Tag Archives: Bayesian

I read Douglas Hofstadter’s new book I am a Strange Loop, which argues that consciousness happens spontaneously after a system of dynamic patterns is sufficiently complex.  Strange loops of self-awareness  existing on multiple levels (as in Godel’s famous proof) create hallucinations of a hallucination, and so an "I" forms.  Anyway, as I often do when reading nonfiction, I read a little bit more about the author, and was struck by Hofstadter’s law: It always takes longer than you expect, even when you take into account Hofstadter’s law (note this is recursive and paradoxical, which is Hofstader’s specialty). This turns out to be pretty well known among programmers where everyone has read Hofstadter’s Godel, Escher, Bach.

As they say, Hofstadter’s Law is funny because it rings true to many programmers, who often work on complex projects that take years to complete.  Clearly an alternative to the Law of Iterated expectations.  Why might people involved in sufficiently complicated tasks–writing a paper, a book, building a deck–generally underestimate their length?  I think the main reason is that goals become self-fulfilling, so any lengthening of a goal time would add to the total time  the way bureaucracies spend the limit of their budget whatever it is.  Just like a group of people, people themselves have multiple goals; to watch tv, to get a project done, to be a better golfer.  A successful goal needs a  bias to compete with your other goals, who probably also have biased homunculus advocating for them in your mind. 

On one level an unbiased expectation is optimal because it allows us to allocate our resources more efficiently.  But there are many cases where this is not true, where a little too much hope and faith actually makes you a more successful person, and more fun to be around.  Just think about how annoying ‘brutally frank’ people are–they are jerks.  Think about the guy who thinks he is a better dancer than he really his confidence actually makes him a better dancer, because part of good dancing is not being self-conscious.  Robert Trivers has pointed out that self-deception is, in moderation, an evolutionary advantage, in that a liar who believes his own lies is a more effective persuader than a lie who knows he is lying, and fundamentally we are social animals trying to convince others to do this or think that.

In January I claimed:

An extraordinary claim is usually itself extraordinary evidence … I would be very unlikely to make such claims in situations where I did not have good reasons to think them true.  The times to be more skeptical of unlikely claims are when there is a larger than usual chance that someone would make such a claim even if it were not true. 

Eliezer responded, and then I outlined a formal model.  I now have a working paper.  In it, I consider the effect of people being organized into a reporting chain, such as up the levels of an organization, or from researcher to referee to editor to reporter to editor and so on.  The new interesting result:

When people are organized into a reporting chain, noise levels grow exponentially with chain length; long chains seem incapable of communicating extraordinary evidence.   

Continue reading "Reporting Chains Swallow Extraordinary Evidence" »

Last week I claimed that the saying "extraordinary claims require extraordinary evidence" is appropriate anytime people too easily make more extreme claims than their evidence can justify.  Eliezer, however, whom I respect, thought the saying appropriate anytime people make claims with a very low prior probability.  So I have worked out a concrete math model to explore our dispute.  I suggest that if you are math averse you stop reading this post now. 

Continue reading "A Model of Extraordinary Claims" »

There is a common saying used to dismiss surprising claims: "extraordinary claims require extraordinary evidence."  This idea is used to justify holding controversial claims to a higher standard of evidence than uncontroversial claims.   

Now the saying is obviously true in a simple Bayesian sense:  the lower your pre-evidence probability for a claim, the stronger your evidence must be (in likelihood ratio terms) to raise your post-evidence probability above any given threshold.  But this saying can be a misleading way to think about testimonial evidence. 

Consider that in ordinary conversation we commonly believe claims with very low pre-evidence probabilities.  Imagine that I were to tell you that my children had just died in a horrible freak accident involving a cell phone, a plane and a gas truck, or that I would meet you next Tuesday at 8:47am at 11 feet NW of the smaller statue in a certain square.  You would probably just believe me, as you usually believe things I tell you, even though you would have assigned a very low probability to those claims before you heard my statement.   

Are we gullible to believe such unlikely claims without asking for extra evidence?  No; the fact that I make such an extraordinary claim is usually itself extraordinary evidence (with a very high likelihood ratio); I would be very unlikely to make such claims in situations where I did not have good reasons to think them true. 

Continue reading "Extraordinary Claims ARE Extraordinary Evidence" »