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

[Richard Moore]

Craig Carey wrote:
   >
   >
   > At 2002\08\01 22:32 -0700 Thursday, Richard Moore wrote:
   > ...
   >  >
   >  >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.
   >  >
   >
   > Members can browse to my long reply which is now at this webpage:
   >
   > http://groups.yahoo.com/group/politicians-and-polytopes/message/184

I don't know why that was posted there instead of here. I had a look 
anyway. That post purports to answer some of my issues but misses the 
mark. I said Craig would have the last word if his reply was not 
relevant to the topic but since he (mostly) stayed on-topic, I'll 
respond. But I'll only address the sections that were on-topic; this 
will therefore be a short message.

To the issue of how to run a two-candidate election without resorting
to a pairwise method, while retaining fairness, he posted a reply
about using SNTV in a 2-winner election. Always picking two winners
out of a field of two candidates is a cop-out. Maybe Craig wants to 
avoid answering this question seriously.

I listed three problems with his P4 criterion. To the first problem,
that FPTP ballot powers vary with power structures, he replied that
there are no electorates in mathematical equations. That flippant
answer was simply an evasion of the issue that was raised.

Craig ignored the second of the three, about the huge disparity
between power=1.0 ballots and power=0.0 ballots within the constraints
of P4. One could define a method that says "Count the ballots as in
FPTP, except that any ballots cast for candidate X are given 0
weight". It would pass P4.

Since he did not try to answer that one, presumably he is conceding
the point.

To the third issue, about how one definition that increases the power
as the number of marked preferences increases conflicts with another
definition that decreases the power, Craig confined his response to
the special case of a zero-preference ballot vs. a single-preference
ballot. Is that the only region that needs to be considered? For N
candidates, a 1-preference approval ballot can cancel N-1
(non-aligned) FPTP ballots; a 2-preference approval ballot can cancel
N-2; etc. Craig stated that the 1-preference ballot offsets a single
"similar paper" rather than N-1. Maybe Craig has a different idea of
what "cancel" or "offset" means, and would like to share it. At any
rate, I could suggest a simple correction to fix problem 3, but it
would leave the problem of the unreliable FPTP "power" standard in place.

In short, I have seen no reason given why anyone should care whether a 
method passes P4 or not.

     -- Richard

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