[EM] Does Droop give the same results as Hare?

[James Gilmour]

Donald wrote:
> There is the possibility that the Hare set of elected members 
> will be different from the Droop set of elected members.
> 
> When this happens, the question must be asked:  `Which set of 
> members is the correct set of members to hold office?'
> 
> The answer is the Hare set because the Hare set is more 
> proportional than the Droop set.

To illustrate this point, I offer 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 Droop quota is that the supporters of  the larger group elect three candidates and
the smaller group elects two.

Perhaps Donald should reconsider the assertion he made above.
Perhaps Donald should answer his own question: "You do support proportionality, don't you???"

James