[EM] "More often" (was: IRV and Condorcet operating identically)
Jan Kok
kok at surfbest.net
Fri Feb 28 16:57:44 PST 2003
----- Original Message -----
From: "Craig Carey" <research at ijs.co.nz>
To: <election-methods-list at eskimo.com>
Sent: Friday, February 28, 2003 1:05 AM
Subject: Re: [EM] "More often" (was: IRV and Condorcet operating
identically)
>
> At 2003\02\27 13:53 -0700 Thursday, Jan Kok wrote:
> >From: "Venzke Kevin" <stepjak at yahoo.fr> ...
> >Sent: Thursday, February 27, 2003 11:49 AM
> >Subject: Re: [EM] IRV and Condorcet operating identically
> >> --- Dave Ketchum <davek at clarityconnect.com> a écrit :
> ...
> >> > The above makes no sense, for IRV and Condorcet use
> >> > identical ballots and,
> >> > most of the time, award identical winners.
> > ^^^^^^^^^^^^^^^^
> ...
> >I'm curious if anyone can mathematically justify such statements as
"Voting
> >method A exhibits property P 'more often' than method B"?
> ...
> >
> >As a concrete example, can someone show that some Condorcet method fails
> >Favorite Betrayal "less often" than IRV?
> ...
>
> As far as I know, it was not true that there is a definition of the
> FBC favourite betrayal thing.
>From http://www.electionmethods.org/evaluation.htm: "By voting another
candidate over his favorite, a voter should never get a result that he
considers preferable to every result he could get without doing so."
Are you saying the definition is not clear enough to be usable, or what?
I have seen a few posts go by about "Strong FBC." Is that related to
Ossipoff's definition?
> Ossipoff always sought to have rules that
> did not actually test methods, but which in a very vague way, allowed him
> to certify methods.
Would you explain what you mean by "testing" and "certifying" and what is
the difference?
> The certification -- eg. FBC certification -- appears
> to have no reality. No matter how inchoate and boundless the generosity
> is towards the authors of messages saying FBC exists, there still seems
> to be no possible path to a conclusion that that whatever-it-was, did
> exist.
Again, I don't understand.
> There is a questionable presumption inside of the question. The question
> can be ignored (in the interim, or else for a longer time or forever) and
> Mr Kok can provide the exact reasoning that was used when the conclusion
> that FBC was worth asking a question about, was arrived at.
I frequently see claims that method A exhibits some property P "more often"
than method B, and I was wondering how one would go about justifying such a
statement. I can't swear that I've seen the claim that "Condorcet fails FBC
less often than IRV," but I bet some Condorcet supporters would agree with
it. For example, this passage from
http://www.electionmethods.org/evaluation.htm goes part of the way when it
says "the probability is very small...":
"Election methods that meet this criterion provide no incentive for voters
to betray their favorite candidate by voting another candidate over him. FBC
is the only criteria that favors Approval over Condorcet. In fact, it is the
only criteria that favors any of the methods listed in Table 1 over
Condorcet. Although Condorcet technically fails to comply with FBC, the
probability is very small that a voter can cause a preferable result by not
voting for his or her favorite in a Condorcet system."
Many third party supporters, including myself, tear their hair out in
frustration over the lesser of two evils problem. FBC is (for me, anyway)
one of the easiest criteria to understand, and to understand the
implications of a voting method failing the criterion: it causes people to
vote for the lesser of two evils, rather than voting their favorite, and it
causes the true level of support for third parties to be underreported. If
a method passes FBC, voters can freely vote their favorite. Thus, I am very
interested in methods that pass FBC.
I know that Condorcet fails FBC, but the claim is that it does so with "low
probability". So, I want to know what that really means; how to quantify
the degree of failure; how to compare the degree of failure between
different methods.
>
> Mr Ossipoff never got FBC defined. Other members suggested that they
> could and in private e-mail gave up on creating a replacement for the
> Ossipoff FBC. There may never every be an FBC rule while there is an
> agreement that it has to be acceptable to MIKE OSSIPOFF of the
> United States of America.
>
>
> >
> >P.S. I ran some crude simulations a few months ago with no strategy
> >(sincere voting) which showed that IRV and Condorcet SSD chose different
> >winners something like 30% of the time.
> >
>
> So what (?) (neither method is correct). Also, the number of candidates
> ought be stated.
