Policy Beats Morality

This is a simple point, but one that gets overlooked, so I think it deserves a clear statement. Morality is less effective than incentives at changing behavior, and most of the time, policy is the way incentives get changed.

Telling people the right thing to do doesn’t work. Even if they believe you, or understand what you are saying, most people will not change their behavior simply because it’s the right thing to do. What works better is changing the incentives. If this is done right, people who won’t do the right thing on their own often support the change, and their behavior will follow.

I remember reading a story that I think was about Martin Gardner’s column in Scientific American in which he asked eminent scientists to write in whether they would cooperate with someone described as being “as intelligent as themselves” in a one-shot prisoner’s dilemma. He was disappointed to find that even many of the smartest people in the world were rational, instead of superrational. Despite his assertion that intelligent enough people should agree that superrationality leads to better outcomes for everyone, those people followed their incentives, and everyone defected. Perhaps we can chalk this up to their lack of awareness of newer variants of decision theory, but the simpler explanation is that morality is a weak tool, and people know it. The beneficial nature of the “morality” of non-defection wasn’t enough to convince participants that anyone would go along.

Environmentalists spent decades attempting “moral suasion” as a way to get people to recycle. It didn’t work. What worked was curb-side pickup of recycling that made money for municipalities, paired with fines for putting recyclables in the regular garbage. Unsurprisingly, incentives matter. This is well understood, but often ignored. When people are told the way to curb pollution is to eat less meat or drive less, they don’t listen. The reason their behavior doesn’t change isn’t because it’s “really” the fault of companies, it’s because morality doesn’t change behavior much — but policy will.

The reason politics is even related to policy is because politicians like being able to actually change public behavior. The effectiveness of policy in changing behavior is the secondary reason why — after donations by Intuit and H&R Block — congress will never simplify the tax code. To paraphrase / disagree with Scott Alexander, “Society Is Fixed, Policy Is Mutable.” Public policy can change the incentives in a way that makes otherwise impossible improvements turn into defaults. Punishment mechanisms are (at least sometimes) sufficient to induce cooperation among free-riders.

Policy doesn’t change culture directly, but it certainly changes behaviors and outcomes. So I’ll say it again: policy beats morality.

*) Yes, technological change and innovation can ALSO drive changes in incentives, but predicting the direction of such changes is really hard. This is why I’m skeptical that innovation alone is a good target for changing systems. Even when technology lowers the cost of recycling, it’s rarely clear beforehand whether new technology will in fact manage to prompt such changes — electric trolleys were a better technology than early cars, but they lost. Electric cars are still rare. Nuclear power is the lowest carbon alternative, but it’s been regulated into inefficiency.

My 2018 Predictions

(Initial Version from Jan 1 — Scott finally posted his predictions on Feb 6, so here I am again on Feb 6th with updates, see lower.)

A hazy future means high uncertainty gets quantified!

Just to clarify what I’m doing here, I’m using my best guesses and knowledge to make predictions about a set of future events. This follows the urgings of Eliezer Yudkowsky, and the example of Scott over at SSC, who does this yearly — and it follows in the footsteps of my participation in the Good Judgement Project.

I’m picking these because they seem to be important things potentially happening in the coming year, not because I have specific domain knowledge. I’m happy to find and hear from people who are more accurate and have better judgement than myself, and can prove it with a public track record — and I know several — because I can learn from them. So If you don’t think I have any basis for these predictions, you may be right, but I am a #superforecaster with a track record. And I challenge those with more knowledge, or claims that they could make guesses as well as I can, to try it and see.

All that said, I’m starting with the things I don’t think Scott over at SSC will predict, then I’ll log my predictions on his list once it’s out. That prevents me from cherry picking easy things to predict, or focusing on ones I have more than normal insight into.

US Politics

Interestingly, these are all gonna be correlated in a way the scoring won’t account for. Still, for predictions, it’s put up or shut up.
(I’m waiting for Scott to list what 2018 Election categories he’s predicting. For now;)

Democrats take the senate: 45%
(The seats up for grabs are largely Democrat controlled — hard to make inroads.)

