[EM] STV and having quotas to eliminate losers
Bart Ingles
bartman at netgate.net
Tue Oct 12 22:45:08 PDT 1999
Am I correct that the loser's quota will cause the following two
examples to elect the same winner as FPP? I would say that it would be
in improvement over Alternative vote in the first example, but not in
the second.
Bart Ingles
Example I:
Sincere Voter Rating:
100 90 10 0
-------------------------------------------------
45% A B C
27% B C A
28% C B A
Example II:
Sincere Voter Rating:
100 90 10 0
-------------------------------------------------
45% A B C
27% B C A
28% C B A
Craig Carey wrote:
>
> At 11:53 13.10.99 , David Catchpole wrote:
> >On Wed, 13 Oct 1999, Craig Carey wrote:
> >
> >> The Droop Quota...
> >>
> >> "[the] Droop Threshold is the number of ballots divided by
> >> (the number of seats plus 1), then adding 1"
> >
> >While this is the usual definition of Droop quota in most legislation, I
> >prefer to think along the lines of Droop simply meaning "votes greater
> >than the number of ballots divided by (the number of seats plus 1) mean a
> >win for the candidate."
>
> Notwithstanding that adding of 1 which might suggest to people who prefer
> the "1/N" of the Hare formula, the Droop Quota actually specifies use of
> 1/N when used in the Alternative Vote method.
>
> Some more details on how to fix STV and not merely make less probable, its
> unacceptable behaviour, but also get it nearer to passing the duality rule
> (which says that 'the method itself results from swapping winners with
> losers and negating votes').
>
> STV could be improved by having quotas applied against losers.
> (Doing that not merely reduces defects but makes the method more like
> First Past the Post (FPP, FPTP).)
>
> Perhaps some of the proponents of electoral reform could identify for
> me, the grounds on which the method tends to be rejected.
>
> Some may find the following arbitrary.
>
> -------------------------------------------------------------------------
>
> TWO QUOTAS
>
> Define the Droop Quota Fraction For Winners to be such that, the
> (Droop Quota) = the (Droop Quota Fraction For Winners) times the
> number of [valid] votes.
>
> In STV, the Droop Quota Fraction For Winners is:
>
> 1 / (number of winners that have still yet to be found)
>
> This modified STV theory has applies a Quota to losers which can be
> called the Droop Quota for Losers.
>
> The Droop Quota Fraction For Losers is:
>
> 1 / (number of losers that yet to be eliminated)
>
>
> Consider STV:
> * the initial number of candidates = NC;
> * the winners that need to be found = NW;
>
> In each stage of vote transferring:
>
> * the number of candidates remaining = N
> * the number of winners have yet to be found = M
> * the number of losers have yet to be found = (N - M)
>
> the two Quotas are:
>
> (Quota for Winners) = 1/(M+1)
> (Quota for Losers) = 1/((N-M)+1)
>
> (Neither STV nor the AV method has a quota for losers).
>
> -------------------------------------------------------------------------
>
> ELECTING ONE WINNER:
>
> The proposed Quotas for a modified Alternative Vote method are
> found by substituting the values in:
>
> * the number of candidates remaining = N
> * the number of winners have yet to be found = M = 1
> * the number of losers have yet to be found = (N - 1)
>
> the two Quotas are:
>
> (Quota for Winners) = 1/2, = 1/(M+1)
> (Quota for Losers) = 1/N, = 1/((N-1)+1) = 1/((N-M)+1)
>
> -------------------------------------------------------------------------
>
> ELECTING TWO WINNERS:
>
> * (Quota for Winners) = 1/(M+1), M = number of winners yet to be found
> * (Quota for Losers) = 1/((N-M)+1), N = number of candidates remaining
>
> When two winners need to be elected, the Quotas would be:
> Case: M=2, i.e. 0 winners have found:
> (Quota for Winners) = 1/3, = 1/(M+1)
> (Quota for Losers) = 1/(N-1), = 1/((N-2)+1) = 1/((N-M)+1)
>
> Case: M=1, i.e. 1 candidate has been picked a winner:
> (Quota for Winners) = 1/2, = 1/(M+1)
> (Quota for Losers) = 1/N, = 1/((N-1)+1) = 1/((N-M)+1)
>
> Information about what STV is, follows.
