# [EM] (P1) tweak up ... Québec Ombudsman, "rank"

Craig Carey research at ijs.co.nz
Fri Feb 4 11:27:52 PST 2000

```Axiom A1 of preferential voting theory is defined.

I fix up some errors I made in this message.

At 10:55 02.02.00 , Craig Carey wrote:
>At 15:04 01.02.00 , Blake Cretney wrote:
...
>>I don't understand.  What do you mean by a paper marked "(...X...)".
>
>There are 5 possibilities. Any one of those possibilities can occur,
> so unless you rule some out, they can all occur.
>
>>Has Y somehow been omitted from the paper?  If the voter has left Y
>>unranked, then that is usually interpreted to mean that the voter has
>>implicitly ranked it under all the explicitly ranked candidates.
...
>
>I regard your statement "usually interpreted ..." as extremely
> controversial if it means that point need not be noted. For example,
> if a paper is altered from (ACB {DE) to (AC {BDE), then B can win
> the first and lose the 2nd. I presume a new method is being built
> on the foundation well understood but still missing definition of
> the term rank. The Blake-C "rank" of B with respect to all other
> candidates if totally invariant under that alteration just above,
> yet presumably in a best possible method, the win lose state of B
> can alter.

That would have been a significant paragraph for its rejecting of
Condorcet, but it is wrong.

If (1:ACB {DE) is changed to (1:AC {BDE), then in the 1st paper example,
1 paper ranks B over both D and E, and in the second, 0 papers rank
B over both/either D and/or E.

Hence the words "totally invariant" are false/invalid. This next paragraph
can be wrong too:

>The idea of rank (copied from Condorcet theory, is it?) is not friendly
> with rules such as (3:AB) = (1:ABC,1:ABD,1:ABE) if the candidates are
> {A,B,C,D,E}. That is in my opinion, easily enough to allow a rejection
> of summing ideas borrowed from Condorcet.
...

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

The axiomatic basis of preferential voting method design

I wrote:
...
>My suggestion is: only what interests voters, and politicians get
> nothing but proportionality.  (except for (2:A)=(1:AB,1:AC), and
> possibly anything else)

Actually, there is no need to explicitly say that "(2:A)=(1:AB,1:AC)" is
an exception, since it is not an exception (it is not at all necessarily
global (like proportionality), and it would interest voters).

It may be needed to define methods to be not "proportional" if they
return the wrong number of winners.

A definition of Meta-axiom A1. A lot of best effort methods that might
survive the scrutiny of a committee or civil servant, may not get past
this axiom (FPTP can, with papers lacking 2nd preferences):

-------------------------------------------------------------------
Axiom A1 (the casually worded form)

Axiom limiting implausibility of other axioms

"Only what interests voters, and politicians
get nothing but proportionality."

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

STV has a monotonicity violation w.r.t candidate A, here:

10 ACB
6 BA
5 CBA         STV: B wins

8 ACB
6 BA
7 CBA         STV: A wins

The alteration is : (ACB+)--(CBA+), which is a monotonicity (and P1)
violation.

That example is possibly not be the simplest P1 violation example.

...
In this paragraph, I missed out the word "on":

:Methods do not make decisions on national election outcomes only,
> some methods will turn a vote for candidate A into a vote
> against candidate A. Monotonicity and similar is not really an
> option.

The word "politicians" needs to be replaced with some other word, etc.

Rule A1 implies mathematical complexity that obstructs progress to
a solution. It is a rule that is designed to bring back laymen into
a discussion, along with experts in open government, and it rejects
about all methods (excluding FPP/FPTP and IFPP).

There is no need to tolerate the incomprehensible theory and algorithms
of others, when there clear thinking and a path to a fundamental
axiom that allows others' thinking to be rejected on the grounds that
they can't repair it even if further serious and full consideration
were to occur.

[Some are thinking that they could put a single line on the reverse side
of all voting papers, referring to document where the method can be
seen to clearly violate meta-axiom A1.]

...

```