Charles Dodgson Principles of Parliamentary Representation
p. 23
"the obvious conclusion is - let the districts be as large as possible and let each voter cast one vote only."
The table that proves this was optimistic, saying that 51 percent is the amount that is desired to take a seat in a one-seat district.
it also says that 61 percent is enough in a two-party contest to take all three seats in a three-seat district. (perhaps assuming that the other party runs three candidates and each of them get the same percentage of votes.)
but table can be broadened to be minimum that prevents shut-out from happening.
like this
(assuming minimum of three parties, three candidates
number of candidates never less than 2XDM, if that matters)
33+ means 33 percent plus 1 (or actually 33.3333 percent +1)
DM voter casts lowest percentage that can produce representation
1 seat won 2 seats w. 3 s.w. 5s.w. 8 s.w. 10s.w. 15s.w.
1 1 33+
(from here on, use Droop as lowest percentage that can produce representation, when single voting used, and double that to win two, triple that to win three, etc.)
(when single voting is used in MMD, we assume STV)
2 2 33+ 33+ (voters in voting block casts both their votes)
1 33+ 66.6+
3 3 33+ 33+ 33+ (voting block casts 3 votes each)
2 40+ 50+ 60+
1 25+ 50+ 75+
4 4 33+ 33+ 33+ 33+
3 42+ 50+ 50+ 58+
2 33+ 40+ 60+ 67+
1 20+ 40+ 60+ 80+.
5 5 33+ 33+ 33+ 33+
4 33+ 33+ 33+ 33+
3 42+ 50+ 50+ 58+
2 33+ 40+ 60+ 67+
1 17+ 33+ 50+ 67+ 84+
Can't vouch for his figures for limited voting.
He actually puts 51 percent get as votes desired to take under Block Voting, but I decrease that to 33 percent+1 in the three-corner contests pictured above.
easily seen as he pointed out how the amount needed to take one seat decreases with high DM, making it easier for minority party to win at least one seat, and a larger percentage to win all the seats. (p. 23)
He points out that the percentage in the last column on the right (in single voting/STV) also works as the amount of voters who are represented.
He put forward a liquid democracy system where
-voter would each have one vote,
-Britain would have 180 districts to elect its 660 MPs
-districts would have three or more members [3-4 on avage, but as many as ten envisioned]
-single-member districts would be done away with as much as possible,
-districts would have seats in proportion to their polulation number,
-quota established based on district's valid votes (Droop)
-each candidate would have right to transfer their votes to another candidate, so that the votes would be clubbed together among their group. (p. 43-45)
-elections held simultaneously to prevent one district result affecting others.
Charles Dodgson Principles of Parliamentary Representation
parsed by Duncan Black
"The Central Argument in Lewis Carroll's Principles of Parliamentary Representation"
in Papers on Non-Market Decision Making Vol. 3, No. 1 (Jan., 1967), pp. 1-17 (17 pages)
Published By: Springer Nature
(not read)
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