Tag Archives: Bayesian

Real Rationality

By Robin Hanson · January 20, 2010 12:15 am · Comments (31)

Bayesian probability is a great model of rationality that gets lots of important things right, but there are two ways in which its simple version, the one that comes most easily to mind, is extremely misleading.

One way is that it is too easy to assume that all our thoughts are conscious – in fact we are aware of only a tiny fraction of what goes on in our minds, perhaps only one part in a thousand. We have to deal with not only “running on error-prone hardware”, but worse, relying on purposely misleading inputs. Our subconscious often makes coordinated efforts to mislead us on particular topics.

But at least many folks are aware of and try to deal with this; for example, I’ve seen a lot of good related posts on this at Less Wrong lately. There is, however an even bigger way in which the simple Bayesian model is extremely misleading, and I’ve seen no discussion of it at Less Wrong. We may see one part in a thousand of our minds, but that fraction pales by comparison to the fact that we are each only one part in seven billion of living humanity.

Taking this fact seriously requires even bigger changes to how we think about rationality. OK, we don’t need to consider it for topics that only we can influence. But for most interesting important topics, it matters far more what the entire world does than what we personally do. For such topics, rationality consists mainly in the world having and using good systems (academia, news media, wikipedia, prediction markets, etc.) for generating and distributing reliable beliefs on which everyone can act.

When seven billion minds are involved, the overwhelming consideration must be managing a division of labor, so that we don’t each have to redo the same work. Together we must manage systems for deciding who should be heard on what. Given such systems, each of us will make our strongest contributions, by far, by fitting into these systems.

So to promote rationality on interesting important topics, your overwhelming consideration simply must be: on what topics will the world’s systems for deciding who to hear on what listen substantially to you?   Your efforts to ponder and make progress will be largely wasted if you focus on topics where none of the world’s “who to hear on what” systems rate you as someone worth hearing.  You must not only find something worth saying, but also something that will be heard.

Yes, existing who-to-hear systems are far from perfect, but that fact simply does not make it rational for you to work on topics where a better system would approve you, if only such systems existed. Wishes are not horses. It might make sense for you to work on reforming our systems, but even then your best efforts will work through channels where current systems can rate you as a person to hear on that meta topic.

When what matters is how the world acts, not how you act, rationality on your part consists mainly in improving the rationality of the world’s beliefs, as determined by its main systems for deciding who to believe about what.  Just wishing we had other systems, or acting as if we had them, is delusion, not rationality.

From a conversation with Steve Rayhawk.

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Why Neglect Big Topics

By Robin Hanson · November 16, 2009 3:05 pm · Comments (11)

From an ‘04 review of Robert Triver’s ‘02 book Natural Selection and Social Theory:

[Trivers'] directions on writing a classic paper …:

1. Pick an important topic.
2. Try to do a little sustained thinking on the topic, always keeping close to the task at hand.
3. Generalize outward from your chosen topic.
4. Write in the language of your discipline but, of course, try to do so simply and clearly.
5. If at all possible, reorganize existing evidence around your theory.

Those hoping this advice would get them on the fast lane to their own version of parent-offspring conflict theory or a new and groundbreaking take on reciprocal altruism may find themselves disappointed.  Most of these instructions fall into the category of easier said than done, but as Trivers also notes, “it still seems remarkable to me how often people bypass what are more important subjects to work on less important ones.”

Neglect of important subjects is remarkable if we assume academics mainly seek intellectual progress.  But it makes a lot more sense if we realize academics are not Bayesian:  Academics change their beliefs only when a sufficiently impressive work appears to earn that respect, even if that work provides little info.  And the more apparently important is the topic, the more impressive a work must be to change beliefs.

So a paper suggesting academics change their opinion on a very important subject will be held to a higher standard of impressiveness.  It must use more impressive math, data, analysis, or have a more prestigious author.  “Extraordinary claims require extraordinary evidence” is true, but not so much for evidential reasons.  Academics whose contributions might be informative but cannot rise to this higher impressiveness standard are well advised to stay away from important topics.

These academic blindsides in principle offer an opportunity for bloggers to contribute to intellectual progress via thoughtful posts that add info but are not impressive enough by academic standards, and via drawing reasonable conclusions from these and other unimpressive sources to which academics refuse to listen.  But if blogger customers will not actually pay much for such progress, it is not clear bloggers will bother.

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Contrarian Excuses

By Robin Hanson · November 15, 2009 7:45 pm · Comments (72)

On average, contrarian views are less accurate than standard views.  Honest contrarians should admit this, that neutral outsiders should assign most contrarian views a lower probability than standard views, though perhaps a high enough probability to warrant further investigation.  Honest contrarians who expect reasonable outsiders to give their contrarian view more than normal credence should point to strong outside indicators that correlate enough with contrarians tending more to be right.