The Republicans will maintain control of the House of Representatives in 2018 elections: 45% 
(Last year I said 40% — this is what the prediction markets now say, but I’m updating. I’m skeptical that Trump’s unpopularity convinces the heartland to vote dem, or stay home. But this is a low confidence prediction, made early.)

Republicans win House of Representatives special election in Pennsylvania’s 18th district: 60%

Trump’s approval rating, based on the RCP average, will be over 40% / 45% at some point in 2018: 60% / 25%

Previous-year long-term predictions:

There will be a Republican primary challenger getting >10% of the primary vote in 2020 (conditional on Trump running) — 70%

The stock market will go down under President Trump (Conditional on him having a 4 year term, Inauguration-Inauguration) — 60%

New long-term predictions:

The retrospective consensus of economists about the 2017 tax bill will be;
…didn’t increase GDP growth more than 0.2%: 95%

…that, after accounting for growth, it increased the 10-year deficit
more than $1tr / $1.2tr / $1.5tr, respectively: 90% / 70% / 40%

The House will vote to impeach Trump before the end of his current term: 65% (50% vote needed)

Conditional on impeachment, the senate will convict: 20% (67% vote needed)


I SUCK AT THIS, as the past two years should make clear. (And if you think you can do better, why aren’t you rich? (Alfred, you don’t need to respond, I know.)) But I still think there’s a real chance that the bubbles pop — and even if they don’t, I expect the pace of growth to slow once the regular capital markets have put in their money.

Bitcoin Crashes — “loses more than 50% of peak value”;

Off-the cuff probability distribution: 10% — BTC investment (not use) spreads until much of public holds at these high prices before crashing 
60% — not very soon, but w/in 2–3 years 
15% — Crash During 2018 
15% — (Mid-December 2017) was the top.

I’m on the record already;
Conditional on the crash occurring? 1 year later, I’d predict bitcoin is smaller than at least 2 alternatives, and less than 25% of total cryptocoin market cap, with 80% confidence. (1 altcoin, 33%, 90% conf.)

Global Catastrophic Risks

AI Progress indicators –

AI wins a Real Time Strategy game (RTS — Starcraft, etc.) in full-mode against the best human players before end of;
Within Byun Hyun Woo’s Lifetime: 98% (He claims it won’t, here. Only this low because he might die in the next couple years.)

Scott’s Prediction Topics (His Numbers)

1. Donald Trump remains president at end of year: 98% (95%)
2. Democrats take control of the House in midterms: 55% (80%)
3. Democrats take control of the Senate in midterms: 45% (50%)
4. Mueller’s investigation gets cancelled (eg Trump fires him): 20% (50%) [I assume almost immediately being relaunched by appointing him an independent counsel or equivalent after firing doesn’t count. If it does, I probably agree with Scott.]
5. Mueller does not indict Trump: 80% (70%) [I can’t see him indicting Trump. I think there will be a report with arguably indictable offenses, but even so it very well may come out in 2019.]
6. PredictIt shows Bernie Sanders having highest chance to be Dem nominee at end of year: 60% (60%) [Biden and Warren are more viable choices, and Bernie is really old. But this is predicting the prediction, so I’m less certain about this than I am that he won’t be the nominee.]
7. PredictIt shows Donald Trump having highest chance to be GOP nominee at end of year: 95% (95%)
9. Some sort of major immigration reform legislation gets passed: 80% (70%)
10. No major health-care reform legislation gets passed: 90% (95%)
11. No large-scale deportation of Dreamers: 95% (90%)
12. US government shuts down again sometime in 2018: 60% (50%)
13. Trump’s approval rating lower than 50% at end of year: 95% (90%)
14. …lower than 40%: 60% (50%)
15. GLAAD poll suggesting that LGBQ acceptance is down will mostly not be borne out by further research: 70% (80%) [This is WAY outside my wheelhouse, here.]

