[EM] Probability theory has nothing to do with preferential voting

[Craig Carey]

I suggest that nobody read this. I am just doing a bit of 'sweeping of
 the floor'...

Near the bottom is a comment about simplex coordinate systems.


At 10:34 13.12.99 , David Catchpole wrote:
...

>Now- you ignored the basic properties of the election methods to which
>Regularity has pertinence. These are probabilistic election methods which
>may have a degree of uncertainty in who wins despite certainty about
>votes. Why extend a consideration of election methods to incorporate
>these? Three good answers-
>
>(i) Because they're interesting
>(ii) Because deterministic election methods have drawbacks and paradoxes
>which can be ameliorated by the use of probabilistic methods


Drawbacks can be ameliorated by being vague about which candidate wins?.

If 10 winners are required and the data is historical, then why not
 just simply have the formula pick the same winners each time it
 is run over the same data?. That is the sort of thing that
 politicians can agree with.

...

I note the words above: "despite certainty about votes". So, it is
 correct then?, to say, that the votes are not contaminated with
 random data. That is good news for all the voting counting staff
 who couldn't mess up even on a bad or rainly day. Similarly for all
 those elections where total number of votes was less than 11.

This new Australasian metatheory, to the extent it might ever be
 defined, should be carefully checked to see how it handles election
 examples containing only two candidates. Mr Catchpole has not done
 that?. I don't understand it very well at this time.

--------
...
>> >well, without C: p(A)=2/3, p(B)=1/3
>> >without B: p(A)=2/3, p(C)=1/3
>> >without A: p(B)=2/3, p(C)=1/3

Those are not just equations without an origin. They are also tests
 that will fail many methods, except that they appear to be not able
 to be understood. Demorep1 gave data that lacked randomness, so
 Mr Catchpole must have in mind a method that itself introduces
 randomness. Demorep1's methods will, in my opinion, rise to a far
 greater height of international approval than methods pick winners
 at random.

Politicians can work hard and ask lots of donations and then the
 new quasi-useless winner randomising methods can waste many man
 hours of politicians efforts.

I gave an old list of axioms and I stated that the absence of
 randomness was an axiom for me. Anyway, statisticians would say
 that randomness in findings needs to be "minimised". That is surely
 opposed to the basis of Mr Catchpole's probailistic voting theory.

...
>p(X) represents the probability of X being the winner. From the restraints
>from regularity, in an X-Y contest, if X>Y:Y>X = 2:1 then p(X)=2/3,
>p(Y)=1/3. (more further down)

I note the word "regularity" is used again. Regularity theory was
 destroyed for all eternity by me, and I used mathematical reasoning
 and noted that a B-wins region was not closed. Mr Catchpole, can you
 please either stop implying that your regularity idea has a reality,
 or find a real fault in my argument. Have yuou redefined the word
 "regularity" and if so what are all the definitions?.

...
>> If the probability of a a single candidate winning a 'one winner one
>>  candidate' election is exactly one ("unity"), then isn't the probability
>>  of a winner winning any election exactly "unity"?. ...
>
>_WE ARE TALKING ABOUT PROBABILISTIC ELECTION METHODS_ Grrr! Talk to
>Markus!
>
>Example: when both A and B are running, it may well be we have an equal
>coin toss between A and B- that is, p(A)=1/2, p(B)=1/2. when B withdraws,
>and A is the only candidate, p(A)=1.(more further down)

What is this "when both A and B are running, it may well be we have an
 equal coin toss". Consider the implications:

        In 7 years, 5 UK jail inmates, voted on whether they would
         vote for the Tory party or the Liberal party.
        This is a 2 candidate election.

        Mr Catchpole seemed to be saying that he knows how they may vote
         and that there is a 50:50 chance of either outcome?. I guess
         Demorep1 ought rule out that his data could have come from that
         possible future election.

------------
...
>Well, say n(A>B) is the number of voters who prefer A over B.
>
>x=n(A>B)/( n(A>B)+n(B>A) )
>y=n(C>A)/( n(A>C)+n(C>A) )
>z=n(B>C)/( n(B>C)+n(C>B) )
>

Pairwise comparing is a presumption that destroys the credibility of
 the results. Proponents of STV can find little of value in parwise
 comparing. It is very difficult to see just by how much pairwise
 comparing expells optimality. 

Why not have Condorcet advocates simply never assert pairwise comparing
 but just get the rules right, and then watch it pop out (I don't know
 if that is possible).

------------------------------------------------------------------------

At 10:54 13.12.99 , David Catchpole wrote:
>On Mon, 13 Dec 1999, David Catchpole wrote:
>> "possible configuration of votes" means a likely schema of votes. Where
>> the **** does "simplex" always come from? How can a simplex on the
>> triangle be interpreted as a "possible configuration of votes?"
>
>Should have written "possible schema of votes." Slipped my mind for a
>second that I was referring to possible existence, not likely existence.

If there are 230 counts of papers (i.e. numbers), then the point will
 be placed in space having 229 or 230 dimensions.

That x,y,z you wrote about does not have that many dimensions.

          --------------------------------------------------

            As requested, info on simplex coordinate systems

The possible configuration of votes is every point inside a simplex,
 after each count is required to be non-negative and the sum is made to
 be 1 or some other positive number.

The i-th simplex is constructed by extending the surfaces of the
 (i-1)-th simplex out to a point not in the space of the (i-1)-th simplex.
 The word simplex includes these shapes: point, line segment, triangle,
 and tetrahedron.

Points in the interior of a simplex in n dimensions can be specified with
 (n+1) variables, each of which equals 1 on the variable's vertex.

That x,y,z you have written is Cartesian coordinates (which needs one
 less variable and has no equality constraint applying to the sum of
 the variables.

A simplex in Cartesian coordinates can be said to be merely a coordinate
 system, and then it need not be fully symmetric (regular) in the
 Cartesian coordinate system holding the simplex.


Craig Carey