[EM] A 48% Group elects 60% of the Droop Members

[Bart Ingles]

I get different results; am I misapplying the quotas?

For a four-seat district with 1000 voters voting 600:400, I have both
factions receiving two seats each under Droop Quota:

Droop Quota = 1000/(4 + 1) + 1 = 201

Round 1:  A=600, B=400;  A wins 1st seat
Round 2:  A=399, B=400;  B wins 2nd seat
Round 3:  A=399, B=199;  A wins 3rd seat
Round 4:  A=198, B=199;  B wins 4th seat with 199 votes (2 shy of a
quota)

In the districts where B is ahead, the result is reversed but each group
still wins two seats per district, so 48% of the votes wins half of the
seats (i.e. 50 seats each).  I get the same result with Hare:

Under Hare Quota, the quota is 2000/4 = 250, so

Round 1:  A=600, B=400;  A wins 1st seat
Round 2:  A=350, B=400;  B wins 2nd seat
Round 3:  A=350, B=150;  A wins 3rd seat
Round 4:  A=100, B=150;  B wins 2nd seat with 150 votes (100 shy of a
quota)

If you change the vote slightly from 600:400 to 601:399, then the larger
groups will win 3 seats in a given district under Droop and 2 seats
under Hare.  So the 52% group will win (3 * 15) + (1 * 10) = 55 seats
and the 48% group will win 45 seats under Droop, vs. 50/50 under Hare.

The differences don't seem earth-shattering either way.  The only
difference I see is in a 4-seat district, you need > 60% to win 3 seats
under Droop, and > 62.5% under Hare.  This takes you from 50% of the
seats to 75%.



Donald E Davison wrote:
> 
> Greetings,
> 
>  The following is an example of a 48% group electing a majority of the
> Droop members.
> 
>  * 100 members are to be elected in 25 districts - 4 member districts.
> 
>  * 1000 voters per district - 25,000 total votes in election.
> 
>  * Droop Quota is 200 (1000/5)
> 
>  * The 48% group has 12,000 total votes - distributed as follows:
> 
>      The group has 600 votes in each of 10 districts.
>          In which they are able to elect 3 members per district.
> 
>      And 400 votes in each of 15 districts.
>          In which they are able to elect 2 members per district.
> 
>  * Total members elected by the 48% group is as follows:
> 
>         10 districts electing 3 members each equals 30 members elected.
>         15 districts electing 2 members each equals 30 members elected.
>                                                   -----
>   Total number of members elected by the 48% group: 60
>         (60 of 100 is 60%)
> 
>      It is possible for a 48% group to elect 60% of the members.
>      In a real election the numbers will not fall this even and the 48%
> group most likely will elect less, like 54% of the members, but still a
> majority.
> 
>      Had the count of this election used the Hare Quota, and the 48% group
> attempted to lower their votes on their candidates in order to elect more
> members than their just representation, we could expect that the number of
> members now elected by the 48% group would be less than using the Droop. I
> say less because the group will not be able to lower votes with
> mathematical precision. But, when the Droop Quota is imposed on the STV
> election method, by agreement of the Droop supporters, then the cheating
> can be preformed with mathematical precision, also by agreement of the
> Droop supporters.
>      No matter which quota an election uses, for every member the 48% group
> elects over 48 members, some other group will lose a member.
> 
>      I claim that the real reason the Droop Quota has been made part of STV
> is so that the largest faction can elect a majority, even if that faction
> has less than a majority of the popular vote.
>      The Droop is corruption - corruption by agreement.
> 
> Note: I must point out that the main reason the 48% is able to elect 60% of
> the members in this example is because of the small districts. Had this
> election been held in One-Area of 100 seats, the 48% group would only been
> able to elect 48 members - using Hare or Droop, but the Droop makes it
> easier for the largest group to elect more members in small districts.
> 
> Regards,
> Donald
> 
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