[EM] Mr.SODA

[fsimmons at pcc.edu]

In the discussion of a proportional representation version of SODA it was lamented that the non-
sequential version of PAV was computationally hard, and was suggested to make use of  the PAV 
measure of goodness to pick the winning slate from all of the slates that anybody cared to nominate.

While that would certainly be feasible and very likely near optimal, another possibility is to use non-
sequential PAV to choose the first three members of the slate, and then choose the remaining members 
sequentially, conditioned on the membership of the first three as well as those chosen subsequently.

The number of slates of size three is only  n*(n-1)*(n-2)/6 , which is less than five million when there are 
(n=)three hundred candidates.

If the members of the senate were chosen this way, the first three could be a kind of triumvirate 
presidency of the senate.