Comments on: Words Vs. Bets

By: Douglas Knight

Douglas Knight — Sun, 20 Sep 2009 04:50:20 +0000

Ian Maxwell, I would be happy to bet my $100 against your $10k that PvNP is shown to be undecidable by Peano arithmetic within the next 20 years. If you cap your losses at $100, it doesn’t look to me worth the transaction costs to collect 20 years in the future, so I won’t put up my $1. Similarly, I don’t think my first offer gives you any upside.

By: Phil Goetz

Phil Goetz — Sat, 19 Sep 2009 19:17:11 +0000

Thanks – great story!

I’ll take your bet at, hmm, 20 to 1. Up for it?
Anyone else want to post the odds they’d take the bet at?

By: andrew c

andrew c — Fri, 18 Sep 2009 10:34:58 +0000

Bollocks. I just flipped a coin. It either came up heads or tails. Are you really going to assign a probability of 1 or 0 to either outcome? How does your dutch book work out if the proposition turns out to be true? Can you dutch book someone who assigns 1:1 odds to heads?

By: Ian Maxwell

Ian Maxwell — Thu, 17 Sep 2009 05:51:50 +0000

Immediate revision to my last comment: In retrospect, I am prone to huge overestimates at the far end of my probability scale, so I should probably revise waaaay down to about 10:1 for P != NP and 100:1 for undecidablity.

By: Ian Maxwell

Ian Maxwell — Thu, 17 Sep 2009 05:47:43 +0000

Interesting. I find it really strange that Ken Steiglitz wouldn’t accept any odds steeper than 2:1. I know very little of P vs. NP beyond the question itself (which I do actually understand technically), and so you would think I would be less sure than this fellow of the answer—yet, thinking about it, the point at which I actually feel indifferent about betting is something like 25:1. By contrast, I find it much less likely that P vs. NP is ever proven independent of current axioms—I might take something like 500:1 on that. (I have good reason to think that such a proof is impossible, but I’m still only an amateur mathematician and I may have missed some subtlety.)

If anyone wants to offer me a small-stakes wager based on this, please do. I would be quite willing to bet twenty against one that P != NP, or one against thirty that P = NP, as long as I don’t stand to lose more than $100 or so.

By: Math World | Overcoming Bias : Words Vs. Bets

Math World | Overcoming Bias : Words Vs. Bets — Wed, 16 Sep 2009 23:54:58 +0000

[...] Go here to see the original: Overcoming Bias : Words Vs. Bets [...]

By: Greg Lee

Greg Lee — Tue, 15 Sep 2009 00:26:06 +0000

“Does anyone doubt that two to one better summarizes his evidence than a million to one?”

RH: would you also argue that 35:1 on 00 on a U.S. roulette wheel better summarizes the evidence than 37:1? After all, millions of dollars are bet at 35:1.

By: Daniel B

Daniel B — Mon, 14 Sep 2009 11:11:29 +0000

You should have tried it with 1c vs $10K or even 1c vs $100. An amount like $1M is likely to spook most people because of the non-linear utility value of being completely broke.

But 2:1 says something. It’s funny how people’s ‘intuition’ (or left brain) shifts in to gear when confronted with a situation with actual consequences. For this reason I like the expression ‘Your mouth is writing checks that your ass can’t cash’.

By: Panos Ipeirotis

Panos Ipeirotis — Mon, 14 Sep 2009 01:57:09 +0000

I think that Neel’s comment is both tongue-in-cheek and serious at the same time.

Neel simply points out that the idea of a “rational” agent does not hold. A rational agent (in other words, an agent of infinite computational power) should be able to know whether P=NP, P!=NP, or whether the problem is undecidable. We do not expect time to resolve this question as there is not a random component in this question.

So, a prediction market on this question assumes that the participants are not “rational”, but rather operate under a “bounded rationality” (Rational ==calculating everything to the maximum degree possible.)

By: g

Mon, 14 Sep 2009 01:05:45 +0000

Oops: I see that in fact replies two levels deep (but not more) are allowed, at which point I no longer find it plausible that it was easier to allow that than to allow arbitrary depths.