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Pathological behavior by an apportionment rule
example of the apportionment paradox known as "the Alabama paradox" was discovered in the context of United States congressional apportionment in 1880, when
Apportionment_paradox
Way to distribute seats in a legislative body
related to apportionment. The apportionment by country page describes the specific practices used around the world. The mathematics of apportionment page describes
Apportionment_(politics)
List of statements that appear to contradict themselves
wanted to do. Apportionment paradox: Some systems of apportioning representation can have unintuitive results due to rounding Alabama paradox: Increasing
List_of_paradoxes
Mathematical principles
an apportionment problem involves distributing seats in a legislature between different federal states or political parties. However, apportionment methods
Mathematics_of_apportionment
Proportional-representation voting system
called apportionment paradoxes: Increasing the number of seats in a legislature can decrease a party's apportionment of seats, called the Alabama paradox. Adding
Largest_remainder_method
Self-contradiction of majority rule
social choice theory, Condorcet's voting paradox (also called Condorcet's paradox or the Condorcet paradox) is a fundamental discovery by the Marquis
Condorcet_paradox
Rule in math and political science
proved in 1980 that if an apportionment method satisfies the quota rule, it must fail to satisfy some apportionment paradox. For instance, although largest
Quota_rule
Plurality voting system
Maisano, Domenico A. (2022-06-01). "Analysing paradoxes in design decisions: the case of "multiple-district" paradox". International Journal on Interactive Design
First-past-the-post_voting
Election result affecting losing candidate
method of party-list representation, where it is called the new states paradox. A new party entering an election causes some seats to shift from one unrelated
Spoiler_effect
Property of apportionment methods
state. Some earlier apportionment rules, such as Hamilton's method, do not satisfy VRM, and thus exhibit the population paradox. For example, after the
Vote-ratio_monotonicity
How 435 seats are distributed to 50 states
Huntington–Hill method became the official method of apportionment and was used in the 2020 apportionment and redistricting cycle. The current method solves
United States congressional apportionment
United_States_congressional_apportionment
Criterion for evaluating rules for fair division
first studied in the context of apportionment. In this context, failure to satisfy coherence is called the new states paradox: when a new U.S. state enters
Coherence_(fairness)
Logically self-contradictory statement
A paradox is a logically self-contradictory statement or a statement that runs contrary to expectations. It is a statement that, despite apparently valid
Paradox
Multi-winner electoral system
so called lower apportionment the seats are distributed to the regional party list respecting the results from the upper apportionment. This can be seen
Biproportional_apportionment
Theorem in political science
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Median_voter_theorem
Criterion for evaluating fairness of electoral systems
some rounding method should be used, and this can be done by various apportionment methods. In recent years, there is a growing dissatisfaction with the
Justified_representation
Principle that voting for a candidate should help them
McCune, David; Wilson, Jennifer (2019-01-01). "The elimination paradox: apportionment in the Democratic Party". Public Choice. 178 (1): 53–65. doi:10
Participation_criterion
Proof all ranked voting rules have spoilers
This result was first shown by the Marquis de Condorcet, whose voting paradox showed the impossibility of logically-consistent majority rule; Arrow's
Arrow's_impossibility_theorem
Agreement by all people in a situation
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Unanimity
Rule for proportional allocation
metrics and are less susceptible to apportionment paradoxes. In particular, divisor methods avoid the population paradox and spoiler effects, unlike the largest
Highest_averages_method
Electoral pathology or paradox
said to exhibit negative response, perversity, or an additional support paradox. Perversity is often described by social choice theorists as an exceptionally
Non-negative_responsiveness
Single-winner electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
STAR_voting
Spoiler effect in RCV and two-round systems
Peltola no support at all. The election was also notable as a no-show paradox, where a candidate is eliminated as a result of votes cast in support of
Center_squeeze
Voting systems that use ranked ballots
Gallagher, Michael. "Comparing P.R. Electoral Systems. Quotas, Thresholds, Paradoxes, Majorities" (PDF). "How Ireland's local elections work". May 23, 2024
Ranked_voting
discursive dilemma or doctrinal paradox is a paradox of social choice and judgement aggregation. It extends the voting paradox and Arrow's theorem to situations
Doctrinal_paradox
Top-two primary election
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Nonpartisan_primary
Voting requirement above 50% for passage
requirement for 50% turnout has also been criticized for causing no-show paradoxes. In 2016, the Constitution of Colorado was amended to require a 55% majority
Supermajority
Study of rational collective decision-making
small, found 25 instances of a Condorcet paradox for a total likelihood of 9.4%. While examples of the paradox seem to occur often in small settings like
Social_choice_theory
