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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) 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
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Sequential proportional approval voting (SPAV) or reweighted approval voting (RAV)^[1] is an electoral system that extends the concept of approval voting to a multiple winner election. It is a simplified version of proportional approval voting. It is a special case of Thiele's voting rules, proposed by Danish statistician Thorvald N. Thiele in the early 1900s.^[2] It was used (with adaptations for party lists) in Sweden from 1909 to 1921, when it was replaced by a cruder "party-list" style system as it was easier to calculate,^[3]^[4] and is still used for some local elections.

^ Brams, Steven; Brill, Markus (2018). "The Excess Method: A Multiwinner Approval Voting Procedure to Allocate Wasted Votes". SSRN Electronic Journal. doi:10.2139/ssrn.3274796. ISSN 1556-5068. S2CID 53600917.
^ E. Phragmén (1899): "Till frågan om en proportionell valmetod." Statsvetenskaplig tidskrifts Vol. 2, No. 2: pp 87-95 [1] Archived 2015-06-18 at the Wayback Machine
^ Lewis, Edward G. (1950). "Review of Modern Foreign Governments". The American Political Science Review. 44 (1): 209–211. doi:10.2307/1950372. ISSN 0003-0554. JSTOR 1950372. S2CID 152254976.
^ Humphreys, John H. (2006-01-01). Proportional Representation: A Study in Methods of Election. Archived from the original on 2022-05-11. Retrieved 2022-05-11.