[EM] A 48% Group elects 60% of the Droop Members
DEMOREP1 at aol.com
DEMOREP1 at aol.com
Mon Nov 15 12:51:32 PST 1999
The Droop ratio approaches the Hare ratio with an increasing number of
seats-----
S= Number of Seats, D/H = Droop/Hare ratio (as a percentage)
S D/H (each is little more depending on the total number of votes)
1 50.00
2 66.67
3 75.00
4 80.00
...
9 90.00
...
19 95.00
...
49 98.00
...
99 99.00
...
999 99.90
Can a bare majority of Droop quotas in a single at large district produce
indirect minority rule ?
S= Number of seats, T = Total votes
Odd number of seats-
(S+1)/2 x (T/(S+1) +1) = (T + S + 1)/ 2 votes
Since the result is greater than T/2 the answer is NO.
Note that with a large T and a small S, the result will barely be over 50
percent of T.
Even number of seats-
(S/2 +1) x (T/(S+1) +1) = (S+2)/2 x (T + S + 1)/(S+1) votes
Not obvious.
S Result (votes)
2 2T/3 + 3
4 3T/5 + 5
6 4T/7 + 7
...
10 6T/11 +11
...
100 51T/101 +101
...
1000 501T/1001 +1001
With a large S the result nears T/2.
Since the result is greater than T/2 the answer is NO.
Note that with a large S, the result will barely be over 50 percent of T.
To avoid borderline apportionment problems in multi-party elections, there
would seem to be a need for a majority requirement (i.e. any 2 or more
parties with a majority of the votes must get a majority of the seats -- but
this may not be possible due to conflicting overlapping partial majorities
regarding the marginal seat(s) -- especially with 4 or more parties.)
Again I note that the various ratios of party votes/party seats for the
different parties will almost never be the same (especially with a low number
of seats in the legislative bodies of many private groups and local
governments).
I note again -- proxy p.r. avoids most, if not all, of the above math
problems.
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