Largest remainders method

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Largest remainders method" – news · newspapers · books · scholar · JSTOR (November 2011) (Learn how and when to remove this message)

Part of the Politics and Economics series
Electoral systems
Comparison of electoral systems Social choice theory Mechanism design List (By country)
Single-winner methods Single vote-runoff methods Plurality (FPP) Two-round (US: Jungle primary) Partisan primary Alternative vote (US: Ranked-choice) Condorcet-IRV Condorcet methods Ranked pairs Schulze Minimax Kemeny–Young Nanson Condorcet-IRV Maximal lottery Positional voting First-preference plurality Borda count Anti-plurality voting Cardinal / graded methods Score voting Approval voting Majority judgment STAR voting Quadratic voting
Proportional representation Party-list List type Open list Closed list Localized list Spare vote Apportionment Highest averages Largest remainders National remnant Biproportional apportionment Single transferable vote (Quota methods) Hare STV (Gregory · Wright) Schulze STV CPO-STV Single non-transferable vote Single divisible vote Approval-based committee Thiele's method Phragmen's method Expanding approvals rule Method of equal shares Weighted and Fractional social choice Direct representation Interactive representation Liquid democracy Maximal lottery
Mixed systems By type of representation Winner-take-most Mixed-member proportional Non-compensatory mixed systems Parallel voting Majority bonus Compensatory mixed systems Additional member system Mixed single vote Scorporo Double simultaneous vote Mixed ballot transferable vote Alternative Vote Plus Dual-member proportional Rural–urban proportional
Voting system criteria Spoiler-resistance Condorcet criterion Smith independence Spoiler independence Clone independence Strategy-resistance No lesser evil voting IIA Later-no-harm Later-no-help Rational response Participation criterion Monotonicity criterion Reversal symmetry
Social and collective choice Impossibility theorems Arrow's theorem Impossibility of majority-rule Moulin's impossibility theorem Gibbard's theorem Fishburn's theorem Positive results Median voter theorem Condorcet's jury theorem May's theorem Campbell-Kelly theorem Harsanyi's utilitarian theorem Tournament sets Smith set Landau set Copeland set Split-cycle set Bipartisan set Tournament solution
Politics portal Economics portal
v t e

The largest remainder methods or quota methods are methods of allocating seats proportionally that are based on calculating a quota, i.e. a certain number of votes needed to be guaranteed a seat in parliament. Then, any leftover seats are handed over to "plurality" winners (the parties with the largest remainders, i.e. the most "leftover" votes).^[1] They are typically contrasted with the more popular highest averages methods (also called divisor methods).^[2]

Divisor methods are generally preferred by social choice theorists to the largest remainder methods because they are less susceptible to apportionment paradoxes.^[2][3] In particular, divisor methods satisfy population monotonicity, i.e. voting for a party can never cause it to lose seats.^[3] Such population paradoxes occur by increasing the electoral quota, which can cause different states' remainders to respond erratically.^[4] Divisor methods also satisfy resource or house monotonicity, which says that increasing the number of seats in a legislature should not cause a state to lose a seat (a situation known as an Alabama paradox).^{[3][4]: Cor.4.3.1}

When using the Hare quota, the method is known as the Hare–Niemeyer or Hamilton method.