[EM] Proportional preferential voting

[Craig Carey]

At 17:29 99/09/17, David Cratchpole wrote:
> Oh! It solves the thing on a case by case basis (like finding
>all examples of inversion and using the rule to exclude answers)!

Alteration rules (rules that constrain the effects caused by
 altering preferences on one or more types of papers) hold even
 if other candidates are added to the election.
 Solving sequentially is easy and obvious way to obtain that
 property of invariance wrt. additional candidates, and it
 also allows about-minimal incursions into the unknown topic of
 'just which rules are the ones to require'.

-------------------
At 17:28 99/09/17, David C wrote:
>I was thinking more of explaining what your []or[]'s meant... starting
>from the beginning with a sentence explaining the layout of the model and
>the structure you describe.
>
>> [The STV 2 winner formula is too complex and yet wrong.
>> The transfer denominator is wrong in "the" method as far
>>  as I know. ... 
[>...

The denominator comment is believed by me to be probably wrong.
STV: 3 candidates 2 winners:
   A  670
   AC  10
   B  320
Votes for A = 680
Quota = 333.3..
Transfer value = (680-333.33..)/?

A partial description of STV:
In STV, when a candidate has more than its needed quota of
 votes, the surplus (i.e. votes in excess of the quota it needs
 or else it gets rejected) is transferred to the other
 remaining candidates.
 In versions of STV that transfer all papers (rather than
 just some that were selected randomly), the parcel is split,
 and then the weight of each paper in the parent parcel is
 reduced in weight (multiplied by the transfer value).

In IFPP, no division ever occurs. In STV with more than one
 winner, the boundaries to regions are not actually all
 unions of polytopes.

[>>...
>> What are "norms of voting". The "_complete_" preferences
>>  of voters get separated from the quantities of bundles
>>  of papers. It is possible to make the 'loss' point with
>>  sample election examples.
>
>I'm using what I've been taught in my university's government department's
>parlance- a norm, as in normative economics, is a statement of value or

>an axiom... a principle which either is self-evident or is assumed to be
>so for the best of worlds. Independence of the removal of irrelevant
>alternatives (my particular fave) is a norm of voting because I hold that

What is a 'fave' meth Dave?: is it a threat to any of the strict
 reasonable criteria that some theorists might write about?.

>elections must be "fair" and that "fair" includes a self-evident "right"
>to acknowledge all options without loss whenever one can (which is not
>always, because Condorcet paradoxes are an exception). Another example of
>a norm of voting is monotonicity- a behaviour of indication will always
>have an improving/neutral effect.
[>..
>
>I feel I'm starting to understand... I take it IFPP involves- determining
>the number of electors and dividing it by 3, and then- holding a runoff
>between the one or two candidates who make such a quota. Am I right? A
>similar extension which was mooted by a person on this list a few months
>ago was progressively going from quota to quota until one had a single
>candidate left. For continuous reductions of quota, this evolves into
>common or garden Australian STV (STV is a family, not just one electoral
>system).

What was that idea ? (or what is the date on the message, or quote
 the message).

Anyway, in the 4 candidate IFPP case, there is both a 'divided by 3'
 quota term (or figure) and a divided by 4 quota term.
 From equations I have, which I am not making available [I recall
 suspecting an lack of rigour) on of the pages], there does seem to
 be something like what you describe: candidates are rejected against
 quotas that are smaller when the candidate is closer to losing.

-----------------------------------------------------
                      Principle 1 

     Alterations of preferences after a preference
     for a winning candidate never cause that
     candidate to lose.
-----------------------------------------------------

The rule allows decomposition of STV-like formulae.
STV satisfies the principle because at no time, are effects
 derived from peeking ahead at subsequent preferences.
IFPP satisfies the principle. (It need not be called
 principle 1). 
Principle 1 can apply to more than one voting paper type,
 and when the candidate is in the first preference, then
 it permits deletion.


                CONDORCET AND TRAILING PREFERENCES

I have a question for Mr Catchpole and Mr Markus Schulze, or
 anybody who wishes to answer:

 Does Condorcet (1 winner) satisfy the 'principle 1'
 (given above) ??.

Please respond with a proof or a counter example.

David: what's the University you happen to be studying voting
 theory at?.


>> >> I'd hope to see an example proving that the Condorcet method
>> >>  violates the "one man one vote" idea.
[>> >...
>> 
>> ("man" means "vote", and "vote" means 'effect' or influence).
>
>As in, where n voters of type a are required to change the result, >n of
>type b are required to do the same thing? I'll agree with that and maybe
>soon I'll come back with an example...
>
>> STV passes that test of "one man, one vote" flawlessly.
>
>I'm not entirely sure about this... can you tell us why?

STV loses a few votes when surpluses are transferred.
Voting in STV just requires a little extra thinking (or
 instructing) on the part of voters. It is not merely a
 problem for mathematicians and the public, politicians
 are quite wary of the method.



Mr Craig Carey

E-mail: research at ijs.co.nz

Auckland, Nth Island, New Zealand
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