[EM] STV with which quota?

[James Gilmour]

Stephane.rouillon Sent: Tuesday, October 11, 2005 2:45 PM
> 
> I learned STV about three years ago.

I learned about STV more than 43 years ago, but I am still learning.

> At the time Hare quota appeared to me the most
> proportional quota and thus, in my humble opinion,
> the best quota.
> 
> Now why is Droop better?
> Any comment?

Consider the following example:
In an STV-PR election with 120 voters for five places, the HARE quota would be 24 votes (= 120 / 5).
Suppose the election is contested by two parties (R and S) with three candidates each (A, B, C).
With first preference votes as shown, RA and RB would be elected at the first stage.

Stage 1
RA 24 elected   SA 19
RB 24 elected   SB 19
RC 16              SC 18
      64                   56

Of the four continuing candidates, candidate RC has the fewest votes and so is excluded.  No matter what preferences are
marked on those papers, SA, SB and SC will then be elected.

Stage 2
RA 24 elected   SA 19 elected
RB 24 elected   SB 19 elected
RC 16 excluded  SC 18 elected
      64                     56

Applying the Hare quota, supporters of the larger opinion group (party), who constitute an absolute majority, elect only
two candidates, while the smaller group elects three.


For this election, the DROOP quota would be 20 = (120 / (5 + 1)).  With first preference votes as before, RA and RB
would be elected at the first stage, each with a surplus of 4 votes above the quota. 

Stage 1
RA 24 elected   SA 19
RB 24 elected   SB 19
RC 16              SC 18
      64                   56

If we (reasonably) assume that these surplus votes transfer to the remaining candidate of party R, candidate RC will be
elected, and SA and SB will take the two remaining places.

Stage 2
RA 20 elected   SA 19 elected
RB 20 elected   SB 19 elected
RC 24 elected   SC 18
      64                    56

The outcome with the Droop quota is that the supporters of  the larger group elect three candidates and the smaller
group elects two.

QED.
James Gilmour