[EM] unequal cumulative vote allocation
Although it is generally good strategy to allocate points equally among all choices under cumulative voting, there seem to be exceptions. For example, in an election to fill several seats with a number of different factions, you have two similar factions of equal size, who are just barely "entitled" to three seats between them. Ideally, they should be able to run one candidate each, plus one "shared" candidate that the two groups agree on. With paper ballots, and each voter allowed 3 points to allocate, a voter could give 2 points to his/her "own" candidate, and one point to the "shared" candidate. With the Peoria system, where a vote is always allocated equally among a voter's choices, you can resort to massive coordination, or simply instruct the voters to use a die from a Parcheesi game. If the voter rolls a 1 or 2, he should vote only for the party's favorite. If the voter rolls 3 or higher, vote for both the party favorite and the shared candidate.
Re: [EM] Proportional preferential voting
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
Re: [EM] Voting paradoxes article
Dear David, I am not sure whether I have understood you correctly. That's why I want to ask you to explain your thoughts using the following two examples? ** Example 1: There are 120 voters and 4 candidates for 2 seats. 8 voters vote A C B D. 8 voters vote A C D B. 8 voters vote B C A D. 8 voters vote B C D A. 8 voters vote C A B D. 8 voters vote C A D B. 8 voters vote D A B C. 8 voters vote D A C B. 7 voters vote A D B C. 7 voters vote A D C B. 7 voters vote B D A C. 7 voters vote B D C A. 7 voters vote C B A D. 7 voters vote C B D A. 7 voters vote D B A C. 7 voters vote D B C A. If I understand you correctly, then either (A and B) or (C and D) must be elected in Example 1. Because of the Anonymity Criterion and the Neutrality Criterion, you can presume without loss of generality that C and D are elected. ** Example 2: Now, candidate E is added so that there are 120 voters and 5 candidates for 2 seats. 8 voters vote A E C B D. 8 voters vote A E C D B. 8 voters vote B C A E D. 8 voters vote B E C D A. 8 voters vote C A B E D. 8 voters vote C A D B E. 8 voters vote D A B E C. 8 voters vote D A C B E. 7 voters vote A D B E C. 7 voters vote A E D C B. 7 voters vote B E D A C. 7 voters vote B E D C A. 7 voters vote C B A E D. 7 voters vote C B D A E. 7 voters vote D B A E C. 7 voters vote D B C A E. What does Consider an election of n seats. Are there any combinations of n "Condorcet winners" who win in any consideration of n+1 candidates? If there are more than one combinations which do this it becomes more complex and involves more head-to-head stuff- but, for simplicity, ignore this. I would argue that this setup (with your choice of election rules for the n+1-n election and the head-to-head untying elections) is independent of the removal of irrelevant alternatives wherever an answer exists- just like Condorcet! mean in this context? ** Markus Schulze
Re: [EM] Proportional preferential voting
The "principle 1" is incorrectly defined.
New definition:
Principle 1 (P1), Sat 18 Sept 1999
For all c (c is a candidate), all V, all V' (where
V and V' are election systems), then if
V' in AltAtAfter(V,c) and c loses V, then c
also loses V'.
AltAtAfter(V,c) is defined to be the set of all
election papers collections that can be derived
from V by altering preferences at and/or after the
preference for preference c.
For example,
V:
10 ABC
11 B
S
One system in AltAtAfter(V,'B') is this:
10 A
2 AB
3 ACB
4 AD
1 B
1 C
S
No deletion of the ABC papers was possible, so
since A has 19, 9 papers did come from the alteration
of the 11 B preferential voting papers.
At 06:01 99/09/18, Craig Carey wrote:
[...
-
Principle 1 (later superceded)
Alterations of preferences after a preference
for a winning candidate never cause that
candidate to lose.
-
[...
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 (P1) ('principle 1')
principle that is shown above ?.
Please respond with a proof or a counter example.
...
What's that multiwinner method Schulze has: surely that's failed
by (P1).
There could be a few more theories failed by my principle (P1).
It would be interesting to see if some can get a few of the
giant scurrying brown cockroach like theories that move
past the vision of the recipients of this mailing list (the
'[EMAIL PROTECTED]' mailing list).
G. A. Craig Carey. Avondale, Auckland, NEw Zealand, 18Sep99
Mr Craig Carey
E-mail: [EMAIL PROTECTED]
Auckland, Nth Island, New Zealand
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