Most contrarians, however, prefer less honest positions, like:

  1. “They Laughed At Galileo Too“  Many contrarians seem content merely to point out that contrarian views have sometimes turned out to be right.  Have they no higher aspirations?
  2. “Standard Experts Are Biased” Yes of course we can identify many biases that plausibly afflict standard experts.  But we can also see at least as many biases that plausibly afflict contrarians.  No fair assuming you are less biased just because you feel that way.
  3. “We’ve More Detail Than Critics” Some contrarians say that only explicitly offered detailed arguments and analysis should count; it shouldn’t matter who agrees or disagrees.  And since advocates usually offer more detail in support of their specific arguments than critics offer in response, they automatically win.  They may not have written up their arguments in a standard or accessible style, or published them in standard places, or even submitted them for publication.  But by their “how much stuff we’ve written/done” standard, they win.
  4. “Few Who Study Us Disagree” Some contrarians accept that who agrees or disagrees matters, but say only those who have reviewed most available detail should count.  Since critics have less patience than advocates for studying advocate detail, advocates win.  If many critics do read and reject them, advocates can just add more detail and then complain critics haven’t read that.  If critics do read more advocates can complain critics aren’t of the right sort, e.g., not enough math, sociology, or whatever.  There is usually some way to define “valid” critics so they are outnumbered by advocates.

If you want outsiders to believe you, then you don’t get to choose their rationality standard.  The question is what should rational outsiders believe, given the evidence available to them, and their limited attention.  Ask yourself carefully:  if most contrarians are wrong, why should they believe your cause is different?

(Inspired by this recent argument with Eliezer Yudkowsky.)

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Why Academics Aren’t Bayesian

By Robin Hanson · November 15, 2009 8:45 am · Comments (30)

Bryan Caplan asks Why Aren’t Academic Economists Bayesians?:

Almost all economic models assume that human beings are Bayesians, … [but] academic economists are not Bayesians.  And they’re proud of it!

This is clearest for theorists.  Their epistemology is simple: Either something has been (a) proven with certainty, or (b) no one knows – and no intellectually respectable person will say more.  If no one has proven that Comparative Advantage still holds with imperfect competition, transportation costs, and indivisibilities, only an ignoramus would jump the gun and recommend free trade in a world with these characteristics. …

Empirical economists’ deviation from Bayesianism is more subtle.  Their epistemology is rooted in classical statistics.  The respectable researcher comes to the data an agnostic, and leaves believing “whatever the data say.”  When there’s no data that meets their standards, they mimic the theorists’ snobby agnosticism.  If you mention “common sense,” they’ll scoff.

I’ve argued that the main social function of academia is to let students, patrons, readers, etc. affiliate with credentialed-as-impressive minds.  If so, academic beliefs are secondary – the important thing is to clearly show respect to those who make impressive displays like theorems or difficult data analysis. And the obvious way for academics to use their beliefs to show respect for impressive folks is to have academic beliefs track the most impressive recent academic work.

So it won’t do to have beliefs bounce around with every little common sense thing anyone says, however informative those may be.  That would give too much respect to not-very-impressive sources of common sense. Instead, beliefs must stay fixed until an impressive enough theorem or data analysis comes along where beliefs should change out of respect for it.  Academics also avoid keeping beliefs pretty much the same when each new study hardly adds much evidence – that wouldn’t offer enough respect to the new display.

Relative to the Bayesians that academic economic theorists typically assume populate the world, real academics over-react or under-react to evidence, as needed to show respect for impressive academic displays. This helps assure the customers of academia that by affiliating with the most respected academics, they are affiliating with very impressive minds.

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Simple Forecasts Best

By Robin Hanson · July 6, 2009 7:00 pm · Comments (20)

A fascinating tale, from the book Dance With Chance:

During the 1970s … It bugged the professor greatly that [business] practitioners were making these predictions without recourse to the latest, most theoretically sophisticated methods developed by statisticians like himself. Instead, they preferred simpler techniques which – they said – allowed them to explain their forecasts more easily to senior management. The outraged author … embarked on a research project that would demonstrate the superiority of the latest statistical techniques. …

The professor and his research assistant collected [111] sets of economic and business data over time from a wide range of economic and business sources. … Each series was split into two parts: earlier data and later data. The researchers pretended that the later part hadn’t happened yet and proceeded to fit various statistical techniques, both simple and statistically sophisticated, to the earlier data. Treating this earlier data as “the past,” they then used each of the techniques to predict “the future,” whereupon they sat back and started to compare their “predictions” with what had actually happened.  Horror of horrors, the practitioners’ simple, boss-pleasing techniques turned out to be more accurate than the statisticians’ clever, statistically sophisticated methods. … One of the simplest methods, known as “single exponential smoothing,” in fact appeared to be one of the most accurate. … Continue Reading "Simple Forecasts Best" »

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What Conjunction Fallacy?

By Robin Hanson · June 25, 2009 6:00 am · Comments (5)

Edi Karni:

This paper reports the results of a series of experiments designed to test whether and to what extent individuals succumb to the conjunction fallacy. Using an experimental design of Kahneman and Tversky (1983), it finds that given mild incentives, the proportion of individuals who violate the conjunction principle is significantly lower than that reported by Kahneman and Tversky. Moreover, when subjects are allowed to consult with other subjects, these proportions fall dramatically, particularly when the size of the group rises from two to three. These findings cast serious doubts about the importance and robustness of such violations for the understanding of real-life economic decisions.

