[EM] D'Hondt without lists

Forest Simmons fsimmons at pcc.edu
Fri Aug 16 15:23:27 PDT 2002

The d'Hondt rule is implicit in both Proportional Approval Voting (PAV)
and Sequential PAV.

This latter method is similar to what you refer to as the Swedish method
below, except Approval ballots are used instead of ranked preference

1. In the first round the candidate C1 with the greatest approval sum is
transferred to the winners' circle.

2. In the second round the ballots that approved C1 are given a weight of
one half.  Among the remaining candidates the one with the greatest
weighted approval sum is added to the winners' circle.

3. In each subsequent round the weight applied to each ballot is the
reciprocal of one more than the number of that ballot's approved
candidates that are already in the winners' circle.

Ordinary (i.e. non-sequential PAV) is a little harder to describe, but it
is easy to find by searching for PAV in the EM archives.


On Fri, 16 Aug 2002, Olli Salmi wrote:

> I've been trying to find a way how the d'Hondt rule could be used for PR
> without party lists in meetings. I know of two such methods. One is the way
> we sometimes use in Finland. The first candidate on the ballot paper
> receives one vote, the second half a vote, the third  a third of a vote,
> etc. The votes are added up for each candidate and the ones with the most
> votes are elected.
> If we suppose that the voters vote along strict party lines, this system
> works OK if all voters of a party use the same order of preferences, but if
> the majority party distributes its preferences evenly between its
> candidates it can win more than its due.
> This method was suggested by Burnitz and Varrentrapp (Switzerland) in 1863,
> and, independently of them, by Th. Homén in Finland in 1894. It was used in
> Frankfurt for a while but was abandoned soon because the voters quickly
> learned the strategy. It was included as one model of PR in the Finnish
> Societies Act of 1989. It's easy to count and gives at least some
> proportionality.
> The other method is the one used in Sweden within party lists in local
> councils. Each ballot is counted for only one candidate at a time. The
> candidate with the most votes is elected in each round and his or her votes
> are transferred to the next preferences, the second name counting for half
> a vote, the third name for a third of a vote etc. This method also works OK
> if the supporters of each group give the same preferences, but if the
> voters of a group spread their preferences they can lose seats.
> The Swedish method is can be derived from list PR. In d'Hondt's method the
> votes of a party are divided equally between the successful candidates at
> the top of the party list. From the point of view of a single ballot paper
> your one vote is divided between the successful candidates. That's what the
> Swedish system does.
> The problem with it is that if your first preference is not successful,
> your other preferences don't count because there's no elimination of
> candidates. Since the d'Hondt rule has no quota -- actually it's an
> algorithm to find the quota -- the only sensible way of elimination that
> I've come up with so far is to transfer all preferences until there are
> only two candidates left and then eliminate the one with the lowest number
> of votes. Then the same procedure is repeated again, treating the
> eliminated candidate or candidates as non-existent, until only the required
> number of candidates is left.
> I wouldn't recommend this method as a practical voting system because it's
> tedious to count by hand (I've checked only a few cases), but it seems to
> give pretty satisfactory results, it's nice to play with, and it should be
> computationally rather straightforward. It uses your lower preferences if
> your higher preferences are not successful. Unlike Proportional Approval
> Voting, it takes your preferences into account.
> Colin Rosenstiel recommends something similar for STV in "Selecting an
> ordered Party List using the Single Transferable Vote".
> http://www.cix.co.uk/~rosenstiel/stv/orderstv.htm
> The idea is so simple that it has probably been proposed many times before.
> It should be noted that in the single-winner case this method does not
> reduce to IRV.
> Olli Salmi
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