[EM] Meek style STV - Part One of Two

[Craig Carey]

At 02:29 15.10.99 , Craig Carey wrote:
>
Errata: 
...
>If 20 winners need to be found, and there are 30 candidates, and
> so far 8 candidates have already been selected as winners and
> about 5 were eliminated, then the Droop Quota is close to the
> largest number that would pass 9 (=8+1) candidates:
>
> (The Droop Quota for the stage) = (1/9)+(some small amount)

1/9 is wrong: the Droop Quota fraction for winners = 1/13 + z, z>0.

Mr Davidson was writing on STV quotas. In a quality method, altering
 quotas can lead to vectors through the election simplex seeing the
 wrong side of faces.

 For example, in a 4 candidate preferential voting election there
 are 40 different types of papers. At the first stage of a STV-like
 method using iteration, the candidates have their 1st preference
 votes checked. Each has 10 types of papers.
 The win-lose boundaries which cut up the simplex and represent where
 winners becomes losers, have 39 dimensions. The flats that are Quotas
 for winners and that apply to the 1st preference counts in the 1st
 stage, have their normals pass through the centre of the simplex.
 Adjusting the Quota for winners shifts those flats. If the Quota is
 zero then they contain the candidates 10 vertices.

 These flats need to butress into the joins between other flats or
 else the entire method is more likely to have 39 dimensional surfaces
 that violate the slope costraints that derive from constraints
 in outcomes when various types of alterations of papers are made.

 STV has steps where there is dividing by numbers of votes, and so
 there would be a problem butressing flat flats that result from
 quotas or any of the "if then else"s in the method, into the various
 curved N-2 dimensional edges. 

 New versions of STV, CPO-STV, are being devised that will likely have
  yet more edges.

__________________________________________________________________
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
MEDLINE (PubMed), Public Proxies, Multithreaded Add-URL DNSLookup
__________________________________________________________________