Hat tip to Dan Houser.

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Rarity Anomalies Remain

By Robin Hanson · April 18, 2009 6:00 pm · Comments (3)

Our choices apparently under-weigh rare events when we experience track records, even though we accurately estimate the frequencies of those events.  We over-weigh rare events, however, when we are told their probabilities.  Simple explanations of these anomalies are shot down in a recent Psychological Science:

When making decisions involving risky outcomes on the basis of verbal descriptions of the outcomes and their associated probabilities, people behave as if they overweight small probabilities. In contrast, when the same outcomes are instead experienced in a series of samples, people behave as if they underweight small probabilities. We present two experiments showing that the existing explanations of the underweighting observed in decisions from experience are not sufficient to account for the effect. Underweighting was observed when participants experienced representative samples of events, so it cannot be attributed to undersampling of the small probabilities. In addition, earlier samples predicted decisions just as well as later samples did, so underweighting cannot be attributed to recency weighting. Finally, frequency judgments were accurate, so underweighting cannot be attributed to judgment error. Furthermore, we show that the underweighting of small probabilities is also reflected in the best-fitting parameter values obtained when prospect theory, the dominant model of risky choice, is applied to the data.
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Share likelihood ratios, not posterior beliefs

By Anna Salamon and Steve Rayhawk · February 5, 2009 6:19 pm · Comments (31)

When I think of Aumann's agreement theorem, my first reflex is to average.  You think A is 80% likely; my initial impression is that it's 60% likely.  After you and I talk, maybe we both should think 70%.  "Average your starting beliefs", or perhaps "do a weighted average, weighted by expertise" is a common heuristic.

But sometimes, not only is the best combination not the average, it's more extreme than either original belief.

Let's say Jane and James are trying to determine whether a particular coin is fair.  They both think there's an 80% chance the coin is fair.  They also know that if the coin is unfair, it is the sort that comes up heads 75% of the time.

Jane flips the coin five times, performs a perfect Bayesian update, and concludes there's a 65% chance the coin is unfair.  James flips the coin five times, performs a perfect Bayesian update, and concludes there's a 39% chance the coin is unfair.  The averaging heuristic would suggest that the correct answer is between 65% and 39%.  But a perfect Bayesian, hearing both Jane's and James's estimates – knowing their priors, and deducing what evidence they must have seen - would infer that the coin was 83% likely to be unfair.  [Math footnoted.]

Perhaps Jane and James are combining this information in the middle of a crowded tavern, with no pen and paper in sight.  Maybe they don't have time or memory enough to tell each other all the coins they observed.  So instead they just tell each other their posterior probabilities – a nice, short summary for a harried rationalist pair.  Perhaps this brevity is why we tend to average posterior beliefs.

However, there is an alternative.  Jane and James can trade likelihood ratios.  Like posterior beliefs, likelihood ratios are a condensed summary; and, unlike posterior beliefs, sharing likelihood ratios actually works.

Continue Reading "Share likelihood ratios, not posterior beliefs" »

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Different meanings of Bayesian statistics

By Andrew · January 27, 2009 8:00 pm · Comments (22)

I had a discussion with Christian Robert about the mystical feelings that seem to be sometimes inspired by Bayesian statistics.  The discussion originated with an article by Eliezer so it seemed appropriate to put the discussion here on Eliezer's blog.  As background, both Christian and I have done a lot of research on Bayesian methods and computation, and we've also written books on the topic, so in some ways we're perhaps too close to the topic to be the best judge of how a newcomer will think about Bayes.

Christian began by describing Eliezer's article about constructing Bayes’ theorem for simple binomial outcomes with two possible causes as "indeed funny and entertaining (at least at the beginning) but, as a mathematician, I [Christian] do not see how these many pages build more intuition than looking at the mere definition of a conditional probability and at the inversion that is the essence of Bayes’ theorem. The author agrees to some level about this . . . there is however a whole crowd on the blogs that seems to see more in Bayes’s theorem than a mere probability inversion . . . a focus that actually confuses—to some extent—the theorem [two-line proof, no problem, Bayes' theorem being indeed tautological] with the construction of prior probabilities or densities [a forever-debatable issue].

I replied that there are several different points of fascination about Bayes:

Continue Reading "Different meanings of Bayesian statistics" »

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Beliefs Require Reasons, or: Is the Pope Catholic? Should he be?

By Paul Gowder · November 26, 2008 11:00 am · Comments (26)

In the early days of this blog, I would pick fierce arguments with Robin about the no-disagreement hypothesis.  Lately, however, reflection on things like public reason have brought me toward agreement with Robin, or at least moderated my disagreement.  To see why, it’s perhaps useful to take a look at the newspapers…

the pope said the book “explained with great clarity” that “an interreligious dialogue in the strict sense of the word is not possible.” In theological terms, added the pope, “a true dialogue is not possible without putting one’s faith in parentheses.”

What are we to make of a statement like this?

Continue Reading "Beliefs Require Reasons, or: Is the Pope Catholic? Should he be?" »

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