I just _do not get_ what Craig means by any of this. Can anyone help
translate Craig's response?
PS. I suspect that an example of an "IFPP-like" method is one where-
-you work out the borda score of each candidate
-exclude the candidate with the lowest Borda score
-etc.
I know it has a name, but I can't remember it for the moment. Maybe Craig
should test its results vs. his implicit IFPP method.
On Sat, 9 Sep 2000, Craig Carey wrote:
> At 13:25 00.09.09 +1000 Saturday, David Catchpole wrote:
> >On Sat, 9 Sep 2000, Craig Carey wrote:
> >> At 22:31 00.09.08 +1000 Friday, David Catchpole wrote:
> >> >On Fri, 8 Sep 2000, Craig Carey wrote:
> ...
> >> >> At 08:54 00.09.05 +1000 Tuesday, David Catchpole wrote:
> >> >> >> At 14:36 00.09.04 +1000 Monday, David Catchpole wrote:
> >> >> >> >On Mon, 4 Sep 2000, Craig Carey wrote:
> >> >> >> >> At 02:30 00.09.04 +0000 Monday, [EMAIL PROTECTED]
> wrote:
> ...
>
> >
> >"As yet there are no principles of election methods applied yet.
>
> There are not defined, too. Without some principles, contradictions
> can't be found.
>
> >I'm just demonstrating what may be a useful analytic tool. I know I'm
> >going to be using it with respect to probablistic regularity a'la Peleg
> >and Pattanaik and in fact
> >
>
> I was only able to criticise that because it had bad problems, including
> in systems with just the 3 papers, {(AB),(B),(C)}. Remember, the rule
> tried to be anti-proportional by making the B-wins region concave in
> the junction with the C region, when obviously it should be convex,
> but that is provided one starts looking at the centre and moves down
> to the B-C midpoint. It was an incredibly bad rule. They didn't say
> it was good, but put it to the LHS of an implication. I presume you
> recall the correspondence. It was an unproductive time.
>
>
> "The point is to get the computer to do the hard work for one."
>
> The train would run off the tracks long before you get to the 'work'
> part.
>
>
> Q1:
> What is the simplest example that proves that one of you beliefs requires
> a rejection of truncation resistance?.
>
>
> >> Nothing resolves the problem except a thorough mathematical treatment.
> >> Whatever Nash is, it won't solve this 10**10 dimensional highly
> >> discontinuous 'game playing' problem that you have unclearly argued for.
> >> But any progress you would make on that ought be rejected by politicians,
> >> for being undesirable. They might find that very easy by noting that
> >> your method fails undesirable rules and that it isn't proportional.
> >> Proportionality is a global aim, so I'd say it is suspect. But your
> >> game theory idea of maximising each player's interest is not actually
> >> a local aim but it is also has an aim that is global. You have to
> >> numerically add up each paper and paper coalitions' satisfaction, I
> >> guess. Are the weights going to be arbitrary?.
> >> Which of these 2 is more satisfied?:
> >>
> >>
> >> 7 A B C D E
> >> wins wins
> >>
> >> 4 C A B
> >> wins wins
> >>
> >>
> >> 7 A B C D E
> >> wins wins
> >>
> >> 4 C A B
> >> wins wins
> >>
> >> Can you [deleted & retracted]
> >
> >Huh?
>
> Lower down you write this: "We can simulate their knowledge."
> That is a bad example because both the 1st and 2nd papers prefer
> the first winner set. The example could be fixed so that paper(s)
> X prefer winner W1 over W2 and paper(s) Y prefer W2 to W1. A simple
> dispute. Can you give an example of how you resolve simple disputes,
> for say, just 3 papers. An instance of the general theory, and just
> a check that it can solve simple problems. I guess it can't
>
>
> >
> >>
> >>
> >> I call proportionality a global aim. By game theory you don't really mean
> >> that each player acts for their own interest, but rather that you have
> >
> >I'm proposing simulating voter's responses given an election method. I'm
> >not proposing which election method. I am proposing that such a simulation
> >may be useful in analysis of _many_ election methods. M'kay?
> >
>
> I will give you a problem, an exercise. Write to me the argument that,
> either well or roughly, demonstrates that it is right to eliminate a
> single candidate only (a politician, say), at each stage of an Alternative
> Vote election. I guess you can't find a viewpoint where you can make a
> fully true good argument for that feature of the Alternative Vote. But this
> theory you look as if you will never describe, also is arbitrary.
>
> ...
> >> Game theory here creates an unsolvable problem. It is badly IMPLICIT.
> >
> >It doesn't.
> >
>
> Perhpas instead I could say it is an very high dimensional optimisation
> prob.........
>
> You solution has to be exact?. Lets suppose so. It may be like an
> optimisation of a paper mache model of hilly fields with over 40,000,000
> hills, each of which has >1000 facets. You want me to believe that the
> solution would pop out?. It certainly isn't going to be a computer that
> solves such a problem. They are TOO SLOW.
>
> Reply to me and tell me that the theory can still be turned into a
> success.
>
> What you can do, is solve all elections having only these papers:
>
> AB
> AC
> B
> C
>
> If you can solve that AND if the method is truncation resistant then
> the 3 candidate problem(s) is(are) solved.
>
>
> ...
> >> Optimisation theory can't be used because there could be billions of
> >> local maxima (hills, with flat surfaces, and widespread concavity).
