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

Richard Moore rmoore4 at cox.net
Thu Aug 1 22:32:02 PDT 2002

```Well, as Wolfgang Pauli said, "This is not right... This is not even
wrong!" He could easily have been talking about one of Craig's comments.

I will ignore the straw-man arguments and the many statements and
positions that Craig falsely attributed to me. If I answer them, he
will likely respond with more lies. Instead I will talk about what
Craig failed to do.

Craig, you didn't respond to my simple question about a two-candidate
election. I guess you're smart enough to realize that a correct answer
an incorrect answer would have just made you look foolish. If you took
my hint then I guess that's progress.

Craig Carey wrote:
>  >Craig needs another hint: Pairwise cycles are not "paradoxes"!
>  >
>
> So what?: that word paradoxes is just a word.

It might be argued that "power" is just a word, too, yet you made a
big effort to define it. You used the word "paradoxes" to defend your
statement about pairwise comparisons. If the word has no weight then
neither does your defense. You are not merely being evasive, you are
being inconsistent.

> Here there is a way to address cycles:
>
>  >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.
>  >
>
> Moore seems to not admit that pairwise comparing itself is rejected.

Once again, something is just "rejected" out of the blue because it is
inconvenient. Rejecting pairwise comparison would compromise the
ability to pick a winner in a two-candidate election using a
non-arbitrary and non-dictatorial method. Most election problems begin
at 3 candidates but now they begin at 2. So maybe Craig didn't catch
on to my first clue after all.

Craig wrote a lot about Condorcet and Condorcet methods in that post
though I never brought that topic up, other than a passing reference
in the above list of three. Stating that a pairwise result contains
information is not the same as promoting Condorcet methods. You
certainly missed a big clue there, Craig.

> The One Man One Vote I gave was almost an
> axiom itself, but instead was a corollary on my P4 Equal Suffrage
> equation.
...
> I derived the "One Man One Vote" formula from an "Equal Suffrage"
> formula.

What I got from those two sentences is that the equations posted
yesterday were not a restatement or alteration of P4, but a new
principle. I think you originally called P4 "One Man One Vote" but I
guess you've changed terminology and now use it for this new one.
Hence I assumed that "One Man One Vote" formula was a rehash of P4. So
P4 hasn't improved, and it still hasn't been justified.

Two days ago (was it?) I listed several problems with P4. Craig opted
out of the chance to make a meaningful response to those issues. I
will restate them here.

1. P4 uses FPTP ballots as a unit of "power". But FPTP ballots have a
power that varies with the power structure of the electorate. That
dependency is the very problem that keeps us in a two-party rut.
Something so problematic and so variable can't be held up as a
standard for equal suffrage.

2. P4 passes if ballots in a method range in "power" from 0 to 1, but
fails if they range from, for instance, 1 to 1.1. Yet there is a huge
disparity (potentially an infinite ratio) in the first range.

3. There were two contrary definitions given, one in which "power" is
the number of FPTP ballots a ballot can be replaced by (to get same or
better results), and another in which it is the number of FPTP ballots
a ballot cancels. As the number of check marks on an approval ballot
increases, the first definition has "power" increasing while the
second has "power" decreasing. It makes no sense for the quantity to
be increasing and decreasing at the same time.

This gives Craig another chance to respond, but I expect he will opt
out again and launch into more irrelevancies. If so he will certainly
have the last word.

-- Richard

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