16. Dow does not fall more than 10% from max at any point in 2018: 45% (50%)
17. Bitcoin is higher than $5,000 at end of year: 90% (95%)
18. Bitcoin is higher than $10,000 at end of year: 70% (80%)
19. Bitcoin is lower than $20,000 at end of year: 80% (70%)
20. Ethereum is lower than Bitcoin at end of year: 50% (95%)
21. Luna has a functioning product by end of year: N/A (90%) [I don’t know what this is.]
22. Falcon Heavy first launch not successful: N/A — Just saw this. (70%)
23. Falcon Heavy eventually launched successfully in 2018: N/A — Just saw this. (80%) 
24. SpaceX does not attempt its lunar tourism mission by end of year: 95% (95%) [??]
25. Sci-Hub is still relatively easily accessible from within US at end of year (even typing in IP directly is relatively easy): 95% (95%) [??]
26. Nothing particularly bad (beyond the level of an funny/weird news story) happens because of ability to edit videos this year: 80% (90%) [But I’m putting a major fake news controversy as bad. Unsure Scott agrees.]
27. A member of the general public can ride-share a self-driving car without a human backup driver in at least one US city by the end of the year: 60% (80%)

28. Reddit does not ban r/the_donald by the end of the year: 90% (90%)
29. None of his enemies manage to find a good way to shut up/discredit Jordan Peterson: 70% (70%) [??]

{I don’t follow these.}

PERSONAL (Not Scott’s, but adapted):
47. I move by end of July: 95%
50. I go to Oxford as a visiting researcher: 65%
51. I do a postdoc at Oxford: 30%
53. I get at least one article published in a newspaper or decently large website (not Ribbonfarm or Kol Habirah): 20%
55. I weigh more than 160lb at year end: 50%
63. My paper with Scott G. goes on Arxiv/published: 90%
64. My paper with Abram/Osonde goes on Arxiv/published: 50%

Evidence as Rhetoric — Normative or Positive?

I recently saw an interesting and disturbing paper, “Reframing Evidence Synthesis As Rhetorical Action in the Policy Making Drama.” To vastly simplify and rephrase, they note that rational updating based on evidence is corrupted by policymakers presentation of filtered evidence. Because of this, policy discussion based on evidence is rhetoric, not logic — and it should be viewed in those terms. You might guess from the title that I agree this is a correct description of policy making, but an incorrect and damaging way to make policy.

I want to lay that argument out more fully, including a discussion of bounded rationality, the norms of policymaking, signalling via advocacy of evidence, and the ways in which this problematic norm should be fixed — but for now I think my point is clear.

A Short Explanation of Blame and Causation

The patient, Bob, died due to severe internal bleeding, loss of consciousness following a blunt force trauma. Bob died because he was hit by a car when he ran over the bridge from behind a wall into the cross-street. John was guilty of negligent homicide because he was drunk when he hit Bob while driving. John ran over Bob because when Bob ran into the street, he couldn’t hit the brakes in time.

Multiple Choice Questions:

  1. Why did Bob die?
    A) The laws of physics
    B) John’s wife left him and he’s been depressed
    C) Policy makers have failed to expedite to adoption of self-driving cars
    D) It was karma for ignoring a drowning child in the river
  2. Why did the writer propose different explanations for Bob’s death?
    A) To illustrate the meaningless of causation in a complex world
    B) He wasn’t sure which was correct
    C) He was being paid by the word
    D) Meaning is tied to purely subjective interpretation, so any one explanation can be correct for the reader

So how do explanations compete for the title of “cause” in informal discussion? It should be clear that “cause” is a meaningful term; we can define it rigorously, but its meaning depends on context. Medically, the first sentence is sufficient; “almost all transportation fatalities… result from blunt force trauma.” This is a form of disguised query, and once we know the goal of the discussion, whether legal, moral, or religious, we can attribute cause. The cause is unclear only because informal discussion and made-up context-less quotations don’t have clear definitions of goals or model levels.

But dependence on goals or model levels needn’t make causes unclear; context and thought can reveal that the author wished to illustrate the reasonableness of varying explanations. If the question is legal, the correct model is different than if the question is religious, or medical.

