[EM] Correction. Big CS fault?

[Craig Carey]

At 02\12\20 23:04 +0000 Friday, James Gilmour wrote:
 >> At 02\12\20 14:16 +0000 Friday, James Gilmour wrote:
 >>  >Craig Carey wrote (in part):
 >>  >>
 >>  >> It might seem that in a 6 candidate election, the paper (ABC) is more
 >>  >> about A,B,C, than about D,E,F. But it can be expanded out like this:
 >>  >>
 >>  >> 1(ABC) = ((ABCDEF) + (ABCDFE) + (ABCEDF) + (ABCEFD) + (ABCFDE) + (ABCFED))/6
 >>  >>
 >>  >> So every single paper is a paper that candidates can hold an interest
 >>  >> for.
 >>  >
 >>  >Craig, this my be YOUR interpretation, but I do not think it is valid.
 >>  >
 >>
 >>
 >> I just used the word "can". Certainly that rule (which I name "P2) is rather
 >> simply needed.
 >
 >Craig, I don't understand what you are trying to say.  There is no "rule" in your
 >original expansion - just an expansion based on your (unjustified) interpretation
 >of what the ABC voter marked on the ballot paper.
 >

That seems correct. However there is a rule nearby that says that not a single
candidate has its win-lose state change, when that replacement is done.
That is "P2" and it similarly allows the addition of the 4 papers
1(A)+1(B)+1(C)+1(D), to leave all the winners of a 4 candidate election,
unchanged.


 >
 >> I can't do much if STV fails that and just about every other
 >> rule that ought be imposed too (some are sequences of rules). In the message,
 >> Mr Simmons did not need a method, so rules were not needed too.
 >>
 >
 >I do not understand the reference to "STV".  When you use "STV" on this list, I
 >presume you are drawing some distinction between "STV" and "IRV".

I regard STV plus the added constraint, "one winner", to mean exactly the
"Alternative Vote". So there is nothing to look for except hidden meaning
and normally I have not got much of that when picking between one term
and the other.


 >I thought the
 >discussion above was about an IRV, single-winner election.  (I know all about
 >"STV" applied to single-winner elections, but the confusion of terminology is not
 >helpful on this list where what I have for 40 years called the "Alternative Vote"
 >is known as IRV.)
 >

I am not using the word IRV. They could have some female pop star shift the
country over to some other name.


...
 >Once again you ignore completely a fundamental qualitative difference in what the
 >voter has actual told the Returning Officer.  Neither you nor I should make
 >assumptions about what we have not been told.  Once the choice is among D, E and
 >F, the ABC voter has dropped out and wants to take no more part in the election.
 >The method of counting and determining the winner must respect that and not
 >re-apportion that voter's vote in accordance with some rules we have invented for
 >our convenience.

That is maybe no complaint there at all since the P2 rule requires that there be
no change in the winners.

Here is a geometric interpretation.
Suppose that there 2 other papers instead of 6.
Here this rule is visualised: No winners change when (AB)+(AC)-2(A) is added.

Visualise a tetrahedron. Let the apex of the tetrahedron represent any paper
(e.g. (D) or something else).
Let the base have a flat end nearest, and let the the (A) vertex be on the far
side.

      (A)
      /|\
     / | \
    /  |  \
   +---+---+
(AB)  P  (AC)

An election is a point inside of the tetrahedron. The space is normalised.
Normalising distorts shapes as they near edges and so it quite alters the
shapes visualised.

To add ((AB)+(AC))/2 will shift a point towards the midpoint of the
  (AB)---(AC) line, which is named P.

To add 2(A) will shift the point towards the (A) vertex.

However there was -2(A).
Instead of subtracting, this is the same. These 2 cases are compared and the
rule says they have the same winner:

Case 1: the election point is X + ((AB+(AC))/2: point X moves towards P
Case 2: the election point is X + 2(A)        : point X moves towards (A)

That defines an infinity of line segments. Some or maybe all, are parallel
to the P---(A) line. Across those lines, the winners can't change.

So the rule is able to altering (or fail, etc.) the method.
It might not be preprocessing voters votes at all.

With STV, there are different ways of preprocessing votes that rule says
ought make no difference, and since it does make a difference then someone
would decide (and and one option is to have no preprocessing, and another
is to create variants of STV, but the variants are probably worse since
giving transfer values more scope to multiply to nothing, the weight of
votes. But if the methods had of been better, then reinterpreting the
votes of voters would be a preferred option).


 >
 >
 >> The rule does seem a little
 >> lacking in obviousness but it does appear to be a rule that can't be done
 >> without.
 >
 >I won't comment on the "obviousness" or lack of it in your "rule", but if your
 >methodology does not respect the qualitative information the ABC voter is giving
 >you, then you must change your methodology.  You cannot simply say "it does appear
 >to be a rule that can't be done without."  You must not make assumptions about
 >what voters have not told you, just to satisfy some rule you have invented for
 >another purpose.
 >

You assume that it is preprocessing votes, but the rule says that any
preprocessing has no influence on the outcome. Thus there may be no
preprocessing. Your style of argument can fail to get the rule even if
the rule was one that should not be used.

I would like to absorb the rule into another rule, but it is all about
the centres of faces and faces of faces and ... and edges of a simplex and
it unlike the other axioms and it seems a bit weak too. I don't speak for
the rule.


G. A. Craig Carey



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