Sequential proportional approval voting

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. Proposed by Danish statistician Thorvald N. Thiele in the early 1900s, it was used (with adaptations for party lists) in Sweden for a short period after 1909.

This system converts AV into a multi-round rule, selecting a candidate in each round and then reweighing the approvals for the subsequent rounds. The first candidate elected is the AV winner (w₁). The value of all ballots that approve of w₁ are reduced in value from 1 to 1/2 and the approval scores recalculated. Next, the unelected candidate who has the highest approval score is elected (w₂). Then the value of ballots that approve of w₁ and w₂ are reduced in value to 1/3, and the value of all ballots that approve of either w₁ or w₂ but not both are reduced in value to 1/2.

At each stage, the unelected candidate with the highest approval score is elected. Then the value of each voter’s ballot is set at 1/(1+m) where m is the number of candidates approved on that ballot who were already elected, until the required number of candidates is elected.

The system disadvantages minority groups who share some preferences with the majority. In terms of tactical voting, it is therefore highly desirable to withhold approval from candidates who are likely to be elected in any case, as with cumulative voting and the single non-transferable vote.

It is however a much computationally simpler algorithm than Proportional approval voting, permitting votes to be counted either by hand or by computer, rather than requiring a computer to determine the outcome of all but the simplest elections.

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