Blame is not a useful concept in most discussions. Instead, the question is what causal mechanism is relevant for imposing the desired state of the world. If you can get regulators to approve model cars, answer C is relevant, and if you can change human biology, answer A becomes critical instead.

What question we are trying to answer itself the disguised query in many discussions; we incorrectly assume the meaning of cause in a given situation is a single similarity cluster. Instead, the meaning of cause is a set of different causal models depending on the purpose of discussion. In John’s trial, all four of the answers to the first question are irrelevant to the jury’s deliberations of guilt. In rehabilitating John, his depression and his feelings about Bob and the drowning child may be critical. In each case, there is a concrete decision to be made. In one case, the implications of physics on medicine is irrelevant, legal culpability is critical. In the other, technological policy is irrelevant, but self-imposed moral blame is critical.

And hopefully that explanation dissolves the earlier questions.

A Quick Confidence Heuristic

Let’s say you have well-informed opinions on a variety of topics. Without information about your long term accuracy in each given area, how confident should you be in those opinions?

Here’s a quick heuristic, for any area where other people have well-informed opinions about the same topics; your confidence should be a function of the distance of your estimate from the average opinion, and the standard deviation of those opinions. I’ll call this the wisdom-of-crowds-confidence level, because it can be justified based on the empirical observation that the average of even uninformed guesses is typically a better predictor than most individual predictions.

Why does this make sense?

The Aumann agreement theorem implies that rational discussants can, given enough patience and introspection, pass messages about their justifications until they eventually converge. Given that informed opinions share most evidence, the differential between the opinions is likely due to specific unshared assumptions or evidence. If that evidence were shared, unless the vast majority of the non-shared assumptions were piled up on the same side, the answer would land somewhere near the middle. (This is why I was going to call the heuristic Aumann-confidence, but I don’t think it quite fits.)

Unless you have a strong reason to assume you are a privileged observer, trading on inside information or much better calibrated than other observers, there is no reason to expect this nonshared evidence will be biased. And while this appears to contradict the conservation of expected evidence theorem, it’s actually kind-of a consequence of it, because we need to update on the knowledge that there is unshared evidence leading the other person to make their own claim.

This is where things get tricky — we need to make assumptions about joint distributions on unshared evidence. Suffice it to say that unless we have reason to believe our unshared evidence or assumptions is much stronger than theirs, we should end up near the middle. And that goes back to a different, earlier assumption – that others are also well informed.

Now that we’ve laid out the framework, though, we can sketch the argument.

  1. We can expect that our opinion should shift towards the average, once we know what the average is, even without exploring the other people’s unshared assumptions and data. The distance it should shift depends on how good our assumptions and data are compared to theirs.
  2. Even if we have strong reasons for thinking that we understand why others hold the assumptions they do, they presumably feel the same way about us.
  3. And why do you think your unshared evidence and assumptions are so great anyways, huh? Are you special or something?

Anyways, those are my thoughts.


(Originally posted here on LessWrong)

A cruciverbalist’s introduction to Bayesian reasoning

Mathematical methods inspired by an eighteenth century minister (8)

“Bayesian” is a word that has gained a lot of attention recently, though my experience tells me most people aren’t exactly sure what it means. I’m fairly confident that there are many more crossword-puzzle enthusiasts than Bayesian statisticians — but I would also note that the overlap is larger than most would imagine. In fact, anyone who has ever worked on a crossword puzzle has employed Bayesian reasoning. They just aren’t (yet)aware of it. So I’m going to explain both how intuitive Bayesian thinking is, and why it’s useful, even outside of crosswords and statistics.

But first, who was Bayes, what is his “law” about, and what does that mean?

Sound of a Conditional Reverend’s Dog (5)

“Bayes” of statistical fame, is the Reverend Thomas Bayes. He was a theologian and mathematician, and the two works he published during his lifetime dealt with the theological problem of happiness, and a defense of Newton’s calculus — neither of which concern us. His single posthumous work, however, was what made him a famous statistician. The original title, “ A Method of Calculating the Exact Probability of All Conclusions founded on Induction,” clearly indicates that it’s meant to be a very inclusive, widely applicable theorem. It was also, supposedly, a response to a theological challenge posed by Hume — claiming miracles didn’t happen.

