"Spokane" method

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"Spokane" method

Craig Carey-2
Steve Hill was up here last night talking to the League of Women Voters
in Seattle.  He did a really good job, but he really had his work cut
out for him.  Eyes glazed over quickly, and most people remained unsold,
methinks.  But with time...

Anyhow, I was talking with another CPR member who was there, and he told
me about the "Spokane" method.  I tried to play devil's advocate, but I
found it surprisingly hard to punch holes in it, and even when I worked
it out on paper, it looks remarkably sound.  

The way it works is it is essentially a limited voting instant runoff.  
Voters submit preference ballots, and if there are n candidates, n-1 of
each voters' preferences are counted equally.  The loser is knocked out,
and the process is repeated until a winner emerges.

Here's an example of 10 voters and 5 candidates (a, b, c, d, e)

Round 1:
a,b,c,d
a,b,c,d
a,b,c,d
b,a,c,d
c,b,a,d
c,b,a,d
d,c,e,b
e,d,c,b
e,d,c,b
e,d,c,b

a: 6 votes
b: 10 votes
c: 10 votes
d: 10 votes
e: 4 votes (eliminated)

Round 2:
a,b,c,-
a,b,c,-
a,b,c,-
b,a,c,-
c,b,a,-
c,b,a,-
d,c,-,b
-,d,c,b
-,d,c,b
-,d,c,b

a: 6 votes
b: 10 votes
c: 10 votes
d: 4 votes (eliminated)

Round 3:
a,b,-,-
a,b,-,-
a,b,-,-
b,a,-,-
c,b,-,-
c,b,-,-
-,c,-,b
-,-,c,b
-,-,c,b
-,-,c,b

a: 4 votes (eliminated)
b: 10 votes
c: 6 votes

Round 4:
-,b,-,-
-,b,-,-
-,b,-,-
b,-,-,-
c,-,-,-
c,-,-,-
-,c,-,-
-,-,c,-
-,-,c,-
-,-,c,-

b: 4 votes (eliminated)
c: 6 votes

c wins.

Several questions:
1.  Does this method pass the Condorcet test?
2.  How vulnerable is it to truncation problems?
3.  Is this a credible alternative system?
4.  Does this system have another name that is widely discussed?

Please tell me if this method has another name and is discussed in some
reference material.  Bruce and Mike, I hope you're listening, because I
really need your help here.  

My analysis has been pretty shallow thusfar, so there could be something
obvious I'm overlooking, but I would appreciate examples of bad
situations.
--
Rob Lanphier
[hidden email]
http://www.eskimo.com/~robla

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"Spokane" method

Craig Carey-2
This "Spokane" method sure sounds like the Coombs voting method to me.  The
Coombs method was proposed by Clyde Coombs, and it is "well-known" by that name
in the voting theory literature.

The Coombs method satisfies the majority-winner, majority-loser, and
Condorcet-loser criteria; but it fails the generalized-majority,
Condorcet-winner, generalized-Condorcet, and monotonicity criteria.

I'll conditionally offer to provide precise definitions of these criteria, and
to tabulate which of 29 different voting methods can be proven to pass or to
fail each of these criteria (and which, to the best of my knowledge, remain open
questions), to this list after (if?) I receive Rob's permission to post such a
conditional offer on this list.  The conditions concern formatting issues only.

Bruce

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"Spokane" method

Craig Carey-2
On Fri, 29 Mar 1996, Bruce Anderson wrote:
> This "Spokane" method sure sounds like the Coombs voting method to me.  The
> Coombs method was proposed by Clyde Coombs, and it is "well-known" by that name
> in the voting theory literature.

Thanks.  Scanning the literature becomes much easier with a name to look
for.

> The Coombs method satisfies the majority-winner, majority-loser, and
> Condorcet-loser criteria; but it fails the generalized-majority,
> Condorcet-winner, generalized-Condorcet, and monotonicity criteria.
>
> I'll conditionally offer to provide precise definitions of these criteria, and
> to tabulate which of 29 different voting methods can be proven to pass or to
> fail each of these criteria (and which, to the best of my knowledge, remain open
> questions), to this list after (if?) I receive Rob's permission to post such a
> conditional offer on this list.  The conditions concern formatting issues only.

i just want to fill folks in here.  Bruce has a lot of MSWord docs that
he has already written that he would like to post to the list.  I'm
worried about allowing that because it makes it difficult for me to
archive, and difficult for readers on the list to read.  Since he is doing
formulas and complex tables, it is difficult to express the same thoughts
in plain text, and Bruce has no desire to convert to text.

A possible compromise would be if someone has some extra space on a web
server that Bruce could post his Word docs to, and then could post a URL
to the list.  I'm running up to my limit on my server, but if someone else
has that ability, that would be wonderful.

Rob Lanphier
[hidden email]
http://www.eskimo.com/~robla


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"Spokane" method

Craig Carey-2
In reply to this post by Craig Carey-2

[p.s. Is the Spokane method actually in use? What group or person
is proposing it there?]

The Spokane method remined me, too, of Coombs, but then I noticed
a difference: Coombs repeatedly eliminates the candidate ranked last
by the most voters, but the Spokane method doesn't always do that.
For instance, after e had been eliminated, someone whose ranking
said d,a,b,e,c  would have their ranking, after e's elimination, changed
to d,a,b,-,c  and he's counted as giving a vote to all the candidates
but 1, and that 1 that he isn't giving a vote to is the one who's been
eliminated. That voter with that ranking _is_ counted, in that example,
as giving a vote to c, his last choice. So it's different from Coombs
if it's done just as in that example.

I haven't seem that method before, & I don't know what its properties
are yet. But I'll find out & post about it within a few days.

Don't think you're overlooking something obvious. None of us, as of
the time that I'm writing this, have studied the details of the
results of that method, but there's nothing obvious that we've
overlooked.

***

If the guy _did_ mean to just repeatedly eliminate the candidate who's
the last choice of the most voters, that's one of the best non-pairwise
methods. I consider it 1 of the 2 best non-pairwise methods. The other
is too complicated to justify its consideration, especially since it
isn't nearly as good as Condorcet's method.

If one wants to do an elimination method, instead of a pairwise method,
it's better to go by last choices than 1st choices.

The trouble with Coombs is that the progressives, for instance, might
be split about whom they rank last, among the candidates that they
rank. This could cause a split-vote for last choice, which could
cause last choices to be eliminated from the progressive side
consistently, eating away the whole set of candidates from the
progressive side.

I consider that to not be as bad as MPV's split-vote problem,
because it's easier for the progressives to artificially agree
on how to order their really low choices than it would be for
them all to like to insincerely rank someone 1st, as MPV might
require them to do.

I don't recommend Coombs because the kind of strategy that it
needs, agreeing on lower choices, is unfamiliar to voters, and
the method could fail for that reason. I much prefer a really
strategy-free method like Condorcet.

But, though I don't recommend it for that reason, & because Condorcet
isn't appreciably more complicated anyway, and is strategy-free under
ordinary conditions, and, even under the worst conditions, its
defensive strategy isn't unfamiliar--even so, Coombs has the appeal
that, if, for instance, the progressives can agree on how to order
the lowest candidates they rankk (& of course they need only rank
candidates who have a chance of being Condorcet winner, a needed
compromise), then the method works very well: With a 1-dimensional
political spectrum, the last choices are going to be the extremes.
Everone's last choice will be 1 of the 2 extremes. So Coombs naturally
nibbles from the extreme ends of the spectrum till only the Condorcet
winner is left. But I believe that Coombs's strategy requirement
disqualifies it from being as good as Condorcet, and convincingly
argues against proposing it to the public, or any group taking a vote,
when the better Condorcet's method is available.

***

Though I haven't studied Coombs for a while, it seems to me that
it did ok against truncation, subject to the condition that people
avoid split-vote for last choice by agreeing on low choices, but that
it did require extra strategy to defend against order-reversal.
A defensive strategy more unfamiliar than that of Condorcet under
those conditions, in addition to the need to agree on low choice
orderings. Like I said, I don't recommend Coombs' method.

***

I want to say that what's been called the Generalized Majority
Criterion should, in my opinion, be called the Mutual Majority Criterion,
because it isn't really general. More about that soon, tonight or
early tommorow morning. Briefly, I want it to be possible for a
majority of the voters to get what they want without ranking
a less-liked alternative equal to or over a more-liked one, or,
under specified conditions, using any kind of strategy at all.

The Mutual Majority Criterion overlooks some important violations
of that wish. More later.

***

I have another criterion that I'd call the Generalized Majority
Criterion. It's unashamedly tailored to what seems possible to get
with single-winner methods, and it's wordy to express. It's
a yes/no test based on the generalized majority standard that
I described earlier. More about that tonight or early tomorrow
morning.

***

Also, I'll be checking out the properties of the Spokane method,
as defined by that example. I don't yet know what its properties
are. Someone might point out that there's a simple way of
saying what it does. Someone might point that out before I do.

***

Mike






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