[EM] "More often" (was: IRV and Condorcet operating identically)

[Craig Carey]

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. Ossipoff always sought to have rules that
did not actually test methods, but which in a very vague way, allowed him
to certify methods. 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.

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.

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.


-----------------------------


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,

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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