Erratum Re: [EM] (P1) and monotonicity for single-winner election systems and Condorcet.

[David Catchpole]

On Tue, 26 Oct 1999, Craig Carey wrote:

> 
> What is Pi?. Unnecessarily adding the words, "the truth of", and then with
>  a show a pointers to logic textbooks and guns, removing those very words,
>  does not prove to be a process that in any step provided a definition of Pi.
> My guess is that you would make Pi to be Condorcet pairwise comparison.
> But that has not been stated. 

Pi(A,B,V) _is not_ Condorcet pairwise comparison! It's a proposition
regarding whether a voter i expresses a preference for candidate A over
candidate B in scenario V!

"Colt" in this case wasn't a type of gun. There is in my country a famous
poem, "The Man from Snowy River," by A.B. (Banjo) Paterson, Which opens
with the line-

"There was movement at the station, for the word had got around that the
colt from Old Regret had got away."

[NB "station"="ranch"]

Old Regret is a mare, and the colt is extremely valuable and has left to
join a colony of brumbies (wild horses). Various heroes of the Australian
Alps gather to try to retrieve the colt, including Clancy of the Overflow.
In the end though, a young unknown, the Man from Snowy River, gets to the
brumbies by charging suicidally down a steep hill into a glen. But I
digress- in the logic textbook which I learnt from, use is made of the
poem to demonstrate propositional calculus.  (More further down)

> V =
>    99 C
>    03 D
> 
> V' =
>    99 C
>    01 D

I take it you mean-

V:	99 voters indicate a preference of C over D
	3 voters indicate a preference of D over C

V':	99 voters indicate a preference of C over D
	1 voter indicates a preference of D over C

> 
> -------------------------------------------------------------------------
>  "For all V, all V', W(V)<>W(V') ... there exists i, A, B such that A is
>   an element of W(V), A is not an element of W(V'), [and] ...
> -------------------------------------------------------------------------

WTF? That is nowhere near the expression I gave for monotonicity! Rather,
my statement for monotonicity in part reads-


...For all V, all V', W(V)<>W(V') implies-

there exists i, A, B such that A is an element of W(V), A is not an
element of W(V'), B is an element of W(V'), B is not an element of
W(V), and-...

In other words, if the set of winners stays the same, there is no
implication for monotonicity other than it is not violated.

> Which of C and D is the candidate you would pick for variable A, that
>  would be substituted into your sentence above ??.

Well, assuming that majorities still rule- A is C, if you get
my drift. Now, if D were to win in V'(which would be required for D to
take its place as a B, and for the condition to possibly be violated),
that would quite definitely require some voters C>D to change to C=D or
D>C, so you can see quite casually that monotonicity is far from violated
by this case! (more further down)

> 
> My version was deleted without analysis. This equation:

It wasn't deleted without analysis. I pointed out that it was implied by
monotonicity and left it at that, hoping in some part that you would take
this and run with it and see if the rest of the exploration, which was
specifically for monotonicity, had some similar implications for (P1) if a
comparable exploration were used. (more further down)

> 
> Rule: (All V)(All p in V)(All p')(All A,B)(All V', V' in Alt(V,p,p'))
>         [(P(B,A,p) => P(A,B,p')) => not (A:W(V).-B:W(V).B:W(V').-A:W(V'))]

> In the following, Mr Catchpole had, in a recent message, explained his
>  position as being that the words "a switch in candidates..." meant
>  relettering and had nothing to do with preferences. (It was certainly
>  a surprise to me, to have the truth or falsity of a new voting theorem
>  based upon the truth or falsity of whether or not it is possible to
>  reletter variables).

Again, Ce wha...? Speak English, Kemosabe, your Navaho is shocking. Did
anybody else understand what Craig just said? Markus? (more further down)

> >> Those phrase, "P is a necessary condition for Q" means "Q implies P". In
> >>  other words, Mr Catchpole is saying, wherever a method is neutral to
> 'changes in'
> >>  candidates and it satisfies monotonicity, then the method is Condorcet. 
> >
> >Got it in one, kiddo.
> 
> Your statement is false if it applies to all methods.

Then the onus is on you to demonstrate so. (more further down)

> 
> The First Past the Post Method, satisfies monotonicity but it is not
>  Condorcet, so the statement is false. The term representing neutrality
>  is on the left hand side of an implication. Mr Catchpole defended his
>  position by saying it was clearly true (elettering is possible).

What's the problem with neutrality being on the "left hand side" of the
implication? That I remember, that's where universal assumptions go.

I did not state it as a proven theorem. I consider that it is most
probably true, but there is so far no proof or disproof.

I invite you to test FPTP against the definition for monotonicity I gave
and see what you come up with. If you like, I can send you a copy of an
email I sent to Markus in a sidediscussion of this thread. It provides an
example of monotonicity being violated by FPTP. (more further down)

> 
> I read in a previous message that Mr Catchpole had said that FPTP is not
>  a preferential voting method.

Blah? Probably my Australian heritage catching up. Were eye cum frum, we
call single-seat STV "preferential." (more further down)

>  Preferential voting methods include those methods that accept preference
>  lists, or have outcomes based on STV-like preferential voting papers.
> 
> How could FPTP not be a preferential voting method when it is the method
>  that results from modifying STV so that all subsequent preferences are
>  discarded during transfers and during elimination (approximately).

It is a preferential voting method according to _that_ definition.
Remember- we're dealing with an issue whose nomenclature and features vary
from place to place and from person to person. It is rare when a single
definition of a voting system exists. (more further down)

> >"thorough checks convince me ..."
> 
> >"Ce wha...?" - What did you mean, Mr Catchpole?.

That's my pitiful attempt at Let's Parler Anglese humour. Ce from "Ce
Pas?", etc. and "Wha...?" from a stunned "What?" (more further down)

> At 20:14 25.10.99 , David Catchpole wrote:
> >On Sun, 24 Oct 1999, Donald E Davison wrote:

> >> three features make STV less proportional. One or more of them would not
> >> allow the Eight Percent Group to elect any members, but they would allow
> >> the Forty-Eight Percent Group to elect fifty-eight members per hundred.
> >
> >Droop doesn't do that. Give me an example where it does.
> 
> The last sentence of Mr Davison is sure to be true and there is no need
>  for a sample election proving Mr Catchpole to be in the wrong about
>  Mr Davison's last sentence.

The onus of (dis)proof... I invite you, Craig (plaintiff), to come up with
an example where aforesaid forty-eight percent group elects fifty-eight
members per hundred in an at-large Droop election. Becrying intuition
ain't proof.

And yes, I did write "Arsend" with regard to Hare.