[EM] Electing Cabinets/Executive Committees

[Closed Limelike Curves]

Very helpful, thank you! I'll try and see if there's anything from the fair
division or cake-cutting literature on this.

On Wed, Mar 6, 2024 at 3:01 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 2024-03-06 04:26, Closed Limelike Curves wrote:
> > I assume there's methods for this, but I don't know the search terms:
> > say I want to proportionally elect an inhomogeneous committee, like a
> > Cabinet or a set of executive officers. What methods handle this?
>
> Steven Brams considers this exact problem in the book "Mathematics and
> Democracy" (Chapter 9, "Allocating Cabinet Ministries in a Parliament").
> He first gives the following algorithm:
>
> For i = 1...n:
>         - Let the "current party" be the party next in line according to
> Sainte-Laguë based on votes in the most recent parliamentary election.[1]
>         - Ask the current party which of the remaining positions it would
> like
> to claim (e.g. PM, minister of defense, etc.)
>         - Assign the chosen position to the party.
>
> He then shows that this method, although proportional, is nonmonotone in
> the sense that sometimes a party might want to be asked later. So he
> introduces a "trading step" where at each i, the current party may ask
> some other party if it wants to go first instead. He finally shows that
> this does not completely eliminate tactical voting problems, but that
> "some of the problems of cabinet selection can be ameliorated if not
> solved" (section 9.8).
>
> If you don't have parties, you might want to look into the matrix vote:
> https://en.wikipedia.org/wiki/Matrix_vote. I'm not aware of any
> generalization to methods other than Borda; the obvious multi-way Range
> method[2] is not proportional.
>
> -km
>
> [1] Section 9.3. discusses the different divisor methods, and Brams
> argues that whether you'd prefer D'Hondt or Sainte-Laguë is a matter of
> preference - whether you think large-party bias is worth it for
> stability or not. IMHO, the way to solve kingmaker problems with party
> list parliamentarism is to use a slightly consensus-biased ranked
> method. If that method is house monotone, then it could be used as a
> replacement here. (Note that this is not the same as using D'Hondt, due
> to parallels to center squeeze if only first preferences are used.)
>
> [2] Each voter rates each candidate for each position, then the method
> selects candidates so that the sum of chosen candidate-position pairs is
> maximized. This can be done by linear programming.
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20240307/0eb1abcf/attachment.htm>