[EM] Maybe a new thread is in order ...

[Craig Carey]

At 19:52 28.10.99 , David Catchpole wrote:
>On Thu, 28 Oct 1999, Craig Carey wrote:
...
>couldn't work it out from the plain English, I'll have a go at putting it
>in a formal structure of proof. Later, though...

Proof of what?.

>> FPTP is a monotonic preferential voting method, and it isn't Condorcet.
>> So therefore the and rule is finally rejected.
>
>It's not! Consider the following example I gave to Markus Schultze-

FPTP is monotonic method. There need not be misunderstanding over that.
Mr Catchpole is redefining the word monotonic. I suggest it be called
 David-Catchpole-Monotonicity-version-0.1.


>Say two voters have preferences A>C>B in an election where A has 5
>votes (including that of this voter), B has 4 votes and C has 1. A
>wins. Say that these two voters change their preferences to C>A>B. B now
>wins, even though nobody changed their preferences between A and B. While
>some definitions of monotonicity fail to rule on such a scenario, the one
>I gave in my message does- and rules FPTP out. (more further down)


First example:  (1)
    3  A
    2  AC        A wins
    4  B
    1  C
  FPTP,STV,IFPP: A wins

The Second example:  (2)
    3  A
    4  B
    2  CA        B wins
    1  C
  FPTP,IFPP: B wins  
  STV : draw between A and B

Mr Catchpole probably wants A to win election (2)

Here's why "Catchpole monoticity" is with importance (28 October 1999).

Assume the method need not be STV.

Assume the STV property which is that a candidate's win-lose state
 is unaffected by altering preferences (on any paper or papers) after
 the preference for that candidate.

So A wins the first if and only if A wins this:  (3)
    5  A
    4  B
    1  C

Therefor A wins the first and Mr Catchpole must have been wanting B to
 lose the 2nd election.

Suppose that C won the 2nd; then by applying that invariance of outcome
 on truncating rule, C ought would this:  (4)
    3  A
    4  B
    3  C

That is not permissable, so C does not win the 2nd. Mr Catchpole objected
 to B winning (since it was found that there was no objection to A winning
 the first). So Mr Catchpole must (perhaps), want A to win the second
 example.
Let it be supposed that A does win the second:  (2)
    3  A
    4  B
    2  CA
    1  C

Then A will also win this, by applying the rule that the outcome of
 a candidate is unaffected by alterations after any preference(s) for
 candidate. If A wins this following example then B and C must lose):  (6)

   0.9  A
   2.1  AC
    4   B
    2   CA
    1   C

 An asymmetry style argument would have either C win, or B win, and in
 both cases, A would lose.
 When A loses (6), A must lose (2) too.
 Since C loses (4), C must lose (2) too.
 Since A and C lose (2), then B wins (2) (by using what could be regarded
    as the first axiom of preferential voting theory)
 Mr Catchpole's monotonicity disagreed with A winning (1) or B winning (2),
 and it must have been the latter since A wins (3) and hence it wins (1).

 So Catchpole monotonicity is now a dead idea (or else the saved by the
 presence of a tie on considering just first preferences.)

... [An N rule omitted]

______________________                       ______________________
Mr G. A. Craig Carey   Auckland, New Zealand     research at ijs.co.nz
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