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

James Gilmour jgilmour at globalnet.co.uk
Sat Jul 26 11:33:52 PDT 2003

Kevin wrote:
> I started reading about methods of proportional seat allocation.

You might find it useful to look at few chapters in Robert Newland's little book "Comparative
Electoral Systems".  [ISBN 0 903278 07 3]  It is only 95 pages, but it packs in a lot of
information.  (Robert was a mathematician who wrote very concisely!)

> I have a couple of questions...
> First, what is IRV's relation to Hare (quota of 
> (votes/seats))?  It looks to me
> like it could just as easily be related to Droop (you need 
> 50%+1 to be elected).

I don't find this approach helpful.  Filling a single vacancy is a limiting case and (I think) that
creates special problems just because it is the limiting case.  Single-winner elections are best
treated on their own.  References to a "quota" in the legal language for IRV can just lead to
trouble.  Better by far to define the winner as having as many or more votes than all the other
(continuing) candidates combined.

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

I have always found Newland's analysis helpful.  He has Hare and Droop classified as "Quota
methods", and d'Hondt/Jefferson and Sainte-Lague and some others classified as "Divisor methods".
One of his main conclusions is that neither the Hare quota with the largest remainder nor the Droop
quota with the largest remainder is well-suited to the allocation of places to parties.  I may be
wrong, but I am not aware of any country using a party list PR system with either a Hare or Droop
quota;  I think they all use one or other of the divisor methods (d'Hondt, etc).

> 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'm not sure what your sources meant by "more proportional".  Comparing Hare and Droop for party
list allocations, the Hare quota with the largest remainder over-represents smaller parties at the
expense of larger parties, while the Droop quota does not.  Among the divisor methods used with
party lists, d'Hondt benefits the larger parties.  When Hare and Droop are applied to  transferable
preferential voting (eg STV-PR), the effect of the Hare quota to over-represent smaller groups can
deny a larger party its fair share of the seats to the extent that it gets fewer seats than a
smaller party with fewer votes.


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