[EM] Meek style STV - Part One of Two

[Craig Carey]

Text from a PDF file.

The method described in the Acrobat document at

       http://www.econ.vt.edu/tideman/rmt.pdf

has the authors: Nicolaus Tideman (Department of Economics, Virginia
 Polytechnic Institute and State University, Blacksburg, Virginia) &
 Daniel Richardson (...).

The document describes a method called CPO-STV which I may as well
 not provide information about. There is a bit of mention of it here:
    <http://members.aol.com/loringrbt/FutuRule.htm#CPO>

I am wondering if CPO-STV introduces new bad properties (like (P1)
 violations), while removing other bad properties or just getting
 STV to devalue votes less.


------------------------
FROM the PDF document 

:
: In 1868, another London barrister, H.R. Droop, suggested that if there
: are n votes and k positions to be filled, then the quota of votes
: needed to secure election should be not n/k, rounded down to an
: integer, but rather [n/(k + 1)] + 1, rounded down to an integer. A
: rationale for Droop's suggestion is that when just one candidate is
: elected, a candidate needs barely more than half the votes to be
: assured election. If a candidate has more than half the votes, then no
: other candidate can have as many votes.
: 
: Similarly, if two candidates are to be elected, then any candidate with
: more than a third of the votes ought to be assured election on the
: basis that there can be at most one other candidate (who can be given
: the other position) who will receive as many votes. In general, if
: there are k positions to be filled, then there can be at most k
: candidates who have more than 1/(k + 1) votes. The Droop quota is the
: smallest integer quota such that the number of candidates who achieve a
: quota cannot be greater than the number to be elected.
 

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)

:
: The Droop quota is also valued for its ability to prevent some outcomes
: in which a majority coalition is awarded only a minority of the
: positions.
: 
: Suppose that 48 voters vote as follows to fill three positions:
: 
: 16ABCD
: 10BADC
: 11CDAB
: 11DCBA
: 
: The 26 voters who rank A and B first and second are a majority of the
: electorate. But if the Hare quota of 48/3 = 16 is used, then after A is
: elected B will be excluded, and both C and D will be elected. On the
: other hand, if the Droop quota of (48/4) + 1 = 13 is used, then A is
: elected, A's surplus is transferred to B, producing B's election, and
: one of the remaining two candidates is chosen at random to fill the
: final position.
: 
: The Droop quota is not quite ideal. To guarantee that a solid coalition
: that is supported by a majority of the voters will never receive only a
: minority of the positions, the quota must be the rational number n/(k +
: 1). Then if it should happen that k + 1 candidates receive exactly a
: quota of votes, one must be picked at random to be excluded.
: 

----------------

: 
: Brian Meek (1969) proposed such a method. In Meek's method, a
: "retention fraction," fi, is computed for each elected candidate, such
: that when every elected candidate retains the fraction fi of every
: voter or fraction of a vote that is transferred to him, every elected
: candidate receives exactly a quota of votes. Hill et al. (1987) showed
: that there is an algorithm that generates numbers that converge to the
: retention fractions. The Meek method is applied to Election 53 in Table
: 3.
: 
: The first stage of Table 3 is exactly the same as in the Newland-
: Britain method. At the second stage, Meek's method takes account of the
: votes that cannot be transferred, by reducing the quota to 1/5 of the
: usable votes. Thus the excess of 0.66 at Stage 2 of Table 3 is the 3
: votes for candidate J that could not be transferred, at 0.221 each,
: where the excess of 0.70 in the Newland-Britain method is the remainder
: after dividing 26.00 by 115. The Meek method also computes the quota
: and the fractions of votes that candidates retain to the accuracy of a
: computer, rather than rounding to hundredths.
: 
...
: 
: 5. Warren Meek's view of a just distribution of the power to have one's
: vote transferred was challenged by Hugh Warren (1983). Warren argued
: that in a just vote-counting procedure, if a voter ranks one or more
: elected candidates ahead of his highest-ranked unelected candidate,
: then he should be required to contribute as much as every other
: contributing voter to the quota of each such elected candidate, before
: he is allowed to contribute to the election of any unelected candidate.
: Thus in Warren's method, instead of computing retention fractions, fi,
: one computes candidate prices, pi, with the property that when every
: voter contributes pi (or all of his remaining vote, whichever is
: smaller) to every candidate i to whom the vote is transferred, every
: elected candidate receives exactly a quota of votes. The application of
: Warren's method to Election 53 is illustrated in Table 4.
: 


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At 01:43 14.10.99 , Markus Schulze wrote:
>I want to add:
>
>1) Good descriptions of the Meek Method can also be found in
>
>   I.D. Hill, B.A. Wichmann, Douglas R. Woodall, "Single
>   Transferable Vote by Meek's Method," The Computer Journal,
>   Vol. 30, No. 3, page 277-281, June 1987,
>
>   T. Nicolaus Tideman, "The Single Transferable Vote," The
>   Journal of Economic Perspectives, Vol. 9, No. 1, page 27-38,
>   Winter 1995,
>
>   T. Nicolaus Tideman, Daniel Richardson, "Better Voting Rules
>   Through Technology: The Refinement-Manageability Trade-Off
>   in the Single Transferable Vote," Public Choice, not yet
>   published, 1999. (http://www.econ.vt.edu/tideman/rmt.pdf)
>
>2) The Meek Method is used by the Royal Statistical Society
>   (ca. 6000 members).
>
>Markus Schulze
>
>P.S.: It is sad to hear that Brian Lawrence Meek died.

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