Type of chart used to display election results of a plenary body
election apportionment diagram closely mirroring the actual seating layout of the United States House of Representatives An election apportionment diagram
Election apportionment diagram
Election_apportionment_diagram
Election that narrows the field of candidates before an election for office
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Primary_election
2002 book by George Tsebelis
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Veto_Players
Proportional-representation electoral system
Different apportionment methods, of which the Sainte-Laguë method is one, exist to distribute the seats according to the votes. Different apportionment methods
Sainte-Laguë_method
Method by which voters make a choice between options
results using votes cast in the district and elsewhere. Biproportional apportionment is a system where the total number of votes is used to calculate the
Electoral_system
Single-winner ranked voting rule
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Coombs'_method
Method to make collective decisions
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Voting
Electoral district with one representative in a legislature
by the People of the several States ... Representatives ... shall be apportioned among the several States which may be included within this Union, according
Single-member_district
Selection of decision-makers by random sample
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Sortition
Property of electoral systems
other (rock < paper < scissors < rock). This is called Condorcet's voting paradox, and is analogous to the counterintuitive intransitive dice phenomenon
Condorcet_winner
Proportional electoral system
"Computing Apportionment". United States Census Bureau. Retrieved 2021-04-26. Pukelsheim, Friedrich (2017), "Divisor Methods of Apportionment: Divide and
Huntington–Hill_method
Number of votes a candidate needs to win
(2017), "Quota Methods of Apportionment: Divide and Rank", in Pukelsheim, Friedrich (ed.), Proportional Representation: Apportionment Methods and Their Applications
Electoral_quota
Set preferred to any other by a majority
because of pairwise ties or because of cycles, such as in Condorcet's paradox. The Condorcet winner, if one exists, is the sole member of the Smith set
Smith_set
Type of block voting
General ticket system was common until limited to special use by the 1842 Apportionment Bill and locally implementing legislation which took effect after the
General_ticket
Collective decision-making procedure
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Quadratic_voting
Single-winner electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Nanson's_method
Type of multi-winner plurality/majority electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Block_voting
Voting system that makes outcomes proportional to vote totals
compensatory seats (e.g., mixed-member proportional representation apportionment methods). A legislative body such as an assembly or parliament may be
Proportional_representation
Method of voting
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Mixed ballot transferable vote
Mixed_ballot_transferable_vote
Electoral systems with independent candidate ratings
running fails independence of irrelevant alternatives due to the Condorcet paradox. In addition, there are many different proportional cardinal rules, often
Rated_voting
Votes that do not impact an election
and the Mobilization of Swing Voters, Gul Akdag, 2014 Partisan and apportionment bias in creating a predominant party system, Ali Çarkoğlu, Deniz Aksen
Wasted_vote
Family of voting systems
irrelevant, seat apportionment being calculated at national level. List proportional representation may also be combined with other apportionment methods in
Party-list proportional representation
Party-list_proportional_representation
Votes required to win a seat in proportional systems
Matters (24): 3–6. Pukelsheim, Friedrich (2017). "Quota Methods of Apportionment: Divide and Rank". Proportional Representation. pp. 95–105. doi:10
Droop_quota
Single-winner electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Approval_voting
congressional district Apportionment United States congressional apportionment General ticket Redistricting Apportionment paradox Gerrymandering Voting
List of United States congressional districts
List_of_United_States_congressional_districts
Topics referred to by the same term
Formulary apportionment, a method of allocating corporate taxation between jurisdictions Fair division, in game theory Apportionment paradox, various paradoxical
Apportionment (disambiguation)
Apportionment_(disambiguation)
Phenomenon in electoral systems
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Overhang_seat
Single-winner ranked-voting electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Contingent_vote
Type of mixed electoral system
received in the party portion of the ballot. This can be done by different apportionment methods: such as the D'Hondt method or the Sainte-Laguë method. Subtracted
Mixed-member proportional representation
Mixed-member_proportional_representation
Semi-proportional representation system
distortions of proportional systems. Using an electoral threshold or an apportionment method favoring large parties would give an even larger bonus to the
Majority_bonus_system
Electoral or law making voting system
towards larger states (unlike a simple popular vote)[citation needed]. Apportionment in the European Parliament Corporatism Degressive proportionality Demeny
Weighted_voting
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
List_of_electoral_systems
Grouping of candidates for election
