[EM] Correction. Big CS fault?

Craig Carey research at ijs.co.nz
Fri Dec 20 14:24:42 PST 2002

```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. 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.

>What an "ABC" voter has told the Returning Officer in a preferential vote election
>is:
>1.  I give my vote to A.
>2.  If A cannot be elected, please transfer my vote to B.
>3.  If B cannot be elected, please transfer my vote to C.
>4.  If none of A, B and C can be elected and the choice is among D, E and F, I do
>not wish to express any view and am content to leave that decision to other voters
>who have expressed opinions on the relative merits of D, E and F.
>
>You may argue that by including all possible combinations of D, E and F and by
>giving each equal weight (1/6), you have said the same thing, but I do not think
>it is the same thing at all.

It does seem like the same thing in my opinion. The rule does seem a little
lacking in obviousness but it does appear to be a rule that can't be done
without.

If an axiomatic theory is based on the rule and the rule is believed wrong
then the theory easily would be believed to be wrong. But it has nothing to
do with STV which is down and out and not coming up. I guess you are wondering
if the rule can be deleted without providing a replacement.

I need that rule in my theory so that I can find the winners of the
papers (A),(AB),(AC),(B),(C), once I know the winners of (AB),(B),(C).

If the solution to the 5 paper problem is known, then the solution to
the full 9 or 15 paper 3 candidate (0,1,2, or 3 winner) election is known.

If you don't like the rule, then I could ask for a replacement that provides a
reasoning path between the solutions of the 3 paper problem and the 5 paper
(3 candidate) problem. A method designer can't say that there are too few
axioms any more than a theory of logic is worth knowing about if only 1/3
of the needed axioms were written down.

>                            I cannot say whether it makes any difference to your
>voting geometry,

That P2 specifies lines that must lie inside of the surfaces (that are dividing
different winner sets).

>                 as all of that is beyond me, but to me there is a qualitative and
>quantitative difference between saying that the ABC voter has dropped out when the
>choice falls among D, E and F and saying that the ABC voter can be assumed to have
>allocated his or her last preferences equally to all possible combinations of DEF.
>

STV has bugs that make the rule controversial there. But the rule has is similar
in nature to proportionality. E.g. both would have the transfer values be raised
to equal 1. STV's performance can't be checked because that is an aim that is
secondary to compliance with the 0<=power<=1 sequences rules. So if one can
be left unchecked then both could.

The author of Range Voting once e-mailed me to say he would like to use a
Monte-Carlo method to check methods against that P2 rule. I don't know what
happened.

G. A. Craig Carey

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