Bayesianism for humans: prosaic priors

BT_Uytya

(followup to What Bayesianism has taught me? and Bayesianism for Humans, relevant to Boring Advice Repository )

There are two insights from Bayesianism which occurred to me and which I hadn't seen anywhere else before.
I like lists in the two posts linked above, so for the sake of completeness, I'm going to add my two cents to a public domain. This post is about the second penny, the first one is here.

Prosaic Priors

The second insight can be formulated as «the dull explanations are more likely to be correct because they tend to have high prior probability.»

Why is that?

1) Almost by definition! Some property X is 'banal' if X applies to a lot of people in an disappointingly mundane way, not having any redeeming features which would make it more rare (and, hence, interesting).

In the other words, X is banal iff base rate of X is high. Or, you can say, prior probability of X is high.

1.5) Because of Occam's Razor and burdensome details. One way to make something boring more exciting is to add interesting details: some special features which will make sure that this explanation is about you as opposed to 'about almost anybody'.

This could work the other way around: sometimes the explanation feels unsatisfying exactly because it was shaved of any unnecessary and (ultimately) burdensome details.

2) Often, the alternative of a mundane explanation is something unique and custom made to fit the case you are interested in. And anybody familiar with overfitting and conjunction fallacy (and the fact that people tend to love coherent stories with blinding passion¹) should be very suspicious about such things. So, there could be a strong bias against stale explanations, which should be countered.

* * *

I fully grokked this when being in process of CBT-induced soul-searching; usage in this context still looks the most natural to me, but I believe that the area of application of this heuristic is wider.

Examples

1) I'm fairly confident that I'm an introvert. Still, sometimes I can behave like an extrovert. I was interested in the causes of this "extroversion activation", as I called it². I suspected that I really had two modes of functioning (with "introversion" being the default one), and some events — for example, mutual interest (when I am interested in a person I was talking to, and xe is interested in me) or feeling high-status — made me switch between them.

Or, you know, it could be just reduction in a social anxiety, which makes people more communicative. Increased anxiety levels wasn't a new element to be postulated; I already knew I had it, yet I was tempted to make up new mental entities, and prosaic explanation about anxiety managed to avoid me for a while.

2) I find it hard to do something I consider worthwhile while on a spring break, despite having lots of a free time. I tend to make grandiose plans — I should meet new people! I should be more involved in sports! I should start using Anki! I should learn Lojban! I should practice meditation! I should read these textbooks including doing most of exercises! — and then fail to do almost anything. Yet I manage to do some impressive stuff during academic term, despite having less time and more commitments.

This paradoxical situation calls for explanation.

The first hypothesis that came to my mind was about activation energy. It takes effort to go from "procrastinating" to "doing something"; speaking more generally, you can say that it takes effort to go from "lazy day" to "productive day". During the academic term, I am forced to make most of my days productive: I have to attend classes, do homework, etc. And, already having done something good, I can do something else as well. During spring break, I am deprived of that natural structure, and, hence I am on my own in terms of starting doing something I find worthwhile.

The alternative explanation: I was tired. Because, you know, vacation comes right after midterms, and I tend to go all out while preparing for midterms. I am exhausted, my energy and willpower are scarce, so it's no wonder I am having trouble utilizing it.

(I don't really believe in the latter explanation (I think that my situation is caused by several factors, including two outlined above), so it is also an example of descriptive "probable enough" hypothesis)

3) This example comes from Slate Star Codex. Nerds tend to find aversive many group bonding activities usual people supposedly enjoy, such as patriotism, prayer, team sports, and pep rallies. Supposedly, they should feel (with a tear-jerking passion of thousand exploding suns) the great unity with their fellow citizens, church-goers, teammates or pupils respectively, but instead they feel nothing.

Might it be that nerds are unable to enjoy these activities because something is broken inside their brains? One could be tempted to construct an elaborate argument involving autism spectrum and a mild case of schizoid personality disorder. In other words, this calls for postulating a rare form of autism which affects only some types of social behaviour (perception of group activities), leaving other types unchanged.

Or, you know, maybe nerds just don't like the group they are supposed to root for. Maybe nerds don't feel unity and relationship to The Great Whole because they don't feel like they truly belong here.

As Scott put it, "It’s not that we lack the ability to lose ourselves in an in-group, it’s that all the groups people expected us to lose ourselves in weren’t ones we could imagine as our in-group by any stretch of the imagination"³.

4) This example comes from this short comic titled "Sherlock Holmes in real life".

5) Scott Aaronson uses something similar to the Hanlon's Razor to explain that the lack of practical expertise of CS theorists aren't caused by arrogance or something like that:

"If theorists don’t have as much experience building robots as they should have, don’t know as much about large software projects as they should know, etc., then those are all defects to add to the long list of their other, unrelated defects. But it would be a mistake to assume that they failed to acquire this knowledge because of disdain for practical people, rather than for mundane reasons like busyness or laziness."

* * *

...and after this the word "prosaic" quickly turned into an awesome compliment. Like, "so, this hypothesis explains my behaviour well; but is it boring enough?", or "your claim is refreshingly dull; I like it!".

1. If you had read Thinking: Fast and Slow, you probably know what I mean. If you hadn't, you can look at narrative fallacy in order to get a general idea.

2. Which was, as I now realize, an excellent way to deceive myself via using word with a lot of hidden assumptions. Taboo your words, folks!

3. As a side note, my friend proposed an alternative explanation: the thing is, often nerds are defined as "sort of people who dislike pep rallies". So, naturally, we have "usual people" who like pep rallies and "nerds" who avoid them. And then "nerds dislike pep rallies" is tautology rather than something to be explained.

(followup to What Bayesianism has taught me? and Bayesianism for Humans, relevant to Boring Advice Repository )

Prosaic Priors

The second insight can be formulated as «the dull explanations are more likely to be correct because they tend to have high prior probability.»

Why is that?

In the other words, X is banal iff base rate of X is high. Or, you can say, prior probability of X is high.

This could work the other way around: sometimes the explanation feels unsatisfying exactly because it was shaved of any unnecessary and (ultimately) burdensome details.

* * *

Examples

This paradoxical situation calls for explanation.

4) This example comes from this short comic titled "Sherlock Holmes in real life".

5) Scott Aaronson uses something similar to the Hanlon's Razor to explain that the lack of practical expertise of CS theorists aren't caused by arrogance or something like that:

* * *

1. If you had read Thinking: Fast and Slow, you probably know what I mean. If you hadn't, you can look at narrative fallacy in order to get a general idea.

2. Which was, as I now realize, an excellent way to deceive myself via using word with a lot of hidden assumptions. Taboo your words, folks!

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Bayesianism for humans: prosaic priors

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