If I have one grain of sand, I definitely don't have a heap of sand. If I have two grains of sand, I still don't have a heap. Should I come across a third and quite possibly a fourth grain of sand, a heap still wouldn't lay before me. You can see where the reasoning is leading. The thought is that there will be no definitive grain N which allows us to yell "HEAP!" Why would there be? If there were, then why is it that specific grain? Why not the one before it? Shouldn't the N-1 grain still give us something that looks like a heap? But if something looks like a heap then isn't just a heap? A possible answer to these questions is that maybe 'heap' is a vague term - and perhaps the same could be said about rationality. Now, this is tantamount to saying "Oh, I dunno..." which is like admitting that you're the type of frat bro who doesn't know where the campus library is. Clearly not a satisfactory answer. Precise answers with necessary and sufficient conditions are always preferable to "Well, it's vague."
Game theorists and economists give a precise answer as to what rationality may be. They hold rationality to be fulfillment of preferences. This often means that a person is rational if (and only if) they maximize utility. Intuitively this sounds pretty good, but for reasons soon to be clear this analysis of rationality fails
The 'Prisoners' Dilemma' game is probably the most famous game, and any student of political science, philosophy, economics, math, biology, psychology, or whatever should know about this game. It's that important. Probably its most useful application is as a model for public goods, but that's a story for another time. For now, let's see what we can say about rationality with this game. We'll be assuming that both players are perfectly rational and there is a common knowledge between them.
If you're clever, which you must be since you're reading this blog (excuse the self praise), you'll see that (Defect, Defect) is the NE and can skip this paragraph. If you're a bit dull, then read on! So the concept is actually quite simple. First, note that the payoffs are symmetrical, so the reasoning for Player 1 will also apply for Player 2. So, as Player 1, we ask ourselves what our best move is, given Player 2's strategy of (Cooperate). Just look at the payoffs that we could garner: 6 or 10. (Defect) gives us 10, so our best strategy given that Player 2 cooperates is to defect. Though, this isn't an NE. Obviously, this strategy profile can't be Player 2's best response considering this their payoff would be 0. Now we ask ourselves what our best response is given that Player 2 chooses (Defect). Again, choosing to defect gives us our highest payoff, and as it turns out the same could be said for Player 2. (Defect) is Player 2's best response, given that we defect. Aha! The Nash equilibrium!
Of course, the NE in the Prisoners' Dilemma wouldn't seem to be rational. Clearly the profile (Cooperate, Cooperate) leads to a much better outcome. The point however is that we've used a game theoretic solution concept, the supposed tool of a perfectly rational agent, which contradicts the intuitively rational insight. Thus, the Prisoners' Dilemma models a situation in which rational actions achieve the irrational outcome. For this reason it's been suggested that this is a counterexample to the economic notion of rationality.
Now, maximization of utility definitely seems to be a big part of the rational landscape, but it's 'just the tip of an iceberg' (do these metaphors work together? can you can have icebergs in a landscape?) Perhaps this understanding of the concept is merely underdeveloped. I'll be looking into this over the next few posts. I'll be musing on what the conditions of rationality could be while also attempting to sound as if I know what I'm talking about. I'll even be able to relate this back to the epistemology of disagreement, which is good because I said I would write more about that. Now that's efficiency!