[EM] Proportional preferential voting

[David Catchpole]

By your own admission, though, it gets to be a little bit of a hassle by
the 4th candidate- and finding general rules becomes more and more
important. What could otherwise be a rather painstaking case-by-case
formulation of an answer isn't as much fun as a simple algorithm for every
case. (A similar case-by-case exposition of monotonicity was discussed a
fairly long time ago by Blake Cretney and me).

[more further down]

On Sat, 18 Sep 1999, Craig Carey wrote:

> 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..)/?

Obviously, in this case it would be pretty daft to distribute all of A's
votes to C.

I like to come up with an instantaneous solution for the new quota by-
q=(T-q-i)/n
i=I(V-q)/V

(Haven't given you the explicit solution, but you get my drift)

where q is the quota, T the total number of valid votes, i the number of
votes which fail to be effectively transferred, n the number of seats left
to be filled including the one just filled by the candidate whose votes
are being transferred, I the number of votes for that candidate that
aren't going to any other candidate,  V the number of votes for that
candidate. The value of a votes' transfer is then (V-q)/V

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

We all have our favourites on this list. Over time, this becomes
really apparent- especially with respect to who gets involved in what
discussion. For instance, I will rarely if ever get involved in a "clone
war." (Hee hee)

Arrow, etc. make it clear that the "strict reasonable criteria" are a
threat amongst themselves. IIA and the sub-criteria of it which I
make distinct are strict reasonable criteria used by theorists of voting
and other theorists in social choice (e.g. market theory). The way to
state IIA for deterministic models of choice is this-

"The removal or addition of an option which has not been selected will not
alter the outcome"

for models of preference-

"The removal or addition of an option should not alter the preference
between any other pair of options"

for probabilistic models of choice-

"The removal or addition of an option which has not been selected will not
reduce the chances of any outcome where that option is not chosen"

> >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).

That I understand, it was to use 1/(integer) quotas until someone was
elected.

Oh don't ask me to do that! ;\ I would try searching through our archives
at www.egroups.com (browse through the subjects to find the list) and
using the search keyword "quota." Hopefully the subject line will tell you
which of the umpteen messages you'll see listed are of use to you.

>                 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.

Where a Condorcet winner exists, principle 1 is satisfied as the
preferences between the CW and other candidates are not altered by any
swapping below (or above- as long as it's above-to-above or
below-to-below it's alright) that candidate in anyone's preferences. As a
result, the head-to-head considerations that lead to a Condorcet answer
are unaltered and the CW remains a CW.

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

My yooonivarzitie don't teach voting theory (there is a tiny "elections
and electoral systems" subject which formerly was run by an econometrist
and I expect included considerations of the more theoretical aspects of
voting, but it was hijacked by a psephologist before I did it, and now
it's more on the sociological aspects of voting choice, rather than on the
systems- all the other students think it's cool. Grrr...). However, being
a Science / Arts student I have weird interests and have tried to learn
voting theory on the go (to the detriment of other studies- I'm supposed
to be doing an industrial relations assignment right now). Thankfully we
have a good representation of the relevant books and journals at my uni
library.

The "UQ" in my e-mail address stands for- University of Queensland
(Brisbane)

> 
> 
> >> >> 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...

Actually, after further consideration, I've decided that's wrong. I
haven't worked out how to accurately say why, but I can say this- the
concept becomes absurd if the idea is considered violated if, for
instance, as in FPP, one vote for A is worth the same with respect to A's
win as 10 for B and one for A. I say the same absurdity is generated with
respect to any examples in Condorcet of a group of votes being "worth
less" than another group of votes.

> 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.

werks okae weyr aye cum frum.