[EM] Replies to Craig Carey and David Catchpole

[Craig Carey]

At 03:48 27.10.99 , Donald E Davison wrote:
>Greetings,
>
>Craig Carey wrote:
...
>Craig: The lower the 'quota for winners', the more proportional STV would 
>be(?).
>
>Donald: No, the lower the quota, the less proportional STV will be. Are you
>quoting someone here? I hope it is not me. I don't think I ever made the
>mistake of saying that. If so, please tell me which of my posts contains
>that error.

An example failing to indicate the response is wrong:
Ballots and counts of papers are as shown in the first listing,
  and two winners need to be found. Twelve candidates.

Stage 1a: Find 10 Winners. Only B is over quota for winners
Droop: (11+20+102)/11=12.0909 : B is a winner
Hare.: (11+20+102)/10=13.3000 : B is a winner
  11  A
  20  B
  12  CA
  11  DA
  10  EA
  10  FA
  10  GA
  10  HA
  10  IA
  10  JA
  10  KA
  09  LA

Stage 1b: Find 9 Winners. Only C is over quota for winners:
Droop: (11+102)/10=11.3000 : C is a winner
Hare.: (11+102)/09=12.5555 : Eliminate L.
  11  A
  12  CA
  11  DA
  10  EA
  10  FA
  10  GA
  10  HA
  10  IA
  10  JA
  10  KA
  09  LA

Hare:  {A,B} ?
Droop: {B,C}
'Correct': {A,B}

If the example is not STV then that could be fixed.

A method satisfying (Q1) well would not perform better.
(Q1) as stated by me does not allow papers with the 2nd preference
 being for A, to unite and attempt to strategically vote.
So may there is a case for another rule, or a metric, which allows
 strategic voting by papers and allows uniting of weights of papers
 even when the preceding preferences for losers differ.


>Craig: Previously the test was 'vote wastage', which is different (isn't it?).
>
>Donald: Vote wastage is a result of a method being less proportional.
>Wastage can be used as an indicator of trouble in a method.
>

...
[example was here]
>Craig: How much better is Hare than Droop?
>
>Donald: In this example, Hare is `exactly' 14.3% better than Droop (15/105).
>
At a single point inside the simplex of possible elections, maybe.
A problem is that STV has complex boundary shapes, and any argument
 about a single point with outcomes affected by final stages especially
 isn't particularly convincing (is it Donald?).

Wastage is not defined.
... define what is good in Droop-STV, make the rule general, and code
 it up for a computer [easy] so that a metric of the method can be
 calculated. A metric could be a ratio of 2 hypervolumes. (Mr Fukuda

   <http://www.ifor.math.ethz.ch/staff/fukuda/> has some code to

 has code to calculate hypervolumes (REDLOG can break convex polytopes
 into convex ones); alternatively Monte-Carlo methods could be used or
 integration using some lattice. This has got to be a sounder better
 plan than using GUI code on various single election examples that were
 tested. That might be what happens in Washington, or at the Electoral
 Reform Society (UK), but it is not recommended by me.

Example of REDLOG (http://www.fmi.uni-passau.de/~redlog/htmldoc/)
When is this region (a<x and x<b and 0<x+y and y-x<c) in x and y not empty?.

   1: t := (a<x and x<b and 0<x+y and y-x<c);

   t := a - x < 0 and  - b + x < 0 and  - x - y < 0 and  - c - x + y < 0

   2: rlqe ex ({x,y}, t);

   a - b < 0 and 2*b + c > 0


G. A. Craig Carey, Auckland, New Zealand. 
__________________________________________________________________
Mr G. A. Craig Carey                   E-mail: research at ijs.co.nz
Auckland, Nth Island, New Zealand
Pages: Snooz Metasearch: http://www.ijs.co.nz/info/snooz.htm
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