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Participation criterion AI simulator
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Participation criterion
The participation criterion is a voting system criterion that says candidates should never lose an election as a result of receiving too many votes in support. More formally, it says that adding more voters who prefer Alice to Bob should not cause Alice to lose the election to Bob.
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 could make the result worse for them; such voters are sometimes referred to as having negative vote weights, particularly in the context of German constitutional law, where courts have ruled such a possibility violates the principle of one man, one vote.
Positional methods and score voting satisfy the participation criterion. All deterministic voting rules that satisfy pairwise majority-rule can fail in situations involving four-way cyclic ties, though such scenarios are empirically rare, and the randomized Condorcet rule is not affected by the pathology. The majority judgment rule fails as well. Instant-runoff voting and the two-round system both fail the participation criterion with high frequency in competitive elections, typically as a result of a center squeeze.
The no-show paradox is similar to, but not the same as, the perverse response paradox. Perverse response happens when an existing voter can make a candidate win by decreasing their rating of that candidate (or vice-versa). For example, under instant-runoff voting, moving a candidate from first-place to last-place on a ballot can cause them to win.
The most common cause of no-show paradoxes is the use of instant-runoff (often called ranked-choice voting in the United States). In instant-runoff voting, a no-show paradox can occur even in elections with only three candidates, and occur in 50%-60% of all 3-candidate elections where the results of IRV disagree with those of plurality.
A notable example is given in the 2009 Burlington mayoral election, the United States' second instant-runoff election in the modern era, where Bob Kiss won the election as a result of 750 ballots ranking him in last place.
An example with three parties (Top, Center, Bottom) is shown below. In this scenario, the Center party initially wins. However, say that a group of pro-Top voters joins the election, all of whom cast their ballots with the ranking Top > Center > Bottom:
The participation criterion says that the addition of voters who prefer Center over Bottom should not cause Bottom to win. Yet the increase in support for the Top party allows it to defeat the Center party in the first round. As a result, 15 votes that previously counted toward Center now count toward their second preference, Bottom, which is enough to give Bottom the victory. This makes the election an example of a center-squeeze, a class of elections where instant-runoff and plurality have difficulty electing the majority-preferred candidate.