[EM] Proportional preferential voting
Craig Carey
research at ijs.co.nz
Wed Sep 22 11:11:10 PDT 1999
Note: at the end of my last message there was an outline
of the derivation of the IFPP 3 candidate 1 winner formula.
This message sort of adds to that derivation. Finishing the
derivation needs a corner to be clipped:
make (B wins) = (B wins) & (1/3 < b).
At 23:06 99/09/22 , you wrote:
>Dear Julian,
>
>you wrote (22 Sep 1999):
>> See the "Note of Reservation" by Lord Alexander of Weedon QC in
>> the Report Of The Independent Commission on the Voting System,
>> (http://www.official-documents.co.uk/document/cm40/4090/chap-9.htm#c9-a).
>> His comments are about 'small-STV', called AV, but the point is
>> equally applicable.
>>
>> Indeed, Lord Weedon almost but not quites manages to conclude that
Lord Alexander
>> non-monotonic systems have embedded randomness -- something not
>> widely acknowledged.
>>
>> -----------------------------------------------
>> Julian D. A. Wiseman, http://www.jdawiseman.com
>>
>>
>> > -----Original Message-----
>> > Dear Craig,
>> >
>> > I haven't yet understood the intention of your mails.
>> > To help me understand your thoughts, I want to ask you
>> > to give an explicite example where -to your opinion-
>> > a plain vanilla STV method leads to a problematic
>> > or unjustifiable result. And I want to ask you to
>> > explain why this result is problematic or unjustifiable
>> > to your opinion.
>> >
>> > Markus Schulze
>
>Thank you for your quick reply. But it doesn't seem to me that
>Craig criticizes the currently used STV methods because of their
>lack of monotonicity. Could you -please- quote that part of
>Craig's mails that you interpret as a criticism of the lack of
>monotonicity of the currently used STV methods.
>
>I must admit that I haven't yet understood the aim of Craig's
>mails. Maybe he should give a motivation for his method.
>
>Markus Schulze
------------------
Monotonicity might perhaps mean concave win regions?. I don't
know all the terminology. What is the aim: when a single German
gets into the voting booth, he may expect that his vote does not
become reversed in effect or whatever through some dumb paradox.
If electors don't like votes for candidate A causing A to lose,
then for starter's they could keep away from STV (any number
of winners).
The word randomness may mean: excess of corners of the win-lose
regions. What is the probability of a random line segment
crossing a win-lose boundary (easy to estimate with random
numbers).
Two major problems with STV are (1) it fails (P1), and (2) the
transfer values waste votes.
Lord Alexander writes about AV ("Alternative Vote" sytems, and
identical to 1 winner STV).
: AV comes into play only when a candidate fails to secure a majority
: of first preference votes. It does not, however, then take account
: of the second preferences of all voters, but only of those who have
: supported the least successful candidates. So it ignores the second
: preferences of the voters who supported the two candidates with the
: highest first preference votes, but allows the voters for the third
: or even weaker candidates to have their second votes counted so as
: to determine the result.
I suppose the [IFPP] fix is to test against quotas (S/3, S/4, etc.)
in some way or another.
: I find this approach wholly illogical. Why should the second
: preferences of those voters who favoured the two stronger
: candidates on the first vote be totally ignored and only those who
: support the lower placed and less popular candidates get a second
: bite of the cherry? Why, too, should the second preferences of
: these voters be given equal weight with the first preferences of
: supporters of the stronger candidates? In 1931 Mr Winston Churchill
: described this proposal as taking account of "the most worthless
: votes of the most worthless candidates". He went on to describe AV
After 68 years, the UK government still can't locate original British
research...
: as containing an element of blind chance and accident which would
: lower respect for Parliament. Churchill's comments warrant even
: greater weight because at that time he was not unsympathetic to
: some sensible form of electoral reform. In addition, as all experts
: on electoral systems have acknowledged, AV can operate haphazardly
: depending upon the rank
+++++++++
My last message had at the bottom, much of a derivation of
IFPP. This messages shows that finishing the derivatio of
ISPP is just a matter of clipping the corner out of STV that
causes the (R1) failure.
--------------------------------------------------------------
Alteration Rule (R1):
A voting method satisfies rule (R1) if there are no
instances of this change occuring:
1. B wins: C { B A
2. C wins: AB { C
--------------------------------------------------------------
All preferential voting methods that do not satisfy (R1) also
do not satisfy the rule (P1), because of what happens about
candidate C. (What happens to B is perhaps a little questionable
too, but I suppose it definitely ought be allowed.)
The (P1) failure corollary can be seen by: making the candidate
under consideration 'C', and noting that C flips from losing
to winning when 2 votes having a first preference for C
are altered in the allowed AtAltAfter way.
Here is the simplest example that nearly finishes off STV.
------------------------------------------------
Sample Election example (E1)
V1:
5 AB
6 B
10 C
STV: B, IFPP: C, FPTP: C, Cond: B
V2:
7 AB
6 B
8 C
STV: C, IFPP: C, FPTP: C, Cond: {}
------------------------------------------------
STV fails (R1) and it also fails (P1).
If STV won't make it past a (P1) test then it might as well
be redesigned. I don't suppose the original designers of
STV explained why in example (E1) C loses unless not voted
for.
The defect with (1 winner 3 candidate) STV can be fixed by
tilting some boundaries.
------------------------------------------------
The one winner solution to this voting system:
V:
AB a
B b
C c
The STV winner:
Aw = (b<a)(c<a)
Bw = (a<b)(c<b+a)
Cw = (a<c)[(b+a<c) or (b<a)]
The IFPP winner:
Aw = (b<a)(c<a)
Bw = (a<b)(c+a<2b)(c<b+a)
Cw = (a<c)[(b+a<c) or (2b<c+a)]
A corner is cut off STV to make IFPP.
STV passes the "SPC" test, which is weaker test than (P1).
--------------------------------------------------------
Here's a list of what properties it seems to me that
a preferential voting method resembling STV should
satisfy. It might seem somwhat arbitrary.
Tests:
(P1) [This implies the SPC rule and that itself implies that
problems can be decomposed into sub problems]
The method is multiwinner 'First Past the Post' when there are
no 2nd preferences. That method passes all these tests.
Linear (so polytopes and flats only. Both the vote alteration
constraints and also proportionality give rise to flat
surfaces, and if boundaries (say in STV) are curved, then
they could be optimised until they become the union of
flat surface regions. So no dividing by the number of votes
in parcels would occur in an optimal method)
The method satisfies the Duality relationship. [FPTP does, whye
should't any other method?]
'Absence of constuctable examples of altering the voting paper
that make the method do something wrong or stupid. [The (P1)
rule is an instance of this rule]
Always returns the correct number of winners (Condorcet is
failed by this). Results are unique (excl ties). No random
numbers (cause problems in recounts).
To the extent achievable, absence of arbitrary rules. (They
marr publications that show the derivation).
The effect of a vote is not more than its weight. (E.g. can't
have 5 2nd preferences, causing a win, when it would take 6
1st preferences to do the same). [Maybe this could be
worded as clearly as (P1)]
The method is 'proportional'... For example, the divide
between where B & C win could be (b+Zab = c+Zac).
A computer ought to be able to run the method. (This rule
is probably going to hold OK without it being imposed).
Some of the above is a little imprecise.
Other people will have different criteria.
----------------------------------------------------
_____________________________________________________________
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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