> >
> >Oh bullSHIT. Tell me, when did you last do optimisation theory and
> >calculus of variations. What, dear sir, is a functional?
> >
> That is a mistake. Just considering a vote using only the papers
> {(p:AB),(q:AC),(b:B),(c:C)}, we know that A wins in the tetrahedron when
> (b<p+q)&(c<p+q) if one winner is being elected/selected. There is a
> corner of a wedge-like shape through the interior of the tetrahedron.
> A lot of edges will turn up. You used to write on some invariance for the
> winners on adding/removing other voters. So no matter what the
> dimension of the simplex, you want to embed subproblems. You have the
> ideas ready to produce very many flat faces. Saying "bullSHIT" there is
> wrong.
> Calculus of variations means derivatives. A functional is something to
> do with functions. But it is all piecewise linear. It may better to say
> that it is lot of joined polytopes. It is way of increasing the
> dimensionality, or of turning polytopes wiht nice edges, into vectors.
> Why?.
>
>
> ...
> >> You have a global aim (one that simulates a lot of local aims, while
> >> perhaps discarding truly local aims like truncation resistance), and
> >> global aims always can't agree so proportionality is a casualty in your
> >> theory so far. The whole theory would be a casualty once the public gets
> >> to re-think out this paragraph.
> >
> >Again, it's a tool for analysis I'm talking aboot, not a particular
> >election method. I'm talking about the hammer, not the nail.
> >
> I suppose it could be of interest, except that you haven't defined a
> problem about which people might be interested to have a solution done.
>
> I think it is best to avoid generality and solve fully all the possible
> problems, starting with those that can be drawn in a line segment, then
> those that can be plotted in a triangle. I guess the idea would fail you
> before you got to a tetrahedron (= 4 papers, and 2 or more candidates)
>
> ...
> >Again...
>
>
> ...
> >No. You're taking a demonstration of a probablistic ensemble over a
> >continuum out of context. P|[0,1]=1.
> >
> >Okay. The fact that you've misinterpreted a tool for analysis to mean a
> >method clarifies to me what you mean by "IFPP." You're using
> >that geometrical approach of yours to attempt to _derive_ a
> >winner, not just analyse a given election method. Right?
> >
>
> You haven't rules to allow either to occur: testing, derivation.
>
>
> It is not a geometrical approach of mine. Every preferential voting
> method can be represented geometrically. It is a method of all.
>
>
>
> >OK, so you're basically looking for a method such that, for each
> >candidate, if we were to truncate each vote up to but not including that
> >candidate, only one candidate would be the winner using ballots truncated
> >up to but not including that candidate. Two questions-
> >
> There need not be one winner. I was arguing against the papers truncate
> themselves, mainly since I can't understand how it would be done.
>
> >-Does IFPP have unique solutions, or does it occasionally generate more
> >than one?
>
> Its solutions would be absolutely unique. Shadows are iteratively and
> that grows the must-win and must-lose regions. The final regions have
> to be independent of the order and way that shadowing is done. I am
> sure that that is true. It can be proven later. Then the not known
> region has proportionality pick the winners, using a Approval Vote
> type method, that is sometimes required to find less than the required
> number of winners. E.g. if the point is inside of the E-loses region
> and 5 winners have to be found. Then we might lightly hope to have a
> 4 winner solution embedded in there. You wanted embedding. But the
> moment there is embedding of subproblems' solutions, there is more
> new corners producing hills in the optimisation landscape (if any).
> Maybe you want to optimise in an integrated way but separately for
> each candidate. Why not instead discard their interests and optimise
> proportionality and have strictly satisfied criteria?. That is a
> hypothetical question.
>
> You didn't answer my question: what rule would you have that makes
> the specifying or not specifying of the last preference, without
> effect, ?.
>
> >
> >-It seems to me what one should be looking for is a unique property of the
> >"winner's truncated ballots." Is this an approach you have attempted?
> >
> It is up to my (P1) to truncate ...there has to be truncating before
> summing if Approval Vote style adding would be used. Condorcet can be
> viewed as truncating back to A and B, whenever comparing A and B. I don't
> see this as being useful to think about at the moment.
>
> ...
>
>
> I don't believe that you are defining a new tool. Instead I think you
> investigating a problem that isn't even going to be defined.
>
>
> Suppose that in region R in the simplex, A loses this:
>
> 20 A
> <other papers>
>
> Then a shadow of R is this
>
> x A, 0<=x<=20
> <other papers>
>
>
> Definite things can be known at the surfaces of the simplex because
> there are solved subproblems. Perhaps you reject shadowing. But how
> does your new tool of a method ensure that A also loses the 2nd
> if it loses the 1st?. If you think about that then decide shadowing
> is a good idea, then can we also bring in proportionality, which
> would allow the game theory ideas to be discarded. The quantity to
> maximise in game theory is not known. If there are simultaneous
> maximisations, then ....
> Tell me: how do you sort a vector, each element of which is a
> vector of length 2, and holding 2 real numbers. Sort and subsort
> may be unfair. The first element could be A vs B and the 2nd B vs C,
> ?. There could be dry dusty papers on this topic.
> Extending it to billions of dimensions is one area I have doubts
> about.
>
>
>
>
>
>
>
-------------------------------------------------------------------------------
"Being in politics is like being a football coach. You have to be smart
enough to understand the game, and dumb enough to think it's important"
-Eugene McCarthy
