Bayesianism versus Critical Rationalism

Jayson_Virissimo

I have just rediscovered an article by Max Albert on my hard drive which I never got around to reading that might interest others on Less Wrong. You can find the article here. It is an argument against Bayesianism and for Critical Rationalism (of Karl Popper fame).

Abstract:

Economists claim that principles of rationality are normative principles. Nevertheless,
they go on to explain why it is in a person’s own interest to be rational. If this were true,
being rational itself would be a means to an end, and rationality could be interpreted in
a non-normative or naturalistic way. The alternative is not attractive: if the only argument
in favor of principles of rationality were their intrinsic appeal, a commitment to
rationality would be irrational, making the notion of rationality self-defeating. A comprehensive
conception of rationality should recommend itself: it should be rational to be
rational. Moreover, since rational action requires rational beliefs concerning means-ends
relations, a naturalistic conception of rationality has to cover rational belief formation including
the belief that it is rational to be rational. The paper considers four conceptions
of rationality and asks whether they can deliver the goods: Bayesianism, perfect rationality
(just in case that it differs from Bayesianism), ecological rationality (as a version of
bounded rationality), and critical rationality, the conception of rationality characterizing
critical rationalism.

Any thoughts?

A good nutshell description of the type of Bayesianism that many LWers think correct is objective Bayesianism with critical rationalism-like underpinnings. Where recursive justification hits bottom is particularly relevant. On my cursory skim, Albert only seems to be addressing "subjective" Bayesianism which allows for any choice of prior.

4XiXiDu15y

For people like me who have no clue, if you scroll down a bit here there is a comparison (so you get a vague idea): * Subjective Bayesians emphasize the relative lack of rational constraints on prior probabilities. * Objective Bayesians (e.g., Jaynes and Rosenkrantz) emphasize the extent to which prior probabilities are rationally constrained. More here: And of course Critical rationalism: * Critical rationalism explicitly proposes a third decision rule for rational belief formation: it is rational to believe a hypothesis if it has so far withstood serious criticism better than its competitors.

5Matt_Simpson15y

I'll add that a decent summary of the position espoused in Where recursive justification hits bottom (linked in the grandparent) is that critical rationalism (or something like it) entails objective Bayesianism. It both entails the use of Baye's rule to update on information and it entails a set of correct priors.

1Jayson_Virissimo15y

Thanks for helping me realize that Critical Rationalism and Bayesianism can be compliments rather than substitutes.

2Elliot Temple15y

FYI that is a misleading statement of Critical Rationalism. For one thing, Popper was not a "belief philosopher" so he wouldn't have stated it quite like that. There are a lot of misleading statements about CR floating around. Most come from its opponents trying to make sense of it on their own terms. In trying to formulate it in a way that makes sense given their anti-CR premises, they change it. It's best to read primary sources for this.

It seems to think the problem of the priors does in Bayesianism :-(

Popper seems outdated. Rejecting induction completely is not very realistic.

2Jayson_Virissimo15y

Critical Rationalism has advanced somewhat since Popper. I think Hume would agree.

2timtyler15y

Not very significantly. The revolution happened mostly without them.

5Jayson_Virissimo15y

After reconsidering your statement, I have come to agree.

1Elliot Temple15y

Who do you think advanced CR? I think only David Deutsch has improved on Popper.

2Jayson_Virissimo15y

I had in mind Miller and Deutsch.

2Elliot Temple15y

Which Miller publication or argument?

5Jayson_Virissimo15y

Critical Rationalism: A Restatement and Defense and Out of Error: Further Essays On Critical Rationalism.

1Elliot Temple15y

Thanks I ordered them. I'd only read individual articles of his.

-2[anonymous]15y

Hume would agree because he never accepted the full force of his own argument. He couldn't imagine how people can create knowledge without induction even though he could see that induction is impossible. It took Popper to explain how knowledge can be created without induction.

It is a theorem that every consistent consequentialist decision rule is either a Bayesian decision rule or a limit of Bayesian decision rules.

I've actually been meaning to find a paper that proves that myself. There's apparently a proof in Mathematical Statistics, Volume 1: Basic and Selected Topics by Peter Bickel and Kjell Doksum.

Consequentialism is not in the index.

Decision rule is, a little bit.

I don't think this book contains a proof mentioning consequentialism. Do you disagree? Give a page or section?

It looks like what they are doing is defining a decision rule in a special way. So, by definition, it has to be a mathematical thing to do with probability. Then after that, I'm sure it's rather easy to prove that you should use bayes' theorem rather than some other math.

But none of that is about decisions rules in the sense of methods human beings use for making decisions. It's just if you define them in a particular way -- so that Bayes' is basically the only option -- then you can prove it.

see e.g. page 19 where they give a definition. A Popperian approach to making decisions simply wouldn't fit within the scope of their definition, so the conclusion of any proof like you claimed existed (which i haven't found in this book) would not apply to Popperian ideas.

Maybe there is a lesson here about believing stuff is proven when you haven't seen the proof, listening to hearsay about what books contain, and trying to apply proofs you aren't familiar with (they often have limits on scope).

In what way would the Popperian approach fail to fit the decision rule approach on page 19 of Bickel and Doksum?

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