[EM] Condorcet loser elimination PR

[James Gilmour]

Chris wrote: > James (the other one),
> I seriously doubt your claim that using a Hare instead of a 
> Droop quota "doesn't
> matter for these purposes". I remember long ago getting it on 
> good authority that
> compared to the Droop quota, the Hare quota is correctly 
> superceded rubbish. This
> view has been recently confirmed by James Gilmour:

"correctly superceded rubbish" were not exactly the words I used.

> "When Hare and Droop are applied to transferable preferential 
> voting (eg STV-PR),
>  the effect of the Hare quota to over-represent smaller 
> groups can deny a larger
>  party its fair share of the seats to the extent that it gets 
> fewer seats than a
> smaller party with fewer votes."

This is what I had forgotten (and recently re-discovered) about Hare and Droop quotas:
(example from Robert A Newland's "Comparative Electoral Systems")

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).

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, each with a surplus of 4 votes above the quota. 

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,
RC will be elected.  The outcome now is that the supporters of  the larger group elect three
candidates and the smaller group elects two.

James