Interesting Website

[Anthony Simmons]

>> From: "MIKE OSSIPOFF" <nkklrp at hotmail.com>
>> Subject: Re: Interesting Website

>> I checked out the website you referred to, but are you
>> sure that , when electing an executive who has the power
>> to veto the decisions of a legislature, it's more
>> important to elect someone who has a large 1st-choice base
>> than to elect someone who doesn't have majorities against
>> him?

Are you sure I said any of that?  I don't remember saying it.
Perhaps you confused me with someone else.

I see you don't think the web site is interesting.  You are
mistaken.

Suppose by way of contradiction that the web site (call it W
for convenience) is uninteresting.  Then there is a set of
uninteresting web sites that are larger (character-wise) than
W.  Since there can only be finitely many such web sites,
there must be a largest one.  That is the largest
uninteresting collection of documents on the entire Internet!
A very interesting property, so that web site is very
interesting, and is in the set of uninteresting sites by
mistake.  (There may actually be two or more such sets, all
the same size, a very interesting coincidence.)  Thus, we
must remove it from the set of uninteresting sites.  That
leaves another site as the largest, so that must be removed
for the same reason.  After sufficiently many steps, we find
that there are actually no uninteresting web sites larger
than W, so W must be the largest uninteresting site on the
Internet, and is interesting in that regard if in no other.
Therefore W is not, as you supposed, uninteresting.  Q.E.D.

I see you have some disputes about various claims made by the
author of the site.  So do I, though I am not inclined to
make a pointless issue of them.


>> One would expect that the legitimacy of that executive,
>> and of his vetoes, would be hurt more if it's common
>> knowledge that a majority of the voters indicated that
>> they wanted some other particular candidate(s) instead.

>> And, about Approval, he says that it can cause strategic
>> voting. As if that were a property peculiar to Approval.

>> If you divide the candidates into acceptables &
>> unacceptables, and your goal is to minimize the likelihood
>> of an unacceptable winning, and so you vote for all the
>> acceptables, then someone could say that that doesn't
>> count as strategy, since you're voting for the ones whom
>> you approve. That's how I'd vote if Approval were used in
>> our actual elections, by the way.

>> But of course if you don't divide the candidates in that
>> way, then your Approval voting is almost sure to be
>> strategic. But the people who repeat that seem to be
>> unaware that the other voting systems cause a need for
>> strategy too, and, with nearly all other methods, that
>> strategy often requires dumping one's favorite by voting
>> someone else over him/her.

>> Rank methods look good at first glance, till you find out
>> that most of them cause worse strategy problems, like a
>> cheap laborsaving automatic machine that goes haywire. Of
>> course there are some good rank methods, but IRV isn't one
>> of them. Approval is difficult to improve on much with any
>> 1-balloting method.

>> Of course, in Plurality, if you divide the candidates into
>> acceptables and (absolutely) unacceptables, and you want
>> keep an unacceptable from winning, then you give your
>> Plurality vote to the acceptable who has the best
>> probability that you can help him take victory from an
>> unacceptable. That's the Plurality strategy that I
>> recommend, though we might differ on what we call
>> acceptable...

>> Admittedly, depending on how particular you are, there
>> might often only be one acceptable.

>> I'm not sure what's interesting about that website; it
>> seems to trot out familiar misunderstandings.

>> Mike Ossipoff