A 48% Group elects 60% of the Droop Members

[DEMOREP1 at aol.com]

Mr. Davidson wrote--

 * 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.
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D- A minor point- the Droop Quota is (1000/(4+1)) +1 = 201 so that Mr. 
Davidson's  math should be --

 * Droop Quota is 201 (1000/5 + 1) 

 * The 48.32 % group has 12,080 total votes - distributed as follows:

     The group has 603 votes in each of 10 districts.
         In which they are able to elect 3 members per district.

     And 402 votes in each of 15 districts.
         In which they are able to elect 2 members per district.

6,030 + 6,050 = 12,080 = 48.32 percent of 25,000

Mr. Davidson has indeed noted a very major defect in Droop in multi-member 
districts at the boundary lines for getting seats-- Namely the possibility of 
gerrymanders with 4 member districts.

He has discovered that using Droop  -

(MQ x D1) + (NQ x D2) can be less than a majority of the total votes but 

(M x D1) + (N x D2) can be a majority of the total seats.

M and N = multiples of the Droop Quota (Q),  M > N,  D2 > D1,  D2 + D1 = 
total number of districts.

Thus, it would appear that to eliminate gerrymander possibilities if Droop is 
to be used, then the total math must be looked at in order to apportion seats.

12,080 x 100 seats /25,000 = 48.32 seats

I mention again (for about the 10th time) that (1) BOTH Droop and Hare have 
problems because the total party votes/ total party seats ratios will almost 
never be equal in any district or at large and (2) my suggested proxy p.r. 
method greatly reduces gerrymander possibilities such that X percent of the 
voters end up with X percent of the voting power indirectly in a legislative 
body.