[EM] Compromise allocation of fair share

[fsimmons at pcc.edu]

How to use your homogeneous degree one function ballot to control the distribution of your share of the 
allocation (whether of number of seats or probability):

1.  As proved in the last post, if you want 100% to go to P1, then vote f(p)=p1.

2.  If you want 10%, 20%, 30%, and 40% , respectively of your share to go to P1, P2, P3, and P4, then 
vote 

f(p)=p1^.1*p2^.2*p3^.3*p4^.4, 

and your vote will contribute tot the values of p1, p2, p3, and p4 in the perecise proportion

p1:p2:p3:p4::10:20:30:40

If, on the other hand, you want to move p maximally towards that proportion, you should vote

f(p)=min(p1,p2/2,p3/3,p4/4) .

To be continued...