[EM] General PR question (from Andy Jennings in 2011)

[Kathy Dopp]

Toby,



After looking at how the Sainte-Laguë and D'Hondt methods work, a
similar algorithmic approach to implementing my method can be easily
shown to always provide proportionate results in terms of seat
allocation.

So instead of calculating the somewhat complex (for the average voter)
Sum over i of (v_i/v*Absolute(v_i/v - s_i/s))


The algorithm for my method, as you noticed, would be simply to:
(1)   multiple the overall ratio of the (total # seats)/(total #
voters) times the number of voters in each voting group
(2) the integer portion of each result is the number of seats assigned
to each group
(3) order the remainder decimal portion of each voting group's result
from greatest to least and beginning at the top (group with the
largest remainder) assign one more seat to each  group until the total
number of seats to be elected is achieved.

(4)  Although unlikely in most elections, some tie-breaking procedure
could be needed: E.g. If there are ties towards the end of the
allocation procedure, some random selection or asking tied groups at
the end of the allocation process to co-select a winner, or possibly,
the number of seats could be increased by the number of groups - 1 who
tie for the last seat allocation.


I am unclear why, exactly, either the Sainte-Laguë and D'Hondt methods
would always give exactly proportionate results in all cases, but it
is easy to understand, simply by the cancellation of the units of
analysis seats/voters * voters = seats (as physicists always do) that
the above algorithm always would given the most proportionate outcomes
in seats (disregarding exactly tie votes).