# [EM] Semiproportional Bucklin method

Raph Frank raphfrk at gmail.com
Sat Apr 25 14:26:19 PDT 2009

```On Sat, Apr 25, 2009 at 4:09 PM, Kristofer Munsterhjelm
> Clearly, it detects a Droop set when one exists, since the definition of the
> Droop set is that at least a Droop quota vote these ahead of all others -
> not necessarily in the same order, but Bucklin equalizes the order.

Right, so then it meets Droop, isn't that the definition?

.. or by a Droop set, do you mean one that PR-STV will pick without
the need to eliminate any candidate?

I think my explanation shows that if a party is entitled by Droop to a
seat, then it wins a seat.

> Yeah, I may have described that situation vaguely. Electing more than one
> candidate in a single round is permitted - both between sets and inside a
> single set. For instance, if you have:
>
> 2 Droop quotas support A B C
> 1 Droop quota supports D E F
> 1 Droop quota supports G H I
>
> Then you should elect two from the first set and one from each of the sets
> below, unless they already got what they wanted.

I agree.

> For a more complex example
> that may or may not be impossible, but which shows the point:
>
> 2 Droop quotas support A B C H
> 1 Droop quota supports A C D H
> 1 Droop quota supports E F G H
>
> If you elect A, B, and E, that satisfies all three support sets, because A
> counts to satisfy both the first and second sets. Electing A, C, and E would
> give 2 candidates to the second set, which is more than its fair share,
> hence one can't elect both A and C. In effect, the candidates to be elected
> that would satisfy all three sets would be one of:
> 1. A B E
> 2. A B F
> 3. A B G
> 4. B C E
> 5. B C F
> 6. B C G
> 7. B H

Sounds reasonable.  In effect, you can elect candidates in any order
you like as long as the group in question has fewer seats than it is
entitled to and you cannot proceed to the next round until there are
no more valid seats.

Would you consider A,H acceptable too?  Elect A from the first group,
then group 2 is disabled, then elect H from the 3rd group?

```