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• ## Re: [RangeVoting] Condorcet paradox arises in scientific (physics) experiment

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• ... None. The hypotheses are all lousy. The predictions are unreliable. Is the result really binary? I.e., two-valued only, say B or H, or does a hypothesis,
Message 1 of 7 , Feb 1
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At 10:49 PM 1/31/2013, WarrenS wrote:
>(True story, but abstracted.)
>
>There were three candidate scientific hypotheses named B, F, and H.
>It was possible to perform a pairwise comparison experiment to
>decide which hypothesis
>worked better to explain that experiment, BUT the situation was
>(somewhat strangely, but
>this was the situation) that you only got information about TWO
>among the candidates,
>and it decided which were the two, not you.
>
>Anyhow, after laboriously performing 84 experiments, the results were
>
> BH=14, HB=23, BF=9, FB=8, FH=21, HF=9
>
>i.e. B won 14 of the 37 H-versus-B comparisons, etc.
>
>Ouch.
>
>So... which hypothesis would you like best?

None. The hypotheses are all lousy. The predictions are unreliable.
Is the result really binary? I.e., two-valued only, say B or H, or
does a hypothesis, if usable, come up with a number, and the
experiment comes up with a number, and the better match was the
"winner" of that individual experiment?

If so, then the variation in the numbers would surely be important!

And I'd want to judge this election using Range. I.e., each
experiment would produce a value for the accuracy of the result, from
each hyppothesis. And the inapplicable hypothesis would be an
"abstention," and average Range would be used. I do not see how, say,
Hypothesis B could be used to make a prediction for the FH experiments.

Really, it looks to me like there are three different situations,
with H being the best hypothesis for the BH experiments, B being
*slightly best* -- little difference, for the BF experiments, And F
being best for the FH experiments.

But if you cannot know what type of experiment it is, there is simply
no way to make an ordinary, unconditional prediction.

If F is considered the winner, what does that mean? F makes *no
prediction for the HB experiments,* which are the greatest number.

You are right, it's strange, Warren. I don't think there is enough
information to assess this.
Message 1 of 7 , Feb 1
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• We aren t talking about the EPR paradox, are we? Because that would be cheating; the hypotheses would be hidden variable theories and the cyclical result
Message 1 of 7 , Feb 1
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We aren't talking about the EPR paradox, are we? Because that would be
cheating; the "hypotheses" would be hidden variable theories and the
cyclical result would be actually what you'd expect from quantum theory.

2013/2/1 Jan Kok <jan.kok.5y@...>

> **
>
>
>
>

[Non-text portions of this message have been removed]
• ... --well, you ll be sorry you asked, but crystallography & quantum chemistry. The 3 candidate theories yield different predictions of crystal structure under
Message 1 of 7 , Feb 3
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--- In RangeVoting@yahoogroups.com, Jan Kok wrote:
>

--well, you'll be sorry you asked, but crystallography & quantum chemistry.
The 3 candidate theories yield different predictions of crystal structure under certain imposed conditions, and then that can sometimes be compared with the actual crystal structures.

"Theory F" seems to be the best (and indeed may be proven best in a certain asymptotic
limit whose relevance is somewhat questionable)... but the confidence I have in this conclusion is not large.
• ... -yes. Actually, the binary wins actually do come with numbers saying how big a win it was. ... --probably. ... -well, it is binary, i.e. one does not
Message 1 of 7 , Feb 3
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> None. The hypotheses are all lousy. The predictions are unreliable.
> Is the result really binary? I.e., two-valued only, say B or H, or
> does a hypothesis, if usable, come up with a number, and the
> experiment comes up with a number, and the better match was the
> "winner" of that individual experiment?

-yes. Actually, the binary "wins" actually do come with numbers saying "how big a win" it was.

> If so, then the variation in the numbers would surely be important!

--probably.

> And I'd want to judge this election using Range. I.e., each
> experiment would produce a value for the accuracy of the result, from
> each hyppothesis.

-well, it is binary, i.e. one does not get a 3-way choice, the experiment really only decides between two.

> And the inapplicable hypothesis would be an
> "abstention," and average Range would be used. I do not see how, say,
> Hypothesis B could be used to make a prediction for the FH experiments.

--I like your "range vote with abstentions" idea, I'll try that.

> Really, it looks to me like there are three different situations,
> with H being the best hypothesis for the BH experiments, B being
> *slightly best* -- little difference, for the BF experiments, And F
> being best for the FH experiments.
>
> But if you cannot know what type of experiment it is, there is simply
> no way to make an ordinary, unconditional prediction.
>
> If F is considered the winner, what does that mean? F makes *no
> prediction for the HB experiments,* which are the greatest number.
>
> You are right, it's strange, Warren. I don't think there is enough
> information to assess this.

--well, I more or less agree, there was not enough data to get enough confidence to decide, and it might be that all the hypotheses are wrong (or the uber-hypothesis that one is better than the other two, is wrong). But, it was amusing, so I posted it.
• ... Yeah, I got that. However, it seems, you are attempting to judge an *overall theory*, yet the theory cannot predict the outcome in all specific
Message 1 of 7 , Feb 3
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At 03:01 PM 2/3/2013, WarrenS wrote:

> > And I'd want to judge this election using Range. I.e., each
> > experiment would produce a value for the accuracy of the result, from
> > each hyppothesis.
>
>-well, it is binary, i.e. one does not get a 3-way choice, the
>experiment really only decides between two.d

Yeah, I got that. However, it seems, you are attempting to judge an
*overall theory*, yet the theory cannot predict the outcome in all
specific experiments, only in some.

> > And the inapplicable hypothesis would be an
> > "abstention," and average Range would be used. I do not see how, say,
> > Hypothesis B could be used to make a prediction for the FH experiments.
>
>--I like your "range vote with abstentions" idea, I'll try that.

Maybe it's useful. What was not defined well was what "correctness"
was. It's obvious that none of the theories can accurately predict
the outcome of all thee experiments. But if we have a good definition
of "correct," then it may be possible to judge.

There is an ontological problem that arises in science when we think
the goal is to find the "truth."

Some may certainly want to do that, but my training is that this is a
fool's errand. No model is the "truth." Reality is not a model. No
model can completely represent reality. At least that's a reasonable
operating assumption. But models may be more or less useful at
predicting outcomes.

And at that, when we are dealing with the QM level, outcomes are not
specifically and individually predictable. However, good theory, so
far, can be, in situations where the math is sufficiently simple, be
highly accrate as to average outcome over many experiments.

In this case, if a value is assigned to a relatively accurate
prediction, zero value to no prediction (for a case that arises), and
negative value to a poor prediction, then Range will generate an
expected value for each of the theories.

I have no idea why one is attempting to choose *one* theory. It looks
like three are necessary here, at least. Or more. The uber-theory,
then, gets complex, unfortunately, it's *conditional*.

If outcome AB, then the theories A and B apply, with these
probabilities. If outcome BC, then B and C, and if outcome CA, then C and A.

The *reality* is something else. How many realities are there in the
experiment?

> > You are right, it's strange, Warren. I don't think there is enough
> > information to assess this.
>
>--well, I more or less agree, there was not enough data to get
>enough confidence to decide, and it might be that all the hypotheses
>are wrong (or the uber-hypothesis that one is better than the other
>two, is wrong). But, it was amusing, so I posted it.

Just don't run too fast with it, you might fall down and break your crown.

(Quantm Mechanics Proves that Range Voting is the Best Voting System.