I was saying that, contrary to the claim in the original title of this
thread, IRV and Condorcet don't operate identically in about 30% of the
elections that I simulated. I don't have the details at hand (and as I said
the simulations were somewhat crude, not taking strategy into account, for
example) but I think the 30% figure would apply for about four candidates
and about four issues (e.g. abortion, gun control, foreign affairs) that
voters use to evaluate and choose candidates.
>
>
> -----------------------------
>
>
> At 03\02\27 17:54 -0800 Thursday, Alex Small wrote:
> >Jan Kok said:
> >> I'm curious if anyone can mathematically justify such statements as
> >> "Voting method A exhibits property P 'more often' than method B"?
> >
> >Well, for methods that use strictly ranked ballots to pick among N
> >candidates I would represent all possible electorates with an N!
> >dimensional vector space. Each direction would correspond to the number
> >of voters with a given (sincere, normally) preference order.
> >
>
>
> Given what exactly ?
>
> It says "sincere, normally", and so I ask:
>
> what exactly are the ideas of normality and sincerity,
I think what he meant was, "with a given sincere preference order."
He was using "normally" in the sense of "usually," i.e. you might sometimes
consider voted preference order.
I'll send this mail now and consider the rest later.
- Jan
>
> It looks like information about sincerity exists for each ballot paper
> and it might cause some to be rejected.
>
> --
>
> If there are 4 candidates, then we want to be able to use 65
> dimensions rather than 64, to describe the counts of the papers.
>
> Strangely Mr Small says that the number of dimensions is N!, i.e.
> 1*2*3*4 = 24.
>
> Doubtless it is one of the big problems necessitating an eternal
> and total rejection of the thinking of Mr Small, i.e. that thing
> he calls the "electoral space", in the context of a method (i.e.
> a sequence of polytopes or shapes in the full dimension) being
> tested.
>
> ---
>
> The whole question was not answered:
>
> At 03\02\27 17:54 -0800 Thursday, Alex Small wrote:
> >Jan Kok said:
> >> I'm curious if anyone can mathematically justify such statements as
> >> "Voting method A exhibits property P 'more often' than method B"?
> >
> >Well, for methods that use strictly ranked ballots to pick among N
> >candidates I would represent all possible electorates with an N!
>
>
> The correct answer appears to be a simple "no'.
>
> The method would be perfectly stable and unchanging and the
> statement to be justified did presume that.
>
> So the statement won't be justifiable.
>
> ---
>
> A note to Mr Schulze: I contradicted this wrong statement at my
> mailing list. It had algebra in it.
>
> ------------------------------------------------------------------
> >From: Markus Schulze <markus.schulze at ...
> >Date: Wed Feb 26, 2003 12:09 pm
> >Subject: Re: [EM] Might IRV adoption be inevitable?
> >
> >Venzke Kevin wrote (25 Feb 2003):
> >> I wonder if the only reason IRV has more apparent
> >> backing than approval or Condorcet is because it would
> ...
> >
> >And in so far as there is no known version of proportional
> >representation by the [Alternative Vote method] that has been
> >proven to meet monotonicity,
> ...
> ------------------------------------------------------------------
>
> The method of Vermont, as described by Mr Kok in this
> message, seems to be perfectly monotonic, and it is a variant
> of the Alternative Vote:
>
> http://groups.yahoo.com/group/election-methods-list/message/10947
>
> >From: "Jan Kok" <kok at s.
> >Date: Tue Feb 25, 2003 8:55 am
> >Subject: [EM] Vermont IRV is nonstandard
>
>
> I have online here an argument demonstrating that that method
> of Vermont is monotonic:
>
> http://groups.yahoo.com/group/politicians-and-polytopes/message/220
>
> It can be called the 2nd is a sequence of methods that has
> k-candidate IFPP attached to a preprocessing stage that
> deletes enough candidates.
>
> The 3rd in the sequence is apparently far better than the
> Alternative Vote.
>
> A description of the method is this:
>
> It is the 3 candidate Alternative Vote but with a
> pre-processing candidate-deleting stage that has all the
> expected transferring [i.e. preferences are deleted], and
> also, [if 1 winner only then] there is a 1/3 [IFPP] quota
> (applied after the other preprocessing) that sometimes
> finds two losers.
>
> Replacing IRV is certainly not a prime purpose of the
> members at the Politicians and Polytopes mailing list. It
> is too slight to interact with, I suppose.
>
>
>
>
>
>
> Craig Carey
>
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