[EM] D'Hondt without lists

[Olli Salmi]

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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