Proving B loses with heaps of votes (Re: [EM] Query for Approval advocates

[Craig Carey]

At 2003-08-21 12:36 -0400 Thursday, Eric Gorr wrote:
>At 11:49 PM -0700 8/20/03, Bart Ingles wrote:
>>Why should it be considered important to find a majority when none
>>exists?  In my view, the very concept of 'majority' is meaningless when
>>there are three or more candidates, and appears to be based on several
>>logical fallacies including:
>>
>>(1) Round number fallacy:  The 50% figure is viewed as magical because
>>it has the appearance of being a "natural" threshold.  Which it is--if
>>there are only two candidates.
...

Have you a meta-rule saying that rules should not be too weak ?. Both the
2 candidate embedded FPTP method and whatever shadows it has, contain very
little of the full space representing the real-valued ballot paper
counts.



>Take this example:
>
>   40:A
>   35:C>B
>   30:B
>
>That I believe B should win, is independent of any particular method.
>
>Why should B win?
>
>Because it is obviously preferred by a majority of people over every 
>other option.
>


There are no people in that example: the two ASCII letters "3","5",
construct what readers know to be a number. There are no "people" in
that small patch of ASCII text.

Let's go over that again. Here I number the lines for you:

[1] Take this example:
[2] 
[3]    40:A
[4]    35:C>B
[5]    30:B

There are no people in those 5 lines that you wrote, for that is only
symbols (mainly numbers and letters, and 3 ":" characters).

I hope you write in a brighter style. You wanted to present a false
idea as being true. Then you postulated the existence of "people".
The word "majority" suggests that there were many people. They don't
carry a lot of reasoning since not existing and having absolutely no
argument that you divulged. Added to your large group of stupid
hypothetical "people" who apparently would not all unite to laugh at
you when you said you used belief instead of reasoning, it is not 
obvious what you want the real readers and subscribers to do.

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

If there is something wrong with the reasoning here, then do let all
the people that read the messages, know what that is.



THE ARGUMENT

V1
   (AB.) 33.33% 
   (B..) 28.57%
   (C..) 38.01%

Mr G says B should "obviously" win.
Though it is not said, and saying it is certainly required, it seems
that Mr Gorr has that be a 1 winner election. It is required since
Mr Gorr's claim is obviously untrue when the number of winners is 0.

By the IFPP method, candidate A wins. The claim has to be un-political
and built over unfairness since it had B win. Now it is proven that
an argument exists. Here is an argument:

(1) B is claimed to win V1 [which is wrong in fact, hence both A and C
lose V1, by the axiom of the right number of winners.

(2.1) By (1) and Truncation Resistance, C also loses election V1C:

V1C =
   (AB.)  33.33% 
   (B..)  28.57%
   (CAB)  38.01%

(2.2) By (2.1) and the axiom/corollary of Monotonicity, C also loses
 V1C2:

V1C2 =
   (AB.)  34.33%  [up 1%]
   (B..)  28.57%
   (CAB)  37.01%  [down 1%]

(2.3) By (2.2) and the axiom of Truncation Resistance, C also loses V2:

V2 =
   (AB.)  34.33%
   (B..)  28.57%
   (C..)  37.01%

(3.1) By the axiom of FPTP embedded, A loses this election, election V3,
 and candidate C wins has most of the votes:

V3 =
   (A..)  34.33%
   (B..)  28.57%
   (C..)  37.01%

(3.2) By (3.1) and the axiom of Truncation Resistance, candidate A loses
 election V2.

(4) Result (2.3) has C lose V2, and result (3.2) has A lose V2. Using
 the axiom of 'Right number of winners', candidate B wins V2.

(5) By (4) and the axiom of Truncation Resistance, B wins V4:

V4 =
   (AB.)  34.33%
   (BC.)  28.57%
   (C..)  37.01%

(6.1) By (5) and the axiom/corollary of Monotonicity, candidate B also
 wins V4B:

V4 =
   (AB.)  34.33%
   (BC.)  32.57%  [up 4%]
   (C..)  33.01%  [down 4%]

(6.2) By (6.1) and the axiom of Truncation Resistance, candidate B also
 wins V4B:

V4B =
   (AB.)  34.33%
   (B..)  32.57%
   (C..)  33.01%

(7) By the axiom of the Right number of winners, candidate A loses
 election V4B (and candidate C also loses election V4B).

(8) By (7) and the axiom of Truncation Resistance, candidate A loses
 election V5 since A lost election V4B:

V5 =
   (A..)  34.33%
   (B..)  32.57%
   (C..)  33.01%

(9) A contradiction has appeared: the axiom of FPTP embedded
 requires that candidate A win election V5. The result of (8) had
 candidate A lose election V5. Hence the claim of Eric Gorr was
 untrue for there is no [[significant]] mistake in the reasoning.

--------


A derivation of the 1 winner IFPP method is here: 1/3 quota:
   http://www.ijs.co.nz/quota-13.htm


--

...
>If all 25% prefer B over A, why should B not win?


To say that B should win is to say that B sometimes will win, which
is invalid (= not always true), and so we would conclude that B
should not win.

B loses in every 0 winner election provided that B is a candidate.


----

What is the purpose of saying that many people agree with an untrue
statement ?. I have a speculation on whay that would be, but I don't
want to say it since I would say that something unreasonable would
allow Mr Gorr to reject reasoning that he did actually follow. At the
moment, there is no indication that Mr Gorr can follow the argument
that I put higher up in this message.

I am still waiting for Mr Gorr to write on sincerity. I recall that
Mr Gorr tried to trail past the eM list an idea that he owned a whole
lot of people that were voters. Then he said that they were sincere,
i.e. he carefully allowed each one of them to be liars. Also the liars
were ignored. As might be expected, Mr Gorr did not get to infer any
new equations representing justice from those ideas.




Craig Carey