Wonders at distance travelled without vehicle upset (8)

“Miracles”, Hume’s probabilistic argument said, are improbable, but incorrect reports are likely— so, the argument goes, it is more likely that the reports are incorrect than that the miracle occurred. This way of comparing probabilities isn’t quite right, statistically, as we will suggest later. But Bayes didn’t address this directly at all.

Taking a risk bringing showy jewelry to school (8)

“Gambling” was a hot topic in 19th century mathematics, and Bayes tried to answer an interesting question; when you see something happen several times, how do can you figure out, in general, the probability of it occurring? His example was about throwing balls onto a table — you aren’t looking, and a friend throws the first ball. After this, he throws more, each time, telling you whether the ball landed to the left or right of the first ball. After a doing this a few times, you still have’t seen the table, but want to know how likely is it that the next ball land to the left of that original ball.

To answer this, he pointed out that you get a bit more information about the answer every time a ball is thrown. After the first ball, for all you know the odds are 50/50 that the next one will be on either side. after a few balls are thrown, you get a better and better sense of what the answer is. After you hear the next five balls all land to the left, you’ve become convince that the next ball landing to the left is more likely than landing to the right. That’s because the probabilities are not independent — each answer gives you a little bit more information about the odds.

But enough math — I’m ready to look at a crossword.

Could wine be drunk by new arrival? (6)

“Newbie” is how I’d prefer to put my ability with crossword puzzles. But as soon as I started, I noticed a clear connection. The method of reasoning I practice and endorse as a decision theorist are nearly identical to the methods that are used by people in this everyday amusement. So I’ll get started on filling in (only one part of) the crossword I did yesterday, and we’ll see how my Bayesian reasoning works. I start by filling in a few easy answers, and I’m pretty confident in all of these. 6 Down — Taxing mo. for many, 31 Across — Data unit, 44 Across — “Scream” actress Campbell.

The way I’ve filled these in so far is simple — I picked answers I thought were very likely to be correct. But how can I know that they are correct? Maybe I’m fooling myself. The answer is that I’ve done a couple crosswords before, and I’ve found that I’m usually right when I’m confident, and these answers seem really obvious. But can I apply probabilistic reasoning here?

Distance into which vehicle reverses ___ that’s a wonder (7)

“Miracles,” or anything else, according to Reverend Bayes, should follow the same law as thrown balls. If someone is confident, that is evidence, of a sort. Stephen Stigler, a historian of math, argues that Bayes was implying an important caveat to Hume’s claim — the probability of hearing about a miracle increases each time you hear another report of it. That is, thee two facts are, in a technical sense, not independent — and the more independent accounts you hear, the more convinced you should be.

But that certainly doesn’t mean that every time a bunch of people claim something outlandish, it’s true. And in modern Bayesian terms, this is where your prior belief matters. If someone you don’t know well at work tells you that they golfed seven under par on Sunday, you have every reason to be skeptical. If they tell you they golfed seven over par, you’re a bit less likely to be skeptical. How skeptical, in each case?

We can roughly assess your degree of belief— if a friend of yours attested to the second story, you’d likely be convinced, but it would take several people independently verifying the story for you to have a similar level of belief in the first. That’s because you’re more skeptical in the first place. We could try to quantify this, and introduce Bayes’ law formally, but there’s no need to bring algebra into this essay. Instead, I want to think a bit more informally — because I can assess something as more or less likely without knowing the answer, without doing any math, and without assigning it a number.

When you hear something outlandish, your prior belief is that it is unlikely. Evidence, however, can shift that belief — and enough evidence, even circumstantial or tentative, might convince you that the claim is plausible, probably, or even very likely. And in a way it doesn’t matter what your prior is, if you can accumulate enough different pieces of trustworthy evidence. And that leads us to how I can use the answers I filled in as evidence to help me make further plausible guesses.

