Quota Borda system

A joint Politics and Economics series
Social choice and electoral systems
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) Condorcet methods Condorcet-IRV Round-robin voting Minimax Schulze Ranked pairs Maximal lottery Positional voting Plurality (el. IRV) Borda count (el. Baldwin) 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 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
Politics portal Economics portal Mathematics portal
v t e

The Quota Borda system or quota preference score is a voting system that was devised by the British philosopher Michael Dummett and first published in 1984 in his book, Voting Procedures, and again in his Principles of Electoral Reform.

If proportionality is required in a Borda count election, a quota element should be included into the counting procedure, which works best in multi-member constituencies of either 4 or 6 members. The threshold used is the Droop quota; in a single-seat constituency, the quota is an absolute majority, i.e., more than half of the valid vote; in a 2-seat constituency, it is the smallest number more than a third; in a 3-seat, it's the smallest number more than one fourth; and in a 4-seat constituency, it is the smallest number greater than one fifth of the valid vote.

The four-seat selection goes as follows;

1. Any candidate gaining a quota of 1st preferences is elected.
2. Any pair of candidates gaining 2 quotas is elected. (A pair of candidates, Ms J and Mr M, say, gains 2 quotas when that number of voters vote either 'J-1, M-2' or 'M-1, J-2'.) If seats still remain to be filled, then, ignoring all those candidates who have already been elected;
3. Any pair of candidates gaining 1 quota gains 1 seat, and the seat is given to the candidate of that pair who has the higher Modified Borda Count score.
4. Any seats still remaining are given to those candidates with the highest Modified Borda Count scores.^[1][2]