[EM] Replies to Craig Carey and David Catchpole

[Bart Ingles]

Donald E Davison wrote:
[...]
> Donald: Vote wastage is a result of a method being less proportional.
> Wastage can be used as an indicator of trouble in a method.
> 
[...]
> Craig: If you have in mind some little sample elections that test methods'
> proportionality then perhaps you could give them.
> 
> Donald: Yes, I do have `some little sample election' in mind, and I will
> give it.
>      Suppose an association of 120 persons is having its election for board
> of directors. There are ten candidates running to fill five seats. The
> election method is STV with random transfer of ballots.
>      Further suppose that the voters know all the ten candidates well
> enough to rank all ten, and that all voters do rank all ten. I know this is
> ideal, but it removes the influence of exhausted votes, because there will
> be no exhausted ballots. I am willing to compare Hare and Droop without
> exhausted votes, but in a real election the Droop will have more exhausted
> ballots because there will be more transferring of ballots. The number of
> possible exhausted ballots is depended directly on the number of ballots
> transferred.
>      Anyway, if this election is conducted using Hare Quota, the quota will
> be 24 votes, and the results will be five candidates elected with 24 votes
> each.

Only if the last faction to elect a candidate can agree on a candidate. 
Otherwise the last candidate could be elected with as few as 13 votes.


>      This is an ideal PR election. Every vote ended up on one or another of
> the winning candidates. Every elected member received the same number of
> votes, a number which is an equal portion of the total votes.

It would be more convincing if you could show the actual example, i.e.
with voter rankings, and not just an outline of a scenario.  This might
be easier with fewer seats, say 2 or 3.

>From what you describe above, this scenario appears to assume that each
voter to belong to a faction with a size equal to a Hare quota, or exact
multiple of a quota.  What if the faction sizes are different, or worse
yet, what if the faction sizes equal the Droop quota?

Also, the requirement that each voter give complete rankings appears to
make things easier for Hare.  Without that requirement, the larger Hare
quotas would exhaust ballots more quickly.

-Bart