I look at some of the clues I didn’t immediately figure out. I wasn’t sure what 6 Across — Completely blows away, would be; there are lots of 4-letter words that might fit the clue. Once I get the A, however, I’m fairly confident in my guess, conditional on this (fairly certain) new information. I look at 31 Down — Military Commission (6), but I can’t think of any that start with a B. I see 54 Across — Place for a race horse, and I’m unsure — there are a few words that fit — it could be “first”, “third”, “fifth,” “sixth” or “ninth”, and I have no reason to think any more likely than another. So I look for more information, and notice 54 Down — It might grow to be a mushroom (5, offscreen). “Spore” seems likely, and I can see that this means “Sixth” works — so I fill in both.

At this point, I can start filling in a lot more of the puzzle, and the pieces are falling in to place — each word I figure out that fits is a bit more evidence that the others are correct, making me confident, but there are a few areas where I seem stuck.

Being stuck is evidence of a different sort — it probably means at least one of two things — either I have something incorrect, or I’m really bad at figuring out crosswords. Or, of course, both.

At this point I start revisiting some of my earlier answers, ones I was pretty confident about until I got stuck. I’m still pretty confident in 39 Down — Was at one time, but ___ now. “Isn’t” is too obvious of an answer to be wrong, I think. On the other hand, 38 Down — A miscellany or collection, has me stumped, but two Is in a row also seem strange. 37 Down — Small, fruity candy, is also frustrating me; I’m not such an expert in candy, but I’m also not coming up with anything plausible. So I look at 50 Across — A tiny part of this?, again, and re-affirm that “Bit” seems like it’s a good fit. I’m now looking for something that can give me more information, so I rack my brains, and 36 Across — Ho Chi Min’s capital, comes to me: Hanoi. I’m happy that 39 Down is confirmed, but getting nervous about the rest.

I decided to wait, and look elsewhere, filling in a bit more where I could. My progress elsewhere is starting to help me out.

Now, I need to re-evaluate some earlier decisions and update my beliefs again. It has become a bit more complex than evaluating single answers — I need to consider the joint probability of several different things at once. I’ll unpack how this relates to Bayesian reasoning afterwards, but first, I think I made a mistake.

I was marginally confident in 50 Across — A tiny part of this? as “bit”, but now I have new evidence. I’m pretty sure Nerb isn’t a type of candy, but “Nerd” seems to fit. I’m not sure if they are fruity, so I’m not confident, and I’m still completely at a loss on 38 Down — A miscellany or collection. That means I need to come up with an alternative for 50 Across; “Dot” seems like an unlikely option, but it fits really well. And then it occurs to me; A dot is a little bit of the question mark. That’s an annoying answer, but it seems a lot more likely than that “Nerb” is a type of candy. And I’m not sure what Olio is, but there’s really nothing else that I can imagine fitting. And there are plenty of words I don’t know. (As I found out later, this is one of them.)

At first, I had a high confidence that “Bit” was the best answer for 50 Across — I had a fairly strong prior belief, but I wasn’t certain. As evidence mounted, I started to re-assess. Weak evidence, like the strange two Is in a row, made me start to question the assumption that I was right. More weak evidence — remembering that there is a candy of some sort called Nerds, and realizing that “Dot” was a potential answer, made me revise my opinion. I wasn’t strongly convinced that I had everything right, but I revised my belief. And that’s exactly the way a Bayesian approach should work; you’re trying to figure out which possibility is worth betting on.

That’s because all of probability theory started with a simple question that a certain gambler asked Blaise Pascal; how to we split the pot when a game gets interrupted. And historians who don’t think Bayes was trying to formulate a theological rebuttal to Hume suggest that he’s really responding to a question posed by de Moivre — from whose book he may have learned probability theory, which we need to mention in order to figure out why I’d pick “Dot” over “Bit” — even though I think it’s a stupid answer. But before I get there, I’ve made a bit more progress — I’m finished, except for one little thing.

31 Down — Military Commission. That’s definitely a problem — I’m absolutely sure Brevei isn’t the right answer, and 49 Down, offscreen, is giving me trouble too. The problem is, I listed all the possible answers for 54 Across — Place for a race horse, and the only one that started with an “S” was sixth.

