[extropy-chat] Bayes, crackpots and psi

[Eliezer Yudkowsky]

Damien Broderick wrote:
> At 07:39 PM 12/20/2004 -0500, Eliezer wrote:
> 
>> Why *isn't* it straightforward, given a couple of thousand Ss, to 
>> produce winning lottery numbers?
> 
> I believe it would be. But wait. How would you propose to get hold of a 
> couple of thousand *pre-screened, high-scoring* Ss? Some sort of glitzy 
> TV show trawl, maybe. (Ever tried to set one of those up?)

If you can get 30% right answers instead of 20% right answers on a 1-in-5 
problem, and you use an error-correcting code, you should be able to solve 
a 1-in-52 problem with 90% reliability using... um... damn, this should be 
simple.  Hold on a second.  Okay.  Each answer starts out with prior odds 
of 1:51.  We need posterior odds of 9:1.  It follows that we need a 
likelihood ratio that favors the correct answer over each of the incorrect 
answers by 459:1.  If we split up the lottery problem into many 1-in-5 
problems using a decent code, then each right sign has a 30% chance of 
yielding that correct answer, and each incorrect sign has a 17.5% chance of 
yielding that incorrect answer.  So each extra answer piled onto the 
correct sign, over and above that piled onto other signs, is worth .7 bits. 
  log2(459) = 8.84.  So we need an excess of 12 correct answers.  To get 
this, we must ask 96 questions.  I'm not sure I did the math correctly, but 
as Brett Pattsch points out, I'm not willing to spend that much time on it. 
  Anyway, unreliable hurried back-of-the-envelope calculations suggest that 
you ought to be able to select the right Mega Ball with 90% probability by 
asking 96 prescreened subjects, *or fewer* if you can ask them multiple 
questions.  In fact, you ought to be able to reliably double your money in 
the Mega Millions lottery by asking twelve prescreened psychics for eight 
predictions on a 1-in-5 problem.  For example, you might show them a matrix 
of eight boxes to be filled in with guesses, each set of signs visually 
different for each box, with the complete solution to be visually presented 
20 minutes later.

How much do you bet that if parapsychologists ran this experiment in some 
harmless, innocuous form that didn't involve predicting lottery numbers, 
why, they would report 30% correct answers instead of the expected 20%?

Yet if we concede that the technology works, you can reliably double your 
money on the Mega Millions lottery.  *Somehow*, I bet that the technique 
that worked so reliably in the laboratory will fail on this new problem.

If you really believe in this, you ought to be able to write a Java applet 
that would ask people to guess signs to be presented 20 minutes later, 
screen the guessers, and then ask for the final lottery-critical digit at 
the appropriate time.  You'd just need 96 post-screened subjects to guess 
one sign, or 12 screened subjects to guess 8 signs.  Of course I may have 
made a mistake in the math.

It's free money.  FREEEE MONEEEEY!

> I used to 
> have high hopes for the web, but plinking away from one link to the next 
> while babbling instant messages (as most people seem to do on-line) is 
> probably not the optimal environment for psi, or for writing great music 
> or great code. I tried to cut through all this by looking at millions of 
> votes actually cast by punters, moderately motivated; the very largest 
> deviations from chance were remarkably associated with winning numbers, 
> but by and large my expectation was falsified. If I'd been permitted to 
> have access to many more weekly draw results I'd have gone further, 
> using my first results as a probe, but the lottery owners came to their 
> senses and shut me down. Too bad, so sad. When someone well-placed and 
> with heaps of grant money finally does it, I might get a small footnote.

You actually tried to investigate this?

I concede ten bonus respect points.

*However*, I'm still not shifting my focus of attention to psi until you 
actually do win the lottery.

-- 
Eliezer S. Yudkowsky                          http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence