[EM] One Man One Vote in equation form; Power and rejecting Approval

Richard Moore rmoore4 at cox.net
Wed Jul 31 22:51:28 PDT 2002

Craig Carey wrote:

 >> >From:· Richard Moore <rmoore4 at c...>
 >> >Date:· Tue Jul 30, 2002· 2:20 pm
 >> >Subject: ·Re: What are we all about?, etc.
 >> http://groups.yahoo.com/group/election-methods-list/message/9924
 >> >It's simple to do this for IRV: If there are N candidates, and M
 >> >candidates are eliminated before there is a pairwise winner against
 >> >the remaining candidates, then it is possible that that winner
 >> >is a pairwise loser in M contests. This looks very bad for IRV
if M =
 >> >N - 2 and N is large. IRV needs to test the winner against M
 >> >additional candidates.
 >> >
 >> The argument is based on an error which is that pairwise losing is
 >> somehow
 >> able to provide information on the right winner.

Now that's a fascinating point of view. I wonder how Craig would
answer the following question:

Question: How do you find the "right winner" of a two-candidate
election? Feel free to conduct the election with either lone-mark 
ballots, approval ballots, or ranked ballots.

Hint: Careful, Craig, it might be a trap!

 >> Pairwise comparing loses
 >> information by producing Boolean values that then lead to tiny little
 >> "paradoxes".

Craig needs another hint: Pairwise cycles are not "paradoxes"!

And here's one big hint, in case he's not catching on yet: There are 
at least three ways to address these cycles -- (1) break the cycles, 
as is done in the Condorcet family of methods; (2) ignore the cycles 
and start eliminating candidates (and thereby ignoring much of the 
information content of the election); (3) for each candidate, derive 
some scalar value from the ballots, and compare the values.

 >> The comment "looks very bad" is simply rejected.

How convenient that a comment can be "simply rejected" without
responding to any of the reasoning that led up to it! I'm going to use
that one myself next time I get a chance.

 >> No method is found to be
 >> wrong by using a wrong test.  It Mr Moore wants to cut the wrong
parts of
 >> a pairwise comparing test out of it then that could be attempted
and then
 >> the details posted up.

De-obfuscation, please?

...Huge snip taken out here...

I won't address that section. It will take a lot of time and it is
plainly based on a wrong conception of "one person, one vote". It is
"simply rejected".

I already discussed the problems with the P4 test (the one Craig said
nobody is allowed to change, so these equations can safely be assumed
to be equivalent).

It is a "wrong test" so no method can be found wrong by it.

If Craig informs me that he has violated his own rule (again) and
changed the definition so that it no longer matches "description_2" or
the other (contrary) description he gave, then I may take a look. But
I'm not going to waste my time checking every algorithm or set of 
equations to see if any insight has crept in.

 >> I can't see how Alex's ideas threaten blacks in USA. But Appoval
 >> could since it presumably disadvantages uneducated persons.

Craig plays the race card. I don't know how that slipped in. At any 
rate he needs another hint: "Blacks in USA" is not synonymous with 
"uneducated persons".

 >> >sufficient number of candidates for his taste. Yet the existence of
 >> >small examples does not imply failure with large numbers of
 >> >candidates. Will Craig point out how increasing the number of
 >> What a dud comment: once a method is failed by a Boolean-valued
test then
 >> the testing can stop since any further "AND"-ing with "False"
won't alter
 >> that fail mark.

That's a strange defense. It was after all Craig who made the 
accusation that small numbers of candidates were being used in 
examples to cover up some problem with approval. Now he defends
his accusation by saying that the problem exists with small numbers of
candidates. How could a problem be covered up by using a class of
examples for which the problem exists?

At any rate what merit was ever found in the test that approval failed?

 >> Of course increasing numbers of candidates make Approval deteriorate.
 >> I will check back every 10 years and see if the Approvalists have
 >> cast comprehensible doubts on my power equation that is continued in
 >> this message. You can test the method yourself, allowing 1 winner,
 >> any number of candidates, and letting no paper have 3 or more
 >> preferences. Some of the Approvalists would live a long time and may
 >> want to investigate the method. Probably not many.

Doing tests that lack merit will provide no useful information. GIGO
principle again.

 >> That "One Man One Vote" is not designed by seeing what passes IFPP
 >> and what fails others methods.

No, and it wasn't designed by considering what the phrase in quotes
might actually mean, either.

 >> Readers can see how the Approvalist's undo the damage to their
 >> that this new mathematical formula is providing.

Yes, we're quaking in our boots. How will we recover when USA Today
or some equally authoritative journal publishes an in-depth article 
about these shattering findings?

     -- Richard

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