Conviction … or what’s almost required for a conviction (9)

“Certainty” can be dangerous, because if something is certain, almost by definition, it means nothing can convince me otherwise. It’s easy to be overconfident, but as a Bayesian, it’s dangerous to be so confident that I don’t consider other possibilities — because I can’t update my beliefs! That’s why Bayesians, in general, are skeptical of certainty. If I’m certain that my kid is smart and doing well in school, no number of bad grades or notes from the teacher can convince me to get them a tutor. In the same way, if I’m certain that I know how to get where I’m going, no amount of confused turns, circling, or patient wifely requests will convince me to ask for directions. And if I’m certain that “Place for a race horse” is limited to a numeric answer, no number of meaningless words like “Brevei” can change my mind.

High payout wagers (9)

“Perfectas” are bets placed on a horse race, predicting the winner and second place finisher, together. If you get them right, they payoff can be really significant — much more than bets on horses to win or to place. In fact, there are lots of weird betting terms in horse racing, and by excluding them from consideration, I may have been hasty in filling out “sixth.” My assumption of having compiled and exhaustive list of terms was premature. Instead, I need to reconsider once again — and that brings us to why, in a probabilistic sense, crosswords are hard.

Disreputable place for a smoke? (5)

“Joint” probabilities are those that relate to multiple variables. And when solving the crossword, I’m not just looking to answer each clue, I’m looking to fill in the puzzle — it needs to solve all of the clues together. Just like figuring out a Perfecta is harder than picking the right horse; putting multiple uncertain questions together is where joint probabilities show up. But it’s not hopeless; as you figure out more of the puzzle, you reduce the remaining uncertainty. It’s like getting to place a Perfecta bet after seeing 90% of the race; you have some pretty good ideas about what can and can’t happen.

Similarly, Bayesians, in general, collect evidence to constrain what they think is and isn’t probable. Once enough balls have been thrown to the left of that first one, you get pretty sure the odds aren’t 50–50. The prerequisite for getting the right answer, however, is being willing to reconsider your beliefs — because reality doesn’t care what you believe.

And the reality is that 31 Down is Brevet, so I need an answer to 54 Across — Place for a race horse that starts “St”. And that’s when it hit me — sometimes, I need to simply be less certain I know what’s going on. The race horse isn’t running, and there are no bets. It’s in a stall, waiting patiently for me to realize I was confused.

A Final Note

I’d note three key lessons that Bayesians can learn from crosswords, since I’ve already spent pages explaining how Crossworders already understand Bayesian thinking. And they are lessons for life, ones that I’d hope crossword enthusiasts can apply more generally as well.

  1. The process of explicitly thinking about what you are uncertain of, and noticing when something is off, or you are confused, is useful to apply even (especially!) when you’re not doing crossword puzzles.
  2. Evaluating how sure you are, and wondering if you are overconfident in your model or assumptions, would have come in handy to those predicting the 2016 election.
  3. Being willing to actually change your mind when presented with evidence is hard, but I hope you’d rather have a messy crossword than an incorrectly solved one.

A Postscript for Pedants

Scrupulously within the rules, but not totally restrictive

“Strict” Bayesians are probably annoyed about some of this — at no point in the process did I get any new evidence. No one told me about any new balls thrown, I only revised my belief based on thinking. A “Real Bayesian” starts with all the evidence already available, and only updates when new evidence comes in. For a non-technical response, it’s sufficient to note that computation and thought takes time, and although the brain roughly approximates Bayesian reasoning, the process of updating is iterative. And for a technical version of the same argument, I’ll let someone else explain that there are no real Bayesians. (And thanks to Noah Smith for that link!)

The crossword clues were a combination of info from http://www.wordplays.com/crossword-clues/, and my own inventions.
The crossword is an excerpt from Washington Post Express’s Daily Crossword for January 11th, 2017, available in full on Page 20, here: https://issuu.com/expressnightout/docs/express_01112017