Re: Query for Approval advocates

At 11:47 AM -0700 8/31/03, Bart Ingles wrote:
>You could say that "B is obviously preferred by *majorities* of people
>over every other option, but even so the "majorities" are merely
>incidental.  B would be the CW without them:
>
>40: A
>10: C>B
>20: C
>35: B>A
>
>Here B is preferred by *pluralities* of people over every other option,
>but is still the CW.
>
>>  Now, the fact that I can point to a method that will select B is a
>>  reason why I would prefer that method to a method that would select
>>  something other then B.
>
>So do you still think the CW should win in the immediately preceding
>example?

There is no good reason I can come up with which would indicate that 
B should not win as > 50% (i.e. a majority) of people in your example 
prefers B over both C and A.

>  If so, your belief must be based on something other than
>majority, since the only majority above is the 75:30 majority which
>prefer A to C.

This is utterly meaningless as RP does not meet IIA. By ignoring B, 
you have essentially provided a completely different example from the 

Re: Query for Approval advocates

Eric Gorr wrote:
> 
> At 11:47 AM -0700 8/31/03, Bart Ingles wrote:
> >You could say that "B is obviously preferred by *majorities* of people
> >over every other option, but even so the "majorities" are merely
> >incidental.  B would be the CW without them:
> >
> >40: A
> >10: C>B
> >20: C
> >35: B>A
> >
> >Here B is preferred by *pluralities* of people over every other option,
> >but is still the CW.
> >
> >>  Now, the fact that I can point to a method that will select B is a
> >>  reason why I would prefer that method to a method that would select
> >>  something other then B.
> >
> >So do you still think the CW should win in the immediately preceding
> >example?
> 
> There is no good reason I can come up with which would indicate that
> B should not win as > 50% (i.e. a majority) of people in your example
> prefers B over both C and A.

I never said that B shouldn't win, merely that B is NOT preferred by a
majority over either A or C.  Only 45/105 prefer B to A, and only 35/105
prefer B to C.  A majority would require 53 votes.

Re: Query for Approval advocates

Kislanko wrote:
>
> bartman writes:
> 
> > >>(1) Round number fallacy:  The 50% figure is viewed as magical
> > because
> > >>it has the appearance of being a "natural" threshold.  Which it
> > is--if
> > >>there are only two candidates. [...]

> First, the >50% IS a magic threshold, if the term democracy is to mean
> anything. In any two-alternative selection process with more than 2
> voters, the majority criterion is decisive. The difficulty that

I refer you to my first paragraph, above (2nd sentence).  There is also
a "first-choice majority" criteria which seems defensible, to the effect
that if one candidate happens to receive a majority of first choice
votes, then that candidate should win.  But if you have three candidates
and no first-choice majority, then neither of the above flavors of
'majority' is applicable.  

> Condercet observed is that for three candidates the majorities that
> prefer one candidate to another can overlap in such a way that most
> prefer A over B, most prefer B over C, and most prefer C over A.

Actually, when Condorcet was writing, the term 'majority' probably meant
what we now call 'plurality'.  Thus it is possible that a Condorcet
winner can fail to have majority support in the modern sense (defined as
> 50% of the electorate) over any candidate, even in the absence of a cycle or

Re: IRV-Approval, Condorcet-Approval hybrids

David's method gives me a similar, simpler idea that would seem to be an
improvement over IRV.  The method would be:

1. The voters rank the candidates they would be willing to support, and also
place an approval cutoff.  (Alternatively, all candidates ranked non-last
could be considered "approved.")
2. While there is no (voted) majority favorite, eliminate the Approval loser.
3. Elect the voted majority favorite.

Actually, I think this is Chris Benham's idea, suggested as a solution to the
strong FBC problem.  At the time I thought it would always elect the Approval
winner, but that's clearly wrong.  An example, where all ranked candidates are 
considered approved:

20: C>A
35: A>B
45: B

B is the Approval winner, but A is a majority favorite once C is eliminated.

A problem with this method, as well as with IRV and David's method (I am pretty
sure), is the incentive to up-rank compromises in attempt to achieve a majority
earlier.

The method wouldn't necessarily elect a CW, but I suspect it would fail to do
so for the same reasons Approval may: In the "weak centrist" scenario, for
instance, a major faction can't support the centrist and also hope to elect
their favorite, so the centrist's value has to be considered.  (Condorcet in
comparison allows the faction to do both.)

Query for one and all

Consider the following single-winner method. Voters submit ranked 
ballots, ties allowed, truncation allowed. (Only one vote allowed for 
each candidate.) First-choice votes are tallied; if anyone gets a 
majority, the one with the largest tally wins. If no one gets a 
majority of first-chioce votes, then second-choice votes are tallied 
and added to the first-choice votes. Again, if anyone has received 
votes from a majority of the ballots, the candidate with the largest 
total wins. And so forth, for as many ranks as there are, until 
someone gets votes from a majority of ballots. If all ballots become 
exhausted and still nobody has received votes from a majority of 
ballots, then the candidate with the largest total wins.

This method has been called "Generalized Bucklin", and AFAICT could 
also be called "Majority Choice Approval".

My question, for one and all: Is there any desirable quality, that 
any single-winner method has, that this method does not have?

One likely answer is "Condorcet-efficiency"; this method does not 
seek directly to find the Condorcet-winner. Merrill's simulations 
found plain Approval to have good levels of c-e but not 100%.

Chris Benham has found something called the "bogey-candidate" effect. 
Add that to the list.

So, please, all chip in: what do you know that's bad, about Majority 
Choice Approval?
--

-- 
----------------------------------
John B. Hodges, jbhodges <at>    <at> usit.net

Re: IRV - Approval, Condorcet-Approval hybrids

RE: Query for one and all

JBH asked: 
> My question, for one and all: Is there any desirable quality, that 
> any single-winner method has, that this method does not have?

Two problems.
1. Your second and subsequent preferences count against your first preference.
2. If more than first preferences have to be counted, the value of the votes of different voters may
be different if the voters truncate after different numbers of preferences.
James

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Re: Query for one and all

Dear John B. Hodges,

you wrote (1 Sep 2003):
> This method has been called "Generalized Bucklin", and AFAICT
> could also be called "Majority Choice Approval". My question,
> for one and all: Is there any desirable quality, that any
> single-winner method has, that this method does not have?

Condorcet, Condorcet Loser, Consistency, Independence of Clones,
Reversal Symmetry, Smith, later-no-harm, Participation.

Markus Schulze
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Re: IRV-Approval, Condorcet-Approval hybrids

Re: Query for one and all

 --- Markus Schulze <markus.schulze <at> alumni.tu-berlin.de> a écrit : 
> Dear John B. Hodges,
> 
> you wrote (1 Sep 2003):
> > This method has been called "Generalized Bucklin", and AFAICT
> > could also be called "Majority Choice Approval". My question,
> > for one and all: Is there any desirable quality, that any
> > single-winner method has, that this method does not have?
> 
> Condorcet, Condorcet Loser, Consistency, Independence of Clones,
> Reversal Symmetry, Smith, later-no-harm, Participation.
> 
> Markus Schulze

John's definition didn't seem to allow for unused ranks, which I believe
is a necessary part of MCA.

I think MCA meets Clone Independence and Participation, but I'd like to hear
reasoning to the contrary.

Kevin Venzke
stepjak <at> yahoo.fr

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