M.E.P.

[DEMOREP1]

Regarding the fractional seat problem---

The method of equal proportions (MEP) has been used since 1940 to deal with
fractions in apportioning the 435 U.S. Representative seats among the States
in the U.S. (with a minimum of one seat per State).

The theory-- P = population,  S = Seats
X and Y - 2 States

The final PX/SX and PY/SY try to be equalized or 
(PX/SX) / (PY/SY)  approaches 1.

In getting to the final result

(PX / (S+1)X) / (PY/SY) is compared to 

(PY / (S+1)Y) / (PX/SX)  or cross multiplying

(PX x PX)/ (SX x (S+1)X)    versus   (PY x PY)/ (SY x (S+1)Y)

The next seat goes to the State that more equalizes the ratios.

The votes for a party would replace populations in the context of p.r.
elections.

Another way to deal with fractional p.r. seats is to have the smallest
fraction go repeatedly to the next choice of the voters.
Example-- A party initially gets 7.26 seats.   Each vote for the party would
be multipled by 0.26/7.26 and be transferred to the voter's next choice.
However, I note again the elementary method of having each legislator have a
voting power in the legislative body equal to the number of votes he/she
receives--- i.e. no ratios and no fractions to worry about.