[EM] Proportional preferential voting

[David Catchpole]

On Thu, 16 Sep 1999, Craig Carey wrote:
> 
> When a candidate alters a vot in a voting booth, the effect
>  of that change is limited. STV has an infinity of its
>  own paradoxes like Condorcet, and they can be removed but
>  with the result of shifting the method slightly towards
>  FPP (although STV is quite strange as votes get wasted at
>  most transfers of parcels).

One can't remove paradoxes of voting (I'm talking here about paradoxes
ala Condorcet) but admittedly other "artificial" problems with voting are 
removable. It's odd that you say that removing some of these problems
leads us towards FPP. In fact, I would say the opposite- as I understand
it, your interpretation is the same as a writer on computer voting (her
name eludes me- Donald knows, I think...) who neglected to acknowledge the
fact that norms of voting extend to the _complete_ preferences of a voter,
not just the marks they put down on paper (in her case, she said
something as silly as "FPP is always independent of irrelevant
alternatives"). So for the norm you give-
 
>  'permuting all preferences before a preference for a
>   particular candidate, never makes a difference to
>   that candidate's win/lose status'.

which is covered by considerations of IIA, FPP is nasty (worst?)...
because obviously, where there are preferences above a winner, how they 
are arranged makes quite a significant impact on whether that candidate
wins (A has 49 votes, B has 50 votes, C has 30 votes... if two other
voters have voting preference A>C>B or they have C>A>B... obviously this 
is for one-seat FPP but similar problems would arise for multi-seat
methods).

>  Unfortunately it cannot be obtained because it would cause
>  about all solutions to degenerate into First Past The Post
>  starting with the 3 candidate solution. I haven't a proof
>  available so that could be conjecture.

> Mr Saari has a duality rule, which I sent to him and which
>  he may be on the verge of saying is not of value. 'll let
>  that respected mathematician decide whether it is worth
>  mentioning or not. One of his publications has the word
>  geometry in it. That why I decided to write: his booklet
>  on 'geometry' in voting.

Well, there's the voting space for three candidates with canonical
preferences...


> What of Condorcet, a topic of this mailing list?:
>  An example: In an election with 2,152,370 candidates and
>  430,927 winners, how can it be certain that pairwise
>  comparing of two candidates is an idea that ever had some
>  mathematical importance on the fist day?, in France is it?.

In practice, it's a bit easier... we don't have 2,152,370 candidates and
more than likely two candidates can be compared and then run through
comparisons with the others.

 
> I'd hope to see an example proving that the Condorcet method
>  violates the "one man one vote" idea.

Huh? (Sorry for abruptness...)

> PS. Thinking numbers is a dead end if the method is based on
>  alteration rules, since election examples cannot be solved until
>  an infinity of other other election examples are found.
>  Quite implicit. That is known: a paper has been published.
>  Lat time I checked there was only one (3-4 years ago).
>  Switching to hypergeometric algreba simply removes the
>  implicitness.

Well, maths is more than numbers... Could you tell us what the paper is
(it's pretty intuitive that a general approach is needed...)?

One would have thought an algebraic approach would make the answers
implicit (as in, non-specific)?
> 
> The 3 candidate methods: 
>   Proportional rule based preferential voting
> 
> 
> ----------------
> |A.. |     |   |
> |AB. | Zab | a |
> |AC. | Zac |   |
> ---------------
> |B.. |     |   |
> |BC. | Zbc | b |
> |BA. | Zba |   |
> ----------------
> |C.. |     |   |
> |CA. | Zca | c |
> |CB. | Zcb |   |
> ----------------
> 
> (A wins) = (b+c<2a)[(b+Zcb<a+Zca) or (2b<a+c)][(c+Zbc<a+Zba) or (2c<a+b)]
> (B wins) = (a+a<2b)[(c+Zac<b+Zab) or (2c<b+a)][(a+Zca<b+Zcb) or (2a<b+c)]
> (C wins) = (b+b<2c)[(a+Zba<c+Zbc) or (2a<c+b)][(b+Zab<c+Zac) or (2b<c+a)]
> 
> ({B,C} win) = (b+c>2a)[(b+Zcb>a+Zca) or (2b>a+c)][(c+Zbc>a+Zba) or (2c>a+b)]
> ({C,A} win) = (c+a>2b)[(c+Zac>b+Zab) or (2c>b+a)][(a+Zca>b+Zcb) or (2a>b+c)]
> ({C,A} win) = (a+b>2c)[(a+Zba>c+Zbc) or (2a>c+b)][(b+Zab>c+Zac) or (2b>c+a)]
> 
> The total number of papers for A is a, etc.
> The number of voting papers marked 'ABC' is Zab, etc.
> The duality relationship that seems to apply to this class
>  of methods, is evident.
> 
> The alteration rules roughly merely define slopes of flats bounding
>  the convex polytope where a single candidate wins.
> 
> The is no arbitrariness introduced into the formulae above.
> There is no proof also, so please regard this message as being
>  perhaps without merit since there is absence of even intent
>  to provide proof.
> 
> I want another mailing list, a place where numerical examples are
>  used just for destroying other methods and algebra of polytopes
>  is used to build rigourously, preferential voting theory.
> Which then gets implemented onto computers.
> 
> [Sent to mailing of
>     http://www.eskimo.com/~robla/cpr/election-methods.html ]
> 
> 16 September 1999
> Mr G. A. Craig Carey
> Avondale
> Auckland
> 
> 
> 
> 
> 
> 
> Mr 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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