= 27d567bc2d48d9f40e9ccc20ea370b15)
PuyaSharif comments on The self-fooling problem. - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (45)
As some comments has pointed out there are some loopholes in the original formulation, and I will do my best to close these or accept the fact that they're not closeable (which would be interesting in its own right).
Lets try a simpler formulation.. Basically what is being asked here is that given two intelligences A and B, where A and B are identical (perfect copies), can A have a strategy that minimizes the probability of B finding the coin?
Further: Any chain of reasoning leading to a constrained set of available locations followed by randomization could be used by B to constrain the set of locations to search. Is it therefore possible to beat complete randomization?
Yes. You need to weight locations according to the time it takes to search them and then make a random selection from that weighted set; that'll give you longer search times on average than an unweighted random pick from a large set where most of the elements take a trivially small time to search. I could take a stab at proving that mathematically, if you're comfortable with some abstraction.
You can beat even that by cleverly exploiting features of the setup, as I and muflax did in our responses to the OP, but that's admittedly not quite in keeping with the spirit of the problem.
I see your point. A reduction of easily searched places will indeed make it more difficult for B to find the coin, even though B will have a smaller space to search. The question that remains is: given a mathematical description of the search/hide-space what probability distribution over locations (randomization process) will minimize the probability of B finding the coin.