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A Bayesian Aggregation Paradox

This seems related to philosophy of science stuff, where updating is about pitting hypotheses against each other. In order to do that you have to locate the leading alternative hypotheses. It doesn't work well to just pit a hypothesis against "everything else" (it's hard to say what p(E|not-H) is, and it can change as you collect more data). You need to find data that distinguishes your hypothesis from leading alternatives. An experiment that favors Newtonian mechanics over Aristotelian mechanics won't favor Newtonian mechanics over general relativity.

A Bayesian Aggregation Paradox

I think I've followed the basic argument here? Let me try a couple examples, first a toy problem and then a more realistic one.

Example 1: Dice. A person rolls some fair 20-sided dice and then tells you the highest number that appeared on any of the dice. They either rolled 1 die (and told you the number on it), or 5 dice (and told you the highest of the 5 numbers), or 6 dice (and told you the highest of the 6 numbers).

For some reason you care a lot about whether there were exactly 5 dice, so you could break this down into two hypotheses:

H1: They rolled 5 dice
H2: They rolled 1 or 6 dice

Let's say they roll and tell you that the highest number rolled was 20. This favors 5 dice over 1 die, and to a lesser degree it favors 6 dice over 5 dice. So if you started with equal (1/3) probabilities on the 3 possibilities, you'll update in favor of H1. Someone who also started with a 1/3 chance on H1, but who thought that 1 die was more likely than 6 dice, would update even more in favor of H1. And someone whose prior was that 6 dice was more likely than 1 die would update less in favor of H1, or even in the other direction if it was lopsided enough.

Relatedly, if you repeated this experiment many times and got lots of 20s, that would eventually become evidence against H1. If the 100th roll is 20, then that favors 6 dice over 5, and by that point the possibility of there being only 1 die is negligible (if the first 99 rolls were large enough) so it basically doesn't matter that the 20 also favors 5 dice over 1. This seems like another angle on the same phenomenon, since your posterior after 99 rolls is your prior for the 100th roll (and the evidence from the first 99 rolls has made it lopsided enough so that the 20 counts as evidence against H1).

Example 2: College choice. A high school freshman hopes & expects to attend Harvard for college in a few years. One observer thinks that's unlikely, because Harvard admissions is very selective even for very good students. Another observer thinks that's unlikely because the student is into STEM and will probably wind up going to a more technical university like MIT; they haven't thought much yet about choosing a college and Harvard is probably just serving as a default stand-in for a really good school.

The two observers might give the same p(Harvard), but for very different reasons. And because their models are so different, they could even update in opposite directions on the same new data. For instance, perhaps the student does really well on a math contest, and the first observer updates in favor of the student attending Harvard (that's an impressive accomplishment, maybe they will make it past the admissions filter) while the second observer updates a bit against the student attending Harvard (yep, they're a STEM person).

You could fit this into the "three outcomes" framing of this post, if you split "not attending Harvard" into "being rejected by Harvard" and "choosing not to attend Harvard".

Dan Luu on Persistent Bad Decision Making (but maybe it's noble?)

Additionally, many of the optimizations that lead to more wins make games more boring, which ultimately costs the entire league money.

This is true of some but not all optimizations. NFL teams punt too often on 4th down, and punting is boring; (in a large set of cases where teams have conventionally decided to punt) keeping your offense on the field to run a play increases your chances of winning and also makes the game more interesting for fans. (Teams have gradually been getting better at these decisions, over the years.)

Dan Luu on Persistent Bad Decision Making (but maybe it's noble?)

Another complication is that various people judge the coach (or team) based on process and not just on results, using their own views about which process is best. So there's a cost to making a decision that other people consider to be a bad decision, even if it maximizes your team's chances of winning.

If the fans think the coach made a bad decision, they might like the team a bit less, spend less money on the team, or want the coach to be fired.

If the players think the coach made a bad decision, they might be a bit less on board with the what the team is doing or less eager to sign a contract with the team.

If the owner/GM thinks that the coach made a bad decision, or that the fans or players don't support the coach as much, they might be a bit more likely to fire the coach.

So if we start in a situation where the fans, players, owner/GM, and coach all believe the conventional wisdom about what decisions are good ones, then the coach doesn't necessarily have much incentive to search for unconventional approaches which are widely seen as bad ideas but actually increase the team's chances of winning.

Paths Forward: Scaling the Sharing of Information and Solutions

Marine Exchange Facebook page has graphs of "container ships at anchor or loitering" for Los Angeles + Long Beach combined. It has been relatively flat in the 70s since mid-October, with an early November dip followed by a bounceback. The peak of 80 was on Oct 24, the current (Nov 8) is 77.

Port of Los Angeles has its own data (current pdf) with POLA Vessels at Anchor; it's the "historical container vessel activity" which you can get from this page by clicking on the picture that says "Working Container Vessels". It shows a peak of 40ish from Oct 19-29, which then dropped to 30ish, but is back up to 40 now (Nov 8).

Port of Long Beach has this page listing the container vessels at anchor there. It currently (Nov 9) lists 43 vessels. I can't find historical data except through internet archive; the most recent archived page shows 31 vessels as of Oct 8.

Paths Forward: Scaling the Sharing of Information and Solutions

Some people like Alex Tabarrok and Zeynep Tufekci were writing on covid in a similar style to Ryan Petersen. The US government did eventually wind up adopting some of their sensible recommendations, but it's hard to track causality since there were more people talking & longer delays before government action.

2020 PhilPapers Survey Results

53% of virtue ethicists one-box (out of those who picked a side).

Seems plausible that it's for kinda-FDT-like reasons, since virtue ethics is about 'be the kind of person who' and that's basically what matters when other agents are modeling you. It also fits with Eliezer's semi-joking(?) tweet "The rules say we must use consequentialism, but good people are deontologists, and virtue ethics is what actually works."

Whereas people who give the pragmatic response to external-world skepticism seem more likely to have "join the millionaires club" reasons for one-boxing.

2020 PhilPapers Survey Results

The survey results page also lists "Strongest correlations" with other questions. If I'm reading the tables correctly for the Newcomb's Problem results, there were 17 groups (in the target population who gave a particular answer to one of the other survey questions) in which one-boxing was at least as common as two-boxing. In order (of one-boxers minus two-boxers):

Political philosophy: communitarianism (84 vs 67)
Semantic content: radical contextualism (most or all) (49 vs 34)
Analysis of knowledge: justified true belief (49 vs 34)
Response to external-world skepticism: pragmatic (51 vs 37)
Normative ethics: virtue ethics (112 vs 100)
Philosopher: Quine (33 vs 22)
Arguments for theism: moral (22 vs 12)
Hume: skeptic (72 vs 63)
Aim of philosophy: wisdom (96 vs 88)
Philosophical knowledge: none (12 vs 5)
Philosopher: Marx (8 vs 2)
Aim of philosophy: goodness/justice (73 vs 69)
A priori knowledge: [no] (62 vs 58)
Consciousness: panpsychism (16 vs 13)
External world: skepticism (20 vs 18)
Eating animals and animal products: omnivorism (yes and yes) (168 vs 168)
Truth: epistemic (26 vs 26)

Petrov Day Retrospective: 2021

200 people (100 for each forum)

Minor mathematical correction: in this case, 100+100<200

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