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f equal shares fractional social choice direct representation interactive representation liquid democracy fractional approval voting maximal lottery random ballot semi proportional representation cumulative sntv limited voting mixed systems by results of combination mixed member majoritarian mixed member proportional by mechanism of combination non compensatory parallel superposition coexistence conditional fusion majority bonus compensatory seat linkage system uk ams nz mmp vote linkage system negative vote transfer mixed ballot supermixed systems dual member mixed proportional rural urban proportional majority jackpot by ballot type single vote double simultaneous vote dual vote paradoxes and pathologies spoiler effects spoiler effect cloning paradox frustrated majorities paradox center squeeze pathological response perverse response apportionment paradox best is worst paradox no show paradox multiple districts paradox strategic voting lesser evil voting exaggeration truncation turkey raising wasted vote paradoxes of majority rule tyranny of the majority discursive dilemma conflicting majorities paradox social and collective choice impossibility theorems arrow s theorem majority impossibility moulin s impossibility theorem mckelvey schofield chaos theorem gibbard s theorem positive results median voter theorem condorcet s jury theorem may s theorem condorcet dominance theorems harsanyi s utilitarian theorem non classical mechanisms vcg mechanism quadratic voting supermajority unanimity politics portal economics portal mathematics portal v t e 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 1 2 more formally it says that adding more voters who prefer alice to bob should not cause alice to lose the election to bob 3 voting systems that fail the participation criterion exhibit the no show paradox 4 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 5 6 7 positional methods and score voting satisfy the participation criterion all deterministic voting rules that satisfy pairwise majority rule 4 8 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 9 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 1 2 10 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 de creasing 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 11 noncompliant methods edit instant runoff ranked choice voting edit see also center squeeze 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 11 and occur in 50 60 of all 3 candidate elections where the results of irv disagree with those of plurality 10 2 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 12 failed verification 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 baseline more votes ranking center bottom round 1 round 2 round 1 round 2 top 25 n 6 top 31 46 center 30 55 y center 30 n bottom 39 39 bottom 39 54 y 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 13 condorcet methods edit 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 4 however with more than 3 candidates hervé moulin proved that every deterministic condorcet method can sometimes fail participation 4 8 similar incompatibilities have also been shown for set valued voting rules 8 14 15 the randomized condorcet rule satisfies the criterion but fails the closely related monotonicity criterion in situations with condorcet cycles 16 studies suggest such failures may be empirically rare however one study surveying 306 publicly available election datasets found no participation failures for methods in the ranked pairs minimax family 17 in addition to participation an even more severe paradox property can occur with condorcet s principle it may be better for a voter to submit a completely reversed ballot than to submit a ballot that ranks all candidates honestly 18 19 implementations of proportional representation edit some proportional representation systems allow for no show paradoxes rules based on the droop quota including all current implementations of the single transferable vote allow for no show paradoxes 5 20 hamilton s method exhibits a milder form of the paradox called the population paradox but does not have a true no show paradox however adding an electoral threshold produces a no show paradox 21 in germany edit 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 negative voting weights 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 npd of germany who argued the election law was unconstitutionally undemocratic 22 the federal constitutional court agreed with the plaintiffs ruling that negative vote weights violate the german constitution s guarantee of equal and direct suffrage the majority wrote that 6 7 a seat allocation procedure that allows an increase in votes to lead to a loss of seats or results in more seats being won if proportionally fewer votes are cast for it contradicts the meaning and purpose of a democratic election such nonsensical relationships between voting and electoral success not only impair the equality of the right to vote and the equal opportunities of the parties but also the principle of a popular election as it is no longer apparent to the voter how their vote results in the success or failure of a candidate 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 to what extent this is true can be set aside as such arbitrary results make a mockery of the democratic competition for support from the electorate the ruling forced the bundestag to abandon its old practice of ignoring overhang seats and instead adopt a new system of compensation involving leveling seats 22 quorum requirements edit a common cause of no show paradoxes is the use of a quorum for example if a public referendum requires 50 turnout to be binding additional no votes may push turnout above 50 causing the measure to pass a referendum that instead required a minimum number of yes votes e g 25 of the population voting yes would pass the participation criterion 23 many representative