[EM] Second order proportional representation.

[Jameson Quinn]

>
>
> For instance, suppose the following parties are represented in
> legislature, with seat counts:
>
> Party A: 55
> Party B: 10
> Party C: 7
> Party D: 1
> Party E: 48
> Party F: 29
> Party G: 10
> Party H: 9
>
> Now suppose that, to make things interesting, parties E, F, and H choose
> to form government. Furthermore suppose there are 10 ministries,


One way to do this would be to say:
Each party gets to "bid" portions of their votes for each of the
ministries. The ministries are then allocated such that for each ministry
and party, you calculate the total votes for that party, divided by the
total "bid" that that party made for all the ministries it "wins", times
the "bid" for the ministry in question, and whichever party has that
quantity greatest "wins". (This might not lead to a stable solution, and if
not, you resolve the mess in favor of the largest party.)

Say there were 3 ministries. Party E can guarantee it gets ministry 1 by
bidding 30 for it; then, it can probably get 2 or 3 by bidding the
remaining 18 on one of them. Or, it can guarantee getting at least 2
ministries by bidding at least 15 on each, putting the final 3 on the one
it wants the most. Thus, party F should bid 19 on the ministry it wants the
most, and 10 on the one it thinks E wants least.
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