You don't really need matrix terminology - just a bit of economic theory and an understanding of basic statistics.
Essentially, you want to measure the 'quality' of each outcome (utility), and the likelihood of each outcome. Then, you calculate the expected utility (which is different from the utility of the expected value - you apply the function before taking the dot product, not afterwards).
I'm blanking on the TeX at the moment, but you basically take the sum of p(i)*U(I), where p(i) is the probability of the i-th outcome occuring, and U(I) is the utility ('benefit') associated with the i-th outcome. Utility is unique to a monotonically increasing function, so that means the individual values are arbitrary, as long as the relative order is preserved.
Then, see if that expected utility is better than the status quo. (Of course, this assumes that you already have a well-defined utility function, which is easy in theory but hard in practice).
Thank you for that. I cannot upvote enough. This subthread, with its heady blend of mathematics, philosophy and violent uprising is why I keep coming back to hacker news.
Essentially, you want to measure the 'quality' of each outcome (utility), and the likelihood of each outcome. Then, you calculate the expected utility (which is different from the utility of the expected value - you apply the function before taking the dot product, not afterwards).
I'm blanking on the TeX at the moment, but you basically take the sum of p(i)*U(I), where p(i) is the probability of the i-th outcome occuring, and U(I) is the utility ('benefit') associated with the i-th outcome. Utility is unique to a monotonically increasing function, so that means the individual values are arbitrary, as long as the relative order is preserved.
Then, see if that expected utility is better than the status quo. (Of course, this assumes that you already have a well-defined utility function, which is easy in theory but hard in practice).
http://en.wikipedia.org/wiki/Expected_utility_hypothesis