Fred Gohlke wrote:
Good Morning, Raph
When I offered to send you a draft of the petition outlining a method of
selecting candidates for public office, I planned to send it privately.
After seeing your response, I asked the author's permission to post it
publicly and he agreed. Here's the draft in its current form:
(draft) (draft) (draft) (draft)
P-E-T-I-T-I-0-N
To the Sefton Metropolitan Borough Council
[SNIP]
ILLUSTRATION
This table describes the method by which the members of the Church Ward
will select candidates for the Sefton Metropolitan Borough Council:
Select
Randomly
From
Full Over Previous Total
Level Candidates Triads flow Level Triads Selected(1)
1) 9001 3000 1 0 3000 3000
2) 3001(2) 1000 1 2 1001 1001
3) 1001 333 2 1 334 334
4) 334 111 1 2 112 112
5) 112 37 1 2 38 38
6) 38 12 2 1 13 13
7) 13 4 1 2 5 5
8) 5 1 2 1 2 2(3)
This sounds a lot like what I've previously referred to as "council
democracy". In a council democracy, you have councils of size p. Each
elect one of its number to the next council. The coverage is exponential
in the number of levels.
I wonder if the problems of council democracy also would affect this
proposal. The first problem of council democracy is that it magnifies
opinion in a possibly chaotic manner. Say, for the sake of the argument,
that there's an opinion held by r% of the people. What value of r is
required so that there's a way that the majority of the final council
will hold that opinion?
That's ((floor(p/2) + 1)/p) ^ q, where there are q levels. Intuitively,
that's a "majority of a majority of a majority ... of a majority". Let's
see what this is for 8 levels and a majority of 2/3 (as with your
triads). In the very worst case, an opinion held by (2/3)^8 = 4% can be
held by a majority of the last triad.
Your randomization thwarts strategists from deliberately poisoning the
triad system, something that could be done in a council democracy, but
the point holds: because the comparisons are local, disproportionality
can accumulate.
Your overflow solution is interesting, as it deals with the second
problem of council democracy in that there's no "obvious" (for
non-random councils at least) way of making the numbers even at each level.
One could reduce the first problem by having a larger group that elects
more than one member. Perhaps a group of five that elects two in a PR
manner? In order for the opinion to be transmitted from a level to the
one above, both must hold it, so two Droop quotas have to have it. That
is, if I'm doing this right, 4/5. The reduction:
Level Candidates 5-groups Overflow Elect from prev.
0 9001 1800 1 0
1 3601(2) 720 1 4
2 1442 288 2 3
3 578 115 3 2
4 232 46 2 3
5 94 18 4 1
6 38 7 3 2
7 14 2 4 1
8 3 1 4 1
9 2 1 (Elect one to fill 5-group)
The minimum possible opinion that can attain a majority here has (4/5)^9
= 13.4% support among the people. That's better, even if it's still low.
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