> Each "if then else" in the method makes STV even more complex when
> the actual shape of the win-lose boundaries are being considered.
>
> -------------------------------------------------------------------------
>
> A DEFINITION OF STV
>
> The text is copied from pages here & around here:
> http://www.cix.co.uk/~rosenstiel/stvrules/index.htm
> http://www.cix.co.uk/~rosenstiel/stvrules/details.htm
>
> (The details about 2 decimal places have been removed).
>
> The basic idea is that at each stage, surpluses of winners are
> transferred and surpluses of losers are transferred. Rules determining
> when transferring stops don't seem to be clearly the rules that would
> be best.
> Paragraph 5.2.5 makes it clear that losers are rejected by rejecting
> them one by one, and no quota exists that causes more than one loser
> to be rejected simultaneously. It is that feature of STV that is
> being said to be a bad feature.
>
>
> ---- Transferring of Surpluses and Finding Winners ----------------------
> 1.2
> (iii) Election by quota, being the minimum number of votes which,
> if attained by as many candidates as there are places to be
> filled, leaves at most a quota of votes unused. This is the
> Droop Quota, being the total valid vote, divided by one more than
> the number of places to be filled. Thus, if seven representatives
> are elected together, and if each of seven candidates obtains a
> Quota of one-eighth of the votes, then at most one-eighth of the
> votes are unused;
>
> 5.1.6
> Calculate the quota by dividing the total valid vote by one more
> than the number of places to be filled.
>
> 5.2.2
> If one or more candidates have surpluses, the largest of these
> should now be transferred. However the transfer of a surplus or
> surpluses is deferred and reconsidered at the next stage, if the
> total of such surpluses does not exceed either:
> (a) The difference between the votes of the two candidates who
> have the fewest votes, or
> (b) The difference between the total of the votes of two or
> more candidates with the fewest votes who could be excluded
> under rule 5.2.5, and the vote of the candidate next above.
>
> 5.3.7
> Calculate the total value of the transferable papers.
> If this exceeds the surplus, determine the transfer value of each
> paper by dividing the surplus by the number of transferable
> papers. If the total value does not exceed the surplus, the
> transfer value of each paper is its present value.
>
> ---- Eliminating Losers and Transferring their Voters ------------------
>
> 5.2.5
> If, after all surpluses have been transferred or deferred, one or
> more places remain to be filled, the candidate or candidates with
> the fewest votes must be excluded. Exclude as many candidates
> together as possible, provided that:
> (a) Sufficient candidates remain to fill all the remaining
> places
> (b) The total votes of these candidates, together with the
> total of any deferred surpluses, does not exceed the vote
> of the candidate next above.
>
> 5.2.7
> Exclusion of one or more candidates constitutes a stage in the
> count. If, after completing this, there are any surpluses to
> transfer, and not all the places have been filled, proceed as in
> paragraph 5.2.2. Otherwise proceed to exclude further candidates
> as in paragraph 5.2.5.
>
> -------------------------------------------------------------------------
>
> Has anybody else got some suggestions on whether or not paragraph 5.2.5
> (or the corresponding paragraph in other documents), should be
> reworded?. If it would be modified, then what would the new wording be?.
> Modifying STV is likely to always to end up with a method that is not
> optimal. So much so, I wouldn't consider it a significant problem if
> ties were resolved by a rule like this [hypothetical]:
>
> ...then all preferences in the parcel that was about to elect a
> Tory candidate (or one in list (1) of Schedule E) that would have
> had tied in outcome to within 2.3% of another candidate but lost,
> shall have all sub-parcels remarked in the way specified in
> Schedule E and the rules ...
>
> Craig Carey
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