Sequential proportional approval voting
electoral system that extends the concept of approval voting to a multiple winner election, proposed by Thorvald N. Thiele in the early 1900s
Sequential proportional approval voting (SPAV) or reweighted approval voting (RAV) 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. It was used in Sweden from 1909 to 1921, when it was replaced by a "party-list" style system, and is still used for some local elections.
Description
Sequential proportional approval voting uses approval voting ballots to elect multiple winners on a round-by-round basis. With approval voting ballots, each voter may support any number of candidates on their ballot as they see fit. For tabulation, each ballot is weighted according to a formula, the candidate with the most support is elected, and the process is repeated until there are no more seats to fill.
The aforementioned formula for each ballot in a given round is as follows:
W
=
1
E
+
1
{\displaystyle W={\frac {1}{E+1}}}
where
E
{\displaystyle E}
is the number of candidates approved on that ballot who were elected in the previous rounds, and
W
{\displaystyle W}
is its weight. For the first round,
E
{\displaystyle E}
is naturally 0, and so each ballot has a weight of 1.
Example
As a clarifying example, consider an election for a committee with three winners.
Begin with the source’s own compact description: “Sequential proportional approval voting” is electoral system that extends the concept of approval voting to a multiple winner election, proposed by Thorvald N. Thiele in the early 1900s. The dossier treats that line as a proposition to test through Sequential, proportional and approval, not as a finished interpretation.
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The record creator and administrative purpose are central evidence, because official documentation reflects both action and institutional priorities. The source revision retrieved here is dated Jul 1, 2026. The linked authority identifier is Q25303915. The first chronological checks are 1909 and 1921.
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