Regarding a practical way to deal with this, I find I have become quite comfortable with flipping a coin (or using some other random choice method, especially for more than 2 options). Frequently, it turns out that making a decision in some reasonable amount of time is more important than making the truly BEST decision (for example, when choosing a venue for dinner). Of course, there's another question to be asked regarding when it is worth going to get a coin--sometimes, the extra time you'd use to do so, if instead applied to the decision process, would allow you to make a decision without the use of the coin. Of course, the same problem occurs with thinking about THIS problem--if, rather than thinking about whether or not it was worth getting a coin, you just went and got it, you might save yourself valuable time; unless it turns out that you SHOULDN'T go get a coin, this is a quicker way to the same result. So even thinking about whether getting a coin is worthwhile is tantamount to admitting that it isn't, and if you know that already, why are you thinking about it at all?

There is, of course, a flaw in the above reasoning (though it sounded appealing to me at first, even though I knew it had to be wrong). Thinking about whether to get a coin only commits you to the proposition that the time lost by so thinking is less valuable than the expected value of the improvement in your decision. Unfortunately, there is still a problem, which is that, until you've carried out any particular process of decision, you can't know when it will end. So you need to make guesses which you know will rely on insufficient information, and that means all of your decisions about what you ought to think about are going to be subject to serious error. This is somewhat reminscent of the Halting Problem, a famous problem in the Theory of Computation.

My suspicion is that, in order to keep us from thinking too long about any one thing, evolution has engineered into us a short attention span (this seems more likely than any sophisticated mechanism for avoiding overly long decision-making processes). This is a little disturbing, because it means that there are probably some things we could deduce, if only we could think about them long enough, but which are forever beyond our grasp. On the other hand, not having a limited attention span would make us subject to some serious problems, so I guess I ought not complain.