[EM] Droop compared with Hare Quota

[Richard Lung]

The Hare quota gives maximum proportional representation. The Droop 
quota gives minimum proportional representation. The reason why we have 
the Droop quota at all is because career politicians wouldn’t tolerate 
the competition of large multi-member constituencies.

Droop is not an improvement on Hare, except in the eyes of monopolistic 
politicians. However both quotas are to some extent undemocratic. 
Candidates may be elected to the Droop quota without a statistically 
significant margin of victory over rival candidates.

Whereas the Hare quota, in relatively small constituencies, cannot elect 
candidates at all, without the deference of some voters, over their 
personal wishes, say, for some party line, or according to some 
religious instruction.

To overcome the mutual democratic deficiencies of both the Hare quota 
and the Droop quota, I introduced their Harmonic Mean quota 
(votes/(seats+1/2) since the average of harmonic series is the harmonic 
mean. (It is one of the four averages, in my voting method, FAB STV: 
Four Averages Binomial Single Transferablee Vote.)

I discovered later that my harmonic mean quota was the equivalent of 
Webster/St Lague apportionment. So I have no reason to believe that 
divisor systems are any better than quota systems. They are just 
complementary means of reckoning.

Divisor methods (mis)applied to party list systems divide the voters 
into conflicting herds. Because, these voting methods lack a 
transferable vote to express unity as well as division.

  Regards,

Richard Lung


On 25/04/2024 02:38, Closed Limelike Curves wrote:
> Funnily enough, I'm actually thinking that wiki article needs to be 
> rewritten from scratch (probably into a section on a broader article 
> on electoral quotas). It doesn't do a very good job of going over the 
> tradeoffs between the two quotas, which are:
> 1. Droop preserves majorities. (A candidate with a majority of the 
> vote will always win a majority of seats.)
> 2. Droop is less vulnerable to strategy, because a Droop quota can 
> always enforce their preferences over another candidate (if a Droop 
> quota prefers A to B, then bullet voting A ensures A has more support 
> than B).
> 3. Hare is /unbiased/, making it more proportional than Droop; every 
> party will, on average, receive a number of seats proportional to 
> their share of the vote. Droop is biased towards large parties.
> 4. Anti-Droop (nonstandard name; divide by n-1 instead of n+1) will 
> always preserve minorities (a party with less than a majority of the 
> vote will always receive less than a majority of the seats). 
> Anti-Droop is biased towards small parties. I've never seen a serious 
> proposal for it.
>
> Most mathematicians consider quota methods inferior to divisor methods 
> in general; HH+Webster satisfy quota in practice anyways.
>
> On Thu, Apr 18, 2024 at 12:38 PM Joseph Malkevitch 
> <jmalkevitch at york.cuny.edu> wrote:
>
>     This Wiki article may help explain the "issues" related to the use
>     of the Droop and Hare quotas.
>
>     https://en.wikipedia.org/wiki/Comparison_of_the_Hare_and_Droop_quotas
>
>     Best,
>
>     Joe
>
>
>     ——————————————
>     Joseph Malkevitch
>
>     Email:
>     jmalkevitch at york.cuny.edu
>     Web page:
>     http://york.cuny.edu/~malk/
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