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Electoral_list
Single-winner electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Ranked_pairs
Type of electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Plurality_voting
Single-winner ranked-choice voting system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Dodgson's_method
Theoretical rule in social choice theory
support from a majority in every subelection, that candidate may lose. Paradox of voting Random ballot Game Theory Second Edition Guillermo Owen Ch 6
Dictatorship_mechanism
Variant of party-list voting system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Closed_list
Voting system
squeeze (a kind of spoiler effect favoring extremists) and the no-show paradox. This has led to the rise of electoral reform movements which seek to replace
Two-round_system
Electoral lists used for gender parity
the zipper system, based on the fair share sequence, biproportional apportionment, and other rules can enforce gender quotas much more precisely, while
Zipper_system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Tournament_solution
Political process
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Political_fragmentation
Technique used for elections
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Localized_list
Individual voter's first choice
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
First-preference_vote
Result in social choice theory
Us from the Plurality Vote". Disposing dictators, demystifying voting paradoxes: social choice analysis. Cambridge, New York: Cambridge University Press
McKelvey–Schofield chaos theorem
McKelvey–Schofield_chaos_theorem
Multiple-winner electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Cumulative_voting
Form of voting that allows delegation
Retrieved 2010-03-18. Russell Neuman, W.; Neuman, W. R. (1986). The paradox of mass politics. Harvard University Press. ISBN 978-0-674-65460-0. Retrieved
Proxy_voting
Electoral system with lottery among ballots
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Random_ballot
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Block_preferential_voting
Tool used to make legislatures more proportional
seats and 6 adjustment seats. Additional Member System Biproportional apportionment Mixed-member proportional representation "Tillægsmandater". Den Store
Leveling_seat
Pairwise-comparison electoral system
lose to "rock". The possibility of such a cycle is known as Condorcet's paradox. (Empirically, however, such cycles are rare, with most large public elections
Condorcet_method
Non-proportional electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Plurality_block_voting
Method of holding two elections with one vote
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Double_simultaneous_vote
Proposed governance system based on election votes
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Interactive_representation
Voting systems using paired comparisons
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Round-robin_voting
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Batch_summability
Multi-winner electoral system
"Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities". British Journal of Political Science. 22 (4): 469–496
Single_transferable_vote
Class of voting systems
Mingsheng (2007-06-25). "Sequential voting rules and multiple elections paradoxes". Proceedings of the 11th conference on Theoretical aspects of rationality
Sequential_elimination_method
Semi-proportional electoral system
dual-member districts the system uses. Within these districts, the apportionment method (between parties, not candidates) is technically proportional
Binomial_voting_system
Function that ranks states of society according to their desirability
welfare Extended sympathy Gorman polar form Justice (economics) Liberal paradox Production-possibility frontier Social choice theory Social policy Welfare
Social_welfare_function
Property of electoral systems
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Majority_winner_criterion
Single-winner ranked-choice electoral system
Ray, Depankar (1986). "On the practical possibility of a 'no show paradox' under the single transferable vote". Mathematical Social Sciences. 11
Instant-runoff_voting
Impossibility of straightforward game forms
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Gibbard's_theorem
Mixed electoral system with compensation
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Alternative_vote_plus
Multiple-winner electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Limited_voting
Personalized list proportional voting system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Open_list
Electoral system quota formula
(2017), "Quota Methods of Apportionment: Divide and Rank", in Pukelsheim, Friedrich (ed.), Proportional Representation: Apportionment Methods and Their Applications
Hare_quota
Single-winner electoral system
procedures for electing a single candidate : proving their (in)vulnerability to various voting paradoxes. Cham, Switzerland: Springer. ISBN 978-3-319-74033-1.
Black's_method
Single-winner electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Schulze_method
Mixed electoral system
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Parallel_voting
Decision rule that selects alternatives that have a majority
B (rank A over B), then A should defeat B unless there is a Condorcet paradox. A common alternative to the majority rule is the plurality-rule family
Majority_rule
Combination of direct and representative democracy
Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting
Liquid_democracy
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