[EM] Compromise allocation of fair share

[fsimmons at pcc.edu]

I would like to modify my proposal for a new kind of list PR method. 

1.  Voters submit ballots indicating their favorite parties.  These ballots are used to find the standard list PR allocation of N seats by some standard method.  We call this allocation the Fallback allocation.

2.  All interested entities submit as many allocation nominations as desired.  We require that these allocate whole numbers of seats to the parties, with the total number of seats equal to the same number N in all cases.  Let the letter S represent the set of these nominated allocations, with the Fallback allocation included,

3.  Voters also submit ballots indicating their criteria for ordering the members of the set S. Let Beta be the set of these ballots.  For example one voter could say that of any two allocations she prefers the one which gives the least number of seats to party P7.

4.  Voters also submit ballots in the form of functions that are homogeneous of degree one for the purpose of contrilling their share of the allocation in the optimization step below.  Call this set of ballots H, for "homogeneous."

5.  Eliminate all of the members of S that do not Pareto dominate the Fallback allocation according to the ballots in the set Beta.  Let S' be the subset of non-eliminated members of S.

6.  Let S'' be the set of all members of S' that are not Pareto dominated by some other member of S'.

7.  Allocate the seats to the various parties P1, P2, ... etc. in accord with the allocation p=(p1, p2, ...) from S'' that maximizes

the product (over f in H) of f(p) .
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