Score cascading vote

Score Cascading Vote (SCV) is a proportional cardinal voting method that is designed to incentivize voters to give nonzero scores to a large number of candidates while also having the lower levels of support still be influential. SCV uses scoring ballots, presumably on a 0-5 scale, and its tabulation algorithm is similar to Single Transferable Vote but with different rules for elimination and with the rules for electing a candidate generalized to allow for equal scores.

Tabulation

The Droop quota is used to determine how many votes are needed for a candidate to be elected. Each voter gets one vote. At each point in tabulation, voters that have yet to use their votes will offer a vote to each of the highest-scored remaining candidates on their ballots. (Unless there are no remaining candidates who received a positive score, in which case the ballot’s vote is exhausted.) For example, if a ballot scores Candidate A at 5 stars, and B and C at 4 stars, at first the voter offers a vote only to Candidate A, but if A is eliminated then the offered vote will “cascade” down to both B and C, each of whom is offered a full vote. Tabulation proceeds in rounds in which either a candidate is elected or a candidate is eliminated.

• If any of the remaining candidates have a full Droop quota of votes being offered to them, whichever of these candidates has the highest score, across all ballots, is elected. The candidate receives the votes of a Droop quota of the voters who offered them a vote, such that these voters cannot offer votes in future rounds.
• Otherwise, the candidate with the lowest score across all ballots is eliminated. Voters who preferred that candidate over all other non-elected, non-eliminated candidates will have their offered votes cascade down to the next highest score at which there are any remaining candidates.

Tabulation continues until either all the seats have been filled or the number of non-eliminated candidates equals the number of seats to fill, in which case all of the remaining candidates are elected.

Note that the steps which care about the scores across all ballots do not distinguish between ballots that have and have not used their votes. The score totals only need to be calculated once, at the start of tabulation.

Surplus Handling

If a winning candidate is offered more votes than the Droop quota, the surplus can be handled via any mechanism used for surplus handling under Single Transferable Vote.

Criteria

SCV passes Proportionality for Solid Coalitions and is clone-proof. It fails Monotonicity and Later-No-Harm.

Strategy

Free riding is less incentivized than with most candidate-based proportional voting methods because every voter’s scores remain equally influential throughout tabulation, regardless of whether their votes go to the first winner or remain unspent until the final round. Woodall free riding is more costly under SCV than STV because using Woodall free riding under SCV requires giving 5 stars only to non-viable candidates, leaving a smaller range of scores to differentiate the viable candidates. (As with STV, Woodall free riding can be made completely ineffective by using Meek transfers.)

Unlike other proportional cardinal voting methods like Allocated Score and Sequentially Spent Score, SCV ensures that voters have no risk of going into a candidate’s quota in a way that prevents them from filling the quota of a candidate they like more. The major strategic considerations under SCV are to:

• Give different scores to the most-liked candidates so that you won’t spend your vote on a candidate who you don’t think is excellent unless your favorite(s) have been elected or eliminated.
• Exaggerate the scores towards 0 and 5 in order to have the scores on your ballot be maximally influential.
• If there are coherent factions and you have significant preferences as to who wins in factions other than your own that are highly likely to win at least one seat, it helps to exaggerate the scores within each faction, e.g. by giving a relatively tolerable candidate within a disliked faction 3 stars and other candidates in that faction 0 stars. However, taking this strategy to the point of dishonesty risks helping less-liked factions in the final round.

Design considerations

SCV was inspired by the observation that the STV algorithm still yields proportional representation no matter what algorithm is used to determine which candidates to eliminate. Score has the advantage of simplicity; another approach would have been to use a ranked ballot and to use some Condorcet method to determine eliminations.

There are several motivations behind the choice to use the same scores throughout tabulation instead only the scores on ballots that have not already spent their votes. First, it is simpler not to have to recalculate the scores every time a candidate is elected. Second, using the scores on all the ballots is fairer; it means that a voter whose vote goes toward the first winner has as much influence over which candidates get eliminated as a voter whose vote ends up going to the final winner. This fairness also removes a major incentive for free riding. However, using the same scores throughout tabulation necessitates the use of the Droop quota instead of the Hare quota; under the Hare quota, a faction that comprised a majority of the elected and had N quotas worth of supporters, plus one additional voter, could ensure that it won N + 1 seats.

Variations

STAR can be used instead of Score for eliminating candidates and for selecting which of the candidates who reach the quota gets elected. That is to say, whichever of the two lowest-scoring candidates is preferred over the other on fewer ballots gets eliminated, and, when multiple candidates reach the quota in a round, whichever of the two top-scoring of these candidates is preferred over the other on more ballots is elected. This variant helps incentive voters to give some candidates one star instead of exaggerating those scores down to zero.