The official blog of University of Missouri Skeptics, Atheists, Secular Humanists, & Agnostics
What if someone is actively trying to mislead you about their goals? What’s a rationalist to do? Nature may be tricky and weird, but none of us thinks that nature is actively trying to deceive us. We are social creatures whose goals often depend on what other people are doing, and people are not always forthcoming about these things. This requires an additional level of rationality, one that accounts for deceptive observations.
Suppose you are playing Poker with someone whose behavior seems like evidence that they have a strong hand. Should you accept that they have a strong hand, and act accordingly? Well, it depends, doesn’t it? They might know that you’ll take their behavior as evidence of a strong hand, and merely be pretending to have a strong hand. In that case, if you have a strong hand, you should bet. But then again, maybe they know you’ll reason that way, too, and anticipate your betting… maybe they are only pretending to pretend to have a strong hand, and they really do have a strong hand! What does Bayes’ Theorem tell us to do?
Bayes’ Theorem is the gold standard of rationality when one is dealing with empirical observations. You want to know if the player has a strong hand, given their behavior (written Pr. (Strong Hand | Behavior)). You calculate this with the following formula:
Pr. (Strong Hand | Behavior) = Pr. (Strong Hand) x Pr. (Behavior | Strong Hand) / Pr. (Behavior).
How do we even start to get a handle on this?
We need to stop trying to reason about their hand, and start reasoning about their brain. We need to start reasoning about the epistemic situation: who knows what about whom. We need to think about things like, “they know that I know that they’ve been caught bluffing in the past,” and “I know that they know that I know this.” We need to figure out how many times “I know that they know that…” repeats itself.
We need to think about these types of things because whoever has the information advantage is in a position to win. The information advantage is when you are one “knows that” step ahead of the other player. When you know something, and they don’t know that you know it, you can win. The trick is figuring out who has the information advantage.
New research in modal logic is addressing these very issues. In a mathematical model of a situation, if you stipulate who has the information advantage, you can prove that they’ll win. This is how we know that reasoning about other players’ knowledge is important. But when the game is actually being played, this type of information is very difficult to come by. Rarely are you certain that you have the information advantage.
But we know that it’s what you should be thinking about. Strategic reasoning is all about getting the information advantage and exploiting it.
Jack Donaghy is an expert strategist in these types of situations.
We see a great example of the information advantage at work in the recent episode of 30 Rock entitled “Game Over.” http://www.hulu.com/watch/444048#i0,p0,d0
Jack Donaghy and Devon Banks, usually steeped in rivalry, team up to defeat Kaylee. However, things are not as they seem, and deception is afoot. Watch the information advantage play out in all its glory.
To summarize, if you are in an adversarial epistemic environment, do the following:
Assess the epistemic situation by figuring out what the other agents know, and what you know.
Figure out who has the information advantage. If it’s you, figure out how to keep it. If it’s someone else, figure out how to get it.