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

[Richard Moore]

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 
would have exposed your falsehood about pairwise comparisons, and that 
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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