The lottery came up in a recent comment, with the claim that the expected return is negative - and the implicit conclusion that it's irrational to play the lottery.  So I will explain why this is not the case.

It's convenient to reason using units of equivalent value.  Dollars, for instance.  A utility function u(U) maps some bag of goods U (which might be dollars) into a value or ranking.  In general, u(kn) / u(n) < k.  This is because a utility function is (typically) defined in terms of marginal utility.  The marginal utility to you of your first dollar is much greater than the marginal utility to you of your 1,000,000th dollar.  It increases the possible actions available to you much more than your 1,000,000th dollar does.

Utility functions are sigmoidal.  A serviceable utility function over one dimension might be u(U) = k * ([1 / (1 + e^-U)] - .5).  It's steep around U=0, and shallow for U >> 0 and U << 0.

Sounds like I'm making a dry, academic mathematical point, doesn't it?  But it's not academic.  It's crucial.  Because neglecting this point leads us to make elementary errors such as asserting that it isn't rational to play the lottery or become addicted to crack cocaine.

Related on OB: Taboo Your Words

I realize this seems odd on a blog about rationality, but I'd like to strongly suggest that commenters make an effort to avoid using the words "rational," "rationality," or "rationalist" when other phrases will do.  I think we've been stretching the words to cover too much meaning, and it's starting to show.

Here are some suggested substitutions to start you off.

Rationality:

• truth-seeking
• probability updates under bayes rule
• the "winning way"

Rationalist:

• one who reliably wins
• one who can reliably be expected to speak truth

Are there any others?