[EM] Hare and Droop, d'Hondt and Sainte-Lague

[Donald Davison]

Re: [EM] Hare and Droop, d'Hondt and Sainte-Lague

Kevin, you wrote:
>I started reading about methods of proportional seat allocation.
>I have a couple of questions...
>
>First, what is IRV's relation to Hare (quota of (votes/seats))?

Donald here: There is no relationship.  Irving is a single seat election
method.  The use of a quota does not come into play with any single seat
election method.  The word quota means a `proportional share of the whole'
(total votes in the case of an election).  A single winner does not share
votes with any other candidates.  A quota in a multi-seat election also
means the limit number of votes a candidate is allowed to have.  The winner
in an Irving election is not limited to how many votes he can receive, he
can receive them all (if the voters so decide).

>It looks to me like it could just as easily be related to
>Droop (you need 50%+1 to be elected).

Donald:  This is sometimes used as a vain argument to support the use of
the Droop `quota' in multi-seat elections, but a single winner is not
limited to only 50%+1 of the votes, he can receive more.  50%+1 is merely
the smallest majority in a single seat election, it is not a quota.

>And second, in "remainder" methods, what happens when, after giving
>seats for quotas, there are more seats left to be allocated than parties?

Donald:  It is mathematically impossible to have more seats left over than
parties.  Each party will have a remainder (rare for a party to have zero).
Each remainder will be less in size than a whole seat quota.  The sum of
all the remainders should equal a whole number of seats, which will be less
in number than the number of parties.

>The various pages I've looked at suggest that Hare and Sainte-Lague
>are more proportional than Droop and d'Hondt, respectively.  But I
>did some examples and I'm a little concerned.  I wonder if someone
>will humor me and have a look at this.
>
>Let's say we're in Chile, so this is a two-member district:
>Party A: 21,000 votes, 67.74%
>Party B: 10,000 votes, 32.26%
>total: 31,000
>
>Hare: Quota is 15500.  A has 1 and B has 0.  Once you take away
>that quota from A [we have a remainder of 5500], B has the
>largest remainder [so] A gets 1 seat and B gets 1 seat.
>
>Sainte-Lague: A gets a seat, and votes are reduced to (21000 / 3)
>or 7000 votes, which means B gets the other one.
>
>Droop: Quota is (31000/(2+1))+1 or 10335 (rounded up).  Only A has
>a quota.  Once you subtract that, party A has (21000-10335) or
>10665 votes, which is more than B, so A gets both seats.
>
>d'Hondt: A gets a seat, and A's votes drop to (21000/2) or
>10500 votes.  That's more than B has, so A gets both seats.
>
>My thought: Although it would be nice to give a seat to a party
>that got nearly a third of the vote, wouldn't it be unfair to
>penalize party A for not splitting into two equal fragments?

Donald:  It's all a question of how much you want an election design
feature to benefit party proportionality.  Each of these design features
will help the second candidate of party A (to different degrees).
   The Hare quota will give  5500 votes to the second candidate.
     Sainte-Lague will give  7000 votes to the second candidate.
          d'Hondt will give 10500 votes to the second candidate.
  The Droop quota will give 10665 votes to the second candidate.
  Imperiali quota will give 13249 votes to the second candidate.

In a partisan election, party proportionality is the main reason to have a
proportional representation method.  While there are other reasons to have
PR, party proportionality should be retained.  Party A does not need to
split into equal fragments, d'Hondt or Droop will split or average the
votes for party A.

In a partisan STV election I prefer my elimination rule which also averages
the votes for each party.  That rule is: `The candidate to be eliminated
shall be the lowest candidate of the party with the lowest average votes
per candidate.'

The main advantage of using this rule over the Droop quota is that my rule
makes the math possible for allowing the voters to rank candidates and/or
parties in any mix.  This is the next big step towards allowing the voter
more choices.

In a non-partisan STV election in which the jurisdiction has voted not to
average votes in order to not benefit any faction, then only the Hare quota
should be used.  The Hare quota does not average votes.  It is the only
proportional quota, any surplus should be transferred to the next choices.
There should also be a law that makes it a crime for anyone to attempt to
average votes at the ballot box.

Donald Davison


>Incidentally I think Chile effectively uses d'Hondt...  The top party
>gets both seats unless the second-place party gets at least half the
>top party's votes.  Personally I can't see a flaw with this.
>
>Comments or corrections...
>
>
>Kevin Venzke
>stepjak at yahoo.fr