Utility theory normally is used, as novasoy writes, in the context of expected utility. To illustrate:

Imagine that I'm playing the lottery. The odds that I will win are one in a million, say, and it costs me five dollars to play. However, if I win, I take home, say, one hundred thousand dollars. The expected utility calculation that utility theory posits is that you can determine whether or not to play by solving the following problem.

(1/1,000,000) X $100,000 >? (999,999/1,000,000) X $5

We see that the inequality above is not satisfied. Therefore, you have a higher expected utility from not playing than from playing. So you should not play the lottery.

It is evident from the above example that expected utility theory is a powerful tool in the analysis of behavior in politics, economics, and other fields of human interaction. It should also be evident, though, that the problem with applying such an analysis to a problem is the possibility of tautology.

Imagine that I wish to figure out why someone voted for Candidate A. I assume that we should use expected utility theory to analyze this problem. Accordingly, I say, "Voting for Candidate A must have given this person her highest expected utility." I then look at her other choices (Candidates B through N), and discern that all other Candidates espoused platforms that give the voter a lower expected utility. Why? Because if not, she would have voted for someone else. So I've solved the problem. Or have I?

The idea of a positivist social science epistemology is that, conceivably, I should be able to be proven wrong. How, if I adopt the analysis above, could I have been proven wrong? I have argued that utility theory gives me a viable explanation for my problem. I have achieved this by assuming utility theory to be correct. If I assume that utility theory is correct, than I can have no result that contradicts the viability of expected utility theory. I cannot be proven wrong. So I can never know if my assumption of expected utility theory is driving my conclusions. We have a tautology.

Such are the strengths and weaknesses of expected utility theory.