47 articles
2020 United States census
24th decennial U.S. population count as of April 1, 2020; apportionment population 331,108,434 (+7.1% vs 2010). Conducted during COVID-19 with internet-first response; citizenship question blocked by the Supreme Court; PES found a 0.24% net undercount.
Allan Lichtman
Allan J. Lichtman, American University historian and co-creator with Vladimir Keilis-Borok of the 13 Keys to the White House election-prediction system; called Reagan 1984 through Biden 2020, missed 2000 and 2024.
Apportionment in the European Parliament
Apportionment in the European Parliament allocates its 720 seats among EU Member States under Article 14(2) TEU: 6 to 96 seats each, degressive proportionality, European Council Decision 2023/2061, no permanent formula yet.
Apportionment paradox
Apportionment paradox: counterintuitive failures of seat-allocation methods, including the Alabama paradox, population paradox, and new-states paradox; Hamilton/largest-remainder method suffers all three while divisor methods avoid them.
Arrow's impossibility theorem
Arrow's impossibility theorem, also called the general possibility theorem from Social Choice and Individual Values, proves no ranked preference aggregation rule satisfies unrestricted domain, Pareto, non-dictatorship, and IIA for three or more alternatives.
Best Loser System
The Best Loser System is a mechanism in the Parliament of Mauritius under which up to eight unelected candidates are given seats to correct ethnic representation.
Bradley effect
Bradley effect: claimed polling bias where pre-election polls overstate support for Black candidates against white opponents, named for Tom Bradley's 1982 California gubernatorial loss; also called Wilder or Dinkins effect; evidence suggests it faded after the early 1990s.
California's congressional districts
California's 52 U.S. House districts, drawn by the independent Citizens Redistricting Commission since 2011, temporarily replaced by legislatively drawn Prop 50 maps (2026–2030) boosting Democrats from 43 toward 48 seats, effective January 2027.
Coherence (fairness)
Coherence in apportionment theory, from Balinski and Young, is the fairness requirement that a seat allocation's parts match the method's solutions for subproblems; the Coherence Theorem shows only divisor methods are coherent.
Comparison of electoral systems
Comparison of electoral systems: comparative study of plurality/majority, proportional representation, mixed, and other voting rules, their design variables (district magnitude, formula, thresholds), effects on proportionality, parties, turnout, and recent reforms in Italy, Mexico, and the UK.
Computational complexity of ranking-rule winner determination
The computational complexity of ranking-rule winner determination studies how hard it is to compute winners under the Dodgson, Young, and Kemeny voting rules, whose problems sit at or above the second level of the polynomial hierarchy.
Condorcet paradox
The Condorcet paradox is a voting situation where majorities cycle: A beats B, B beats C, and C beats A, described by Condorcet in 1785.
Congressional Apportionment Amendment
The Congressional Apportionment Amendment, Article the First of the twelve amendments proposed September 25, 1789, would have tied House size to population with districts capped at 50,000 people; it was never ratified and remains open-ended.
Connecticut Compromise
Connecticut Compromise (Great Compromise), proposed by Roger Sherman and Oliver Ellsworth, adopted July 16, 1787 by one vote; created proportional House representation and equal state representation in the Senate.
Divisor method
A divisor method, also called a highest-averages method, allocates seats by dividing each party's votes by a divisor and rounding under a fixed rule, such as Jefferson's or Webster's.
Duverger's law
Duverger's law: Maurice Duverger's 1951 proposition that single-member plurality (first-past-the-post) elections favor two-party systems, via mechanical and psychological effects, while proportional representation favors multipartyism.
Electoral system of Germany
The electoral system of Germany elects the Bundestag by personalized proportional representation, with each voter casting two votes, one for a candidate and one for a party list.
FiveThirtyEight
FiveThirtyEight (538) is a data-journalism site founded by Nate Silver in 2008, covering poll analysis, politics, economics, and sports; known for pollster ratings, polling averages, and election forecasts under NYT, ESPN, then ABC News.
Gibbard–Satterthwaite theorem
Gibbard–Satterthwaite theorem: impossibility result of Gibbard (1973) and Satterthwaite (1975) that every onto, strategy-proof voting rule over three or more alternatives is dictatorial; central to social choice and mechanism design.
Gibbard's theorem
Gibbard's theorem, also called the Gibbard–Satterthwaite theorem in its voting form, is a 1973 social choice impossibility result: every onto, non-dictatorial decision scheme with three or more outcomes is manipulable by strategic misreporting.
History of apportionment methods
The history of apportionment methods traces US House seat-allocation rules from the 1792 Hamilton-Jefferson dispute and Washington's first veto to the Alabama paradox and Hill's 1941 method.
History of social choice theory
The history of social choice theory traces how individual votes combine into collective decisions, pioneered by Borda and Condorcet in the 1780s and transformed by Arrow's 1951 impossibility theorem.
House monotonicity
House monotonicity is the apportionment requirement that no state lose seats when the house size grows; violating it causes the Alabama paradox. Hamilton's method fails it; divisor methods satisfy it but violate quota.
Independence of irrelevant alternatives
Independence of irrelevant alternatives (IIA): a voting or aggregation criterion requiring the social ranking of any two options to depend only on individual rankings of that pair. Central to Arrow's 1951 impossibility theorem; violated by plurality, Borda, and IRV, satisfied by pairwise majority.
List of United States congressional districts
US congressional districts: the 435 single-member areas electing House representatives, drawn by states after census apportionment, equal in population as practicable; covers numbering, the 119th Congress set, and 2025-2026 mid-decade redistricting.
May's theorem
May's theorem is a 1952 result in social choice theory: simple majority rule is the only two-alternative voting rule that is anonymous, neutral, and positively responsive.
McKelvey–Schofield chaos theorem
McKelvey–Schofield chaos theorem: a social choice result (McKelvey 1976, 1979; Schofield 1978, 1985) that with an empty majority-rule core, agenda-controlled pairwise votes can lead from any policy point to any other.
Median voter theorem
Median voter theorem: with single-peaked preferences on one policy dimension, majority rule selects the median voter's ideal point (Black 1948); Downsian candidates converge there, but multidimensional, probabilistic, and empirical settings often break the result.
Nakamura number
The Nakamura number of a simple voting game is the smallest number of winning coalitions with an empty intersection, taken as infinite when a vetoer exists.
One man, one vote
One man, one vote (one person, one vote) is the equal-suffrage principle requiring roughly equal voting power per person, enforced in US law by Baker v. Carr, Gray v. Sanders, Wesberry v. Sanders, and Reynolds v. Sims (1962–1964).