Droop quota

Social choice and electoral systems
A joint Politics and Economics series

Social choice Mechanism design Comparative politics Comparison List (By country)
Single-winner methods Single vote - plurality methods First preference plurality (FPP) Two-round (US: Jungle primary) Partisan primary Instant-runoff UK: Alternative vote (AV) US: Ranked-choice (RCV) Party block voting Plurality block voting Condorcet methods Condorcet-IRV Round-robin voting Minimax Schulze Ranked pairs Maximal lottery Positional voting Plurality (el. IRV) Borda count (el. Baldwin, Mdn. Bucklin) Antiplurality (el. Coombs) Cardinal voting Score voting Approval voting Majority judgment STAR voting
Proportional representation Party-list Apportionment Highest averages Largest remainders National remnant Biproportional List type Closed list Open list Panachage List-free PR Localized list Quota-remainder methods Hare STV Schulze STV CPO-STV Quota Borda Approval-based committees Thiele's method Phragmen's method Expanding approvals rule Method of 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 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 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 VCG mechanism Quadratic voting
Politics portal Economics portal Mathematics portal

In the study of electoral systems, the Droop quota (sometimes called the Hagenbach-Bischoff, Britton, or Newland-Britton quota) is the minimum number of votes a party or candidate needs to receive in a district to guarantee they will win at least one seat.

The Droop quota is used to extend the concept of a majority to multiwinner elections, taking the place of the 50% bar in single-winner elections. Just as any candidate with more than half of all votes is guaranteed to be declared the winner in single-seat election, any candidate with more than a Droop quota's worth of votes is guaranteed to win a seat in a multiwinner election.

Besides establishing winners, the Droop quota is used to define the number of excess votes, i.e. votes not needed by a candidate who has been declared elected. In proportional quota-based systems such as STV or expanding approvals, these excess votes can be transferred to other candidates to prevent them from being wasted.

The Droop quota was first suggested by the English lawyer and mathematician Henry Richmond Droop (1831–1884) as an alternative to the Hare quota.

Today, the Droop quota is used in almost all STV elections, including those in Australia, the Republic of Ireland, Northern Ireland, and Malta. It is also used in South Africa to allocate seats by the largest remainder method.

Although common, the quota's use in proportional representation has been criticized both for its bias toward large parties and for its ability to create no-show paradoxes, situations where a candidate or party loses a seat as a result of having won too many votes. This occurs regardless of whether the quota is used with largest remainders or STV.