bodies have quorum requirements where the same dynamic can be at play for example the requirement for a two thirds quorum in the oregon legislative assembly effectively creates an unofficial two thirds supermajority requirement for passing bills and can result in a law passing if too many senators turn out to oppose it 24 deliberate ballot spoiling strategies have been successful in ensuring referendums remain non binding as in the 2023 polish referendum manipulation edit 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 4 this can be particularly effective for encouraging honest voting if voters exhibit loss aversion rules with no show paradoxes do not always allow voters to cast a sincere vote for example a sincere palin begich peltola voter in the 2022 alaska special election would have been better off if they had not shown up at all rather than casting an honest 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 25 quorum busting edit this section is an excerpt from quorum quorum busting edit quorum busting also known as a walkout is a tactic that prevents a legislative body from attaining a quorum and can be used by a minority group seeking to block the adoption of some measure they oppose this generally only happens where the quorum is a super majority as quorums of a majority or less of the membership mean that the support of a majority of members is always sufficient for the quorum as well as for passage rules to discourage quorum busting have been adopted by legislative bodies such as the call of the house outlined above quorum busting has been used for centuries for instance in 1840 during his time in the illinois legislature abraham lincoln leapt out of a first story window the doors of the capitol had been locked to prevent legislators from fleeing in a failed attempt to prevent a quorum from being present 26 examples edit majority judgment edit main article majority judgment this example shows that majority judgment violates the participation criterion assume two candidates a and b with 5 potential voters and the following ratings candidates of voters a b excellent good 2 fair poor 2 poor good 1 the two voters rating a excellent are unsure whether to participate in the election voters not participating edit assume the 2 voters would not show up at the polling place the ratings of the remaining 3 voters would be candidates of voters a b fair poor 2 poor good 1 the sorted ratings would be as follows candidate median point a b excellent good fair poor result a has the median rating of fair and b has the median rating of poor thus a is elected majority judgment winner voters participating edit now consider the 2 voters decide to participate candidates of voters a b excellent good 2 fair poor 2 poor good 1 the sorted ratings would be as follows candidate median point a b excellent good fair poor result a has the median rating of fair and b has the median rating of good thus b is the majority judgment winner condorcet methods edit this example shows how condorcet methods can violate the participation criterion when there is a preference paradox assume four candidates a b c and d with 26 potential voters and the following preferences preferences of voters a d b c 8 b c a d 7 c d b a 7 this gives the pairwise counting method pairwise election results x y a b c d a 14 8 14 8 7 15 b 8 14 7 15 15 7 c 8 14 15 7 8 14 d 15 7 7 15 14 8 pairwise results for x won tied lost 1 0 2 2 0 1 2 0 1 1 0 2 the sorted list of victories would be pair winner a 15 vs d 7 a 15 b 15 vs c 7 b 15 b 7 vs d 15 d 15 a 8 vs b 14 b 14 a 8 vs c 14 c 14 c 14 vs d 8 c 14 result a d b c and d b are locked in and the other three can t be locked in after that so the full ranking is a d b c thus a is elected ranked pairs winner voters participating edit now assume an extra 4 voters in the top row decide to participate preferences of voters a b c d 4 a d b c 8 b c a d 7 c d b a 7 the results would be tabulated as follows pairwise election results x y a b c d a does not appear 14 12 14 12 7 19 b 12 14 does not appear 7 19 15 11 c 12 14 19 7 does not appear 8 18 d 19 7 11 15 18 8 does not appear pairwise results for x won tied lost 1 0 2 2 0 1 2 0 1 1 0 2 the sorted list of victories would be pair winner a 19 vs d 7 a 19 b 19 vs c 7 b 19 c 18 vs d 8 c 18 b 11 vs d 15 d 15 a 12 vs b 14 b 14 a 12 vs c 14 c 14 result a d b c and c d are locked in first now d b can t be locked in since it would create a cycle b c d b finally b a and c a are locked in hence the full ranking is b c a d thus b is elected ranked pairs winner by adding a set of voters who prefer a to b see also edit consistency criterion property of electoral systems electoral system method by which voters make a choice between options non negative responsiveness electoral pathology or paradox references edit 1 2 doron gideon kronick richard 1977 single transferrable vote an example of a perverse social choice function american journal of political science 21 2 303 311 doi 10 2307 2110496 issn 0092 5853 jstor 2110496 1 2 3 ray depankar 1986 04 01 on the practical possibility of a no show paradox under the single transferable vote mathematical social sciences 11 2 183 189 doi 10 1016 0165 4896 86 90024 7 issn 0165 4896 woodall douglas december 1994 properties of preferential election rules voting matters issue 3 december 1994 1 2 3 4 5 moulin hervé 1988 06 01 condorcet s principle implies the no show paradox journal of economic theory 45 1 53 64 doi 10 1016 0022 0531 88 90253 0 1 2 3 pukelsheim friedrich 2014 proportional representation apportionment methods and their applications internet archive cham new york springer isbn 978 3 319 03855 1 1 2 dpa 2013 02 22 bundestag beschließt neues wahlrecht die zeit in german issn 0044 2070 retrieved 2024 05 02 1 2 bverfg urteil des zweiten senats 3 july 2008 2 bvc 1 07 2 bvc 7 07 rn 1 145 121 bverfge 2 bvc 1 07 2 bvc 7 07 bverfg 03 july 2008 ecli de bverfg 2008 cs20080703 2bvc000107 1 2...