Open Thread, August 2010-- part 2

NancyLebovitz

This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.

I just read and liked "Pascal's mugging." It was written a few years ago, and the wiki is pretty spare. What's the state of the art on this problem?

While raking, I think I finally thought of a proof that the before-offer-probability can't be known.

The question is basically 'what fraction of all Turing machines making an offer (which is accepted) will then output a certain result?'

We could rewrite this as 'what is the probability that a random Turing machine will output a certain result?

We could then devise a rewriting of all those Turing machines into Turing machines that halt or not when their offer is accepted (eg. halting might = delivering, not halting = welshing on the deal. This is like Rice's ... (read more)

5gwern16y

I haven't seen much response to it. There's a reply in Analysis by Baumann who takes a cheap out by saying simply that one cannot provide the probability in advance, that it's 'extremely implausible'. I have an unfinished essay where I argue that as presented the problem is asking for a uniform distribution over an infinity, so you cannot give the probability in advance, but I haven't yet come up with a convincing argument why you would want your probability to scale down in proportion as the mugger's offer scales up. That is: it's easy to show that scaling disproportionately leads to another mugging. If you scale superlinearly, then the mugging can be broken up into an ensemble of offers that add to a mugging. If you scale sublinearly, you will refuse sensible offers that are broken up. But I haven't come up with any deeper justification for linearly scaling other than 'this apparently arbitrary numeric procedure avoids 3 problems'. I've sort of given up on it, as you can see from the parlous state of my essay.