Quote from: Zangelbert Bingledack on June 06, 2015, 05:26:02 PM

Two can play: https://disqus.com/home/discussion/ethereumproject/the_p_epsilon_attack/#comment-2028779600

Quote from: Google

You're the captain of a pirate ship, and your crew gets to vote on how the gold is divided up. If fewer than half of the pirates agree with you, you die. How do you recommend apportioning the gold in such a way that you get a good share of the booty, but still survive?

Answer: You divide the booty evenly between the top 51% of the crew.

I read this puzzle as intending that only the captain can put a proposal to a vote (and he only gets one shot; presumably it's something like a perfect equal split among the crew if the captain gets voted down and killed*), in which case Google's original answer is right since each winning pirate does stand to lose if they vote no.

*Even if we instead assume that any pirate is allowed to make a counterproposal after the captain is dead, a pirate could just propose voting down the captain and the loot being divided among a different 51% set that includes him (the pirates in the overlap group should side with counterproposal, since they get slightly more loot without the captain around anymore). Of course then another pirate will do that with 52%, knowing his proposition will win. Then 53%, etc. until they end up at an even split among 100% of the crew as the winning proposition by vote count. So assuming the crew is rational they will vote yes if they luck out and make it into the 51%. So either way it seems Google has it right. The "no-voters don't get the loot" proviso is unnecessary, unless maybe we are not assuming rational pirates. (And in fact, this shows you can keep nearly half the loot (assuming you have a decent-sized crew), giving 51% of the crew the other half plus a tiny bit more, which is a bit more than they get if they vote you down. So Google's answer is also too low.)

Too many ways to read it, though, so it's basically indeterminate/underspecified as far as I'm concerned. I think it's called an "IQ test" to obscure the real purpose, that it's way for them to see your thought process during an interview. It's perhaps intentional that everyone will add in their own assumptions, or maybe even harp on the need to specify assumptions, or about the how killing the captain or having 49% be jealous would leave them in worse shape. Each of these kinds of reactions gives useful information to the hirers.

If the captain is offering the booty to only the top 51%, the other 49% will vote against him for sure. If more than 1% of the top 51% decide to try their luck at getting more after the captain is eliminated, then the captain dies. That is not very good odds for the captain (more probable than a coin toss the captain dies). Someone in the 51% may be smart enough to realize that making proposals where death is the result of a No consensus means the odds of getting more loot by continually voting No on each iteration of proposals is going to eliminate the competition for the sharing of the loot (even if there is only one iteration). And that person votes No but doesn't get enough support from the other 51%, he still gets his share of the loot.

Whereas, if the captain says that anyone who votes No does not get a share of the loot, then 100% of the pirates have to weigh the odds that 50% of the others won't vote Yes (a coin toss probability they lose out on the loot, thus much less than a coin toss probability that they risk it and the captain dies).

You speculate about what happens about after the captain dies, but that is not necessary to determine the ratio of the probabilities of the two answers. Since what happens after the captain dies is unspecified, then the odds of just 1% of those in the 51% speculating on the potential to get a better deal is not as good of odds for the captain as my answer.

Clearly my answer was correct on the probabilities in all possible interpretations. However I can't fathom how to access the comparison between my answer and a proposal to share amongst say the top 75% (and it also depends on what % the captain himself constitutes, i.e. the group size) and I think the question is underspecified for that type of proposal for other reasons such as the expectation of the pirates. Thus my answer was the only sure one that was superior to the one Google provided. Thus it is the only unambiguous correct answer.