Erratum Re: [EM] (P1) and monotonicity for single-winner election systems and Condorcet.

[Craig Carey]

A method of Mr Catchpole that falls apart over two candidate election
 is studied here.

     "thorough checks convince me ..."



At 19:46 25.10.99 , David Catchpole wrote:
>(Further down...)
>
>On Sat, 23 Oct 1999, Craig Carey wrote:
>
>> >Let Pi(A,B:V) represent the truth of whether voter i prefers candidate A
>> >over B in voting schema V.
>> >
>> >Let W(V) represent the set of winners of voting schema V
>> >
>> >For all V, all V', W(V)<>W(V') implies-
>> >
>> >there exists i, A, B such that A is an element of W(V), A is not an
>> >element of W(V'), B is an element of W(V'), B is not an element of
>> >W(V), and-
>> >
>> >(i) not Pi(B,A,V) and Pi(B,A,V')
>> >or
>> >(ii) Pi(A,B,V) and not Pi(A,B,V')
>> 
>>---------------------------------------------------------------------------

>
>> Pi hasn't been defined. It can't assumed that the words "the truth of" mean
>>  Condercet because introducing that would be a most arbitrary step and
...
>> If Pi means a Condorcet pairwise comparison then there is quite probably
>>  no need to consider the idea further.


>I would suggest looking at a first year logic textbook. "Pi(A,B,V)
>represents the truth of..." is similar to the way logic
>textbooks say "S represents the truth of 'Clancy of ...


>Consider voter i as an element of the set of voters. Pi(A,B,V) is true iff
>(if and only if) voter i prefers candidate A over candidate B in scenario
>V. (More further down)

What is Pi?. Unnecessarily adding the words, "the truth of", and then with
 a show a pointers to logic textbooks and guns, removing those very words,
 does not prove to be a process that in any step provided a definition of Pi.
My guess is that you would make Pi to be Condorcet pairwise comparison.
But that has not been stated. 


>Nothing's wrong... thorough checks convince me there is nothing to
>criticise in this definition. ...

V =
   99 C
   03 D

V' =
   99 C
   01 D

-------------------------------------------------------------------------
 "For all V, all V', W(V)<>W(V') ... there exists i, A, B such that A is
  an element of W(V), A is not an element of W(V'), [and] ...
-------------------------------------------------------------------------

Which of C and D is the candidate you would pick for variable A, that
 would be substituted into your sentence above ??.

My version was deleted without analysis. This equation:

Rule: (All V)(All p in V)(All p')(All A,B)(All V', V' in Alt(V,p,p'))
        [(P(B,A,p) => P(A,B,p')) => not (A:W(V).-B:W(V).B:W(V').-A:W(V'))]




In the following, Mr Catchpole had, in a recent message, explained his
 position as being that the words "a switch in candidates..." meant
 relettering and had nothing to do with preferences. (It was certainly
 a surprise to me, to have the truth or falsity of a new voting theorem
 based upon the truth or falsity of whether or not it is possible to
 reletter variables).


>> >It has now occured to me that it may be possible to demonstrate that
>> >Condorcet is a necessary condition of monotonicity without assuming
>> >majority rules ("2-candidate FPTP") but instead assuming the system is
>> >neutral to candidates (a switch in candidates brings on a corresponding
>> >change in results). However, this is going to take some effort ....

>> Those phrase, "P is a necessary condition for Q" means "Q implies P". In
>>  other words, Mr Catchpole is saying, wherever a method is neutral to
'changes in'
>>  candidates and it satisfies monotonicity, then the method is Condorcet. 
>
>Got it in one, kiddo.

Your statement is false if it applies to all methods.

The First Past the Post Method, satisfies monotonicity but it is not
 Condorcet, so the statement is false. The term representing neutrality
 is on the left hand side of an implication. Mr Catchpole defended his
 position by saying it was clearly true (elettering is possible).

I read in a previous message that Mr Catchpole had said that FPTP is not
 a preferential voting method.
 Preferential voting methods include those methods that accept preference
 lists, or have outcomes based on STV-like preferential voting papers.

How could FPTP not be a preferential voting method when it is the method
 that results from modifying STV so that all subsequent preferences are
 discarded during transfers and during elimination (approximately).


>"thorough checks convince me ..."

>"Ce wha...?" - What did you mean, Mr Catchpole?.

At 20:14 25.10.99 , David Catchpole wrote:
>On Sun, 24 Oct 1999, Donald E Davison wrote:
>
>>      There are people who support small district STV and/or Droop Quota
>> and/or exhausted ballots being given to the remaining candidates. These
>> three features make STV less proportional. One or more of them would not
>> allow the Eight Percent Group to elect any members, but they would allow
>> the Forty-Eight Percent Group to elect fifty-eight members per hundred.
>
>Droop doesn't do that. Give me an example where it does.

The last sentence of Mr Davison is sure to be true and there is no need
 for a sample election proving Mr Catchpole to be in the wrong about
 Mr Davison's last sentence.

If you missed it the first time:

At 19:51 25.10.99 , David Catchpole wrote:
...
>                   Hare has the 1/2n quota
> on its arsend to make numbers.






-------------------------------------------------------------------------
Errata: I had incorrectly written "Satisfaction(W(V+z))"

G. A. Craig Carey