[EM] Holding byelections with PR-STV

[Raph Frank]

On Wed, Sep 16, 2009 at 12:01 AM, James Gilmour
<jgilmour at globalnet.co.uk> wrote:
> The first statement seems logical, but I don't know about the second statement.
>  I don't understand how an elected candidate could
> be eliminated  -  sounds like a contradiction of terms.

Well, if you just re-run the count and exclude the withdrawn
candidate, there is no guarantee that a candidate would be re-elected.

For example, assume a 2 seater with votes

30: A>B>C>D
20: B>A>C>D
15: C>B>D>A
20: C>D>A>B
15: D>C>A>B

Total 100
Quota 34

Result is
Round 1
A: 30
B: 20
C: 35
D: 15

C elected

Round 2 (1 vote transferred)
A: 30
B: 20
C: 34*
D: 16

D eliminated

Round 3
A: 46
B: 20
C: 34
D: 0

A elected

If C hadn't stood then the results would have been

Round 1
A: 30
B: 35
C: 0
D: 35

B and D win.  Thus A lost his seat because C withdrew.

Ofc, with something like CPO-STV, this would be less of an issue.

> I don't know what any of this means as I am not sufficiently familiar with the inner workings of Meek STV.

In Meek, elected means that you have at least a Droop quota (and can
have any "keep value" between zero and one) .  The method is designed
so that no matter what changes happen to the "keep values", all
elected candidates are guaranteed to have greater than or equal to the
quota after the change.

Each step has been checked and there is a proof that none of the steps
in the procedure can change a candidate who has more than a quota into
a candidate who has less than a quota.  However, the convergence
procedure will tend to bring the elected candidates closer and closer
to the quota, but slightly above.

However, increasing the keep value of eliminated candidates would take
votes from the other candidates and potentially reduce a candidate who
had more than a quota to a candidate that has less than a quota.