When you say that choosing to defect might make it more likely that they defect, do you mean that choosing to defect may cause the probability that the other person will defect to go up, or do you mean that the probability of the other player defecting, given that you defected, may be greater than the probability given that you cooperated?
To quote Douglas Adams, "The impossible often has a kind of integrity to it which the merely improbable lacks." If it is impossible to have off-diagonal results, that is a much stronger argument for cooperating than having it be improbable, even if the probability of an on-diagonal result is 99.99%; as long as the possibility exists, one should take it into consideration.
If it is impossible to have off-diagonal results, that is a much stronger argument for cooperating than having it be improbable
If the probability is epsilon, then having the probability be zero is only an epsilon stronger argument. If you doubt this let epsilon equal 1/googolplex.
Sometimes I see new ideas that, without offering any new information, offers a new perspective on old information, and a new way of thinking about an old problem. So it is with this lecture and the prisoner's dilemma.
Now, I worked a lot with the prisoners dilemma, with superrationality, negotiations, fairness, retaliation, Rawlsian veils of ignorance, etc. I've studied the problem, and its possible resolutions, extensively. But the perspective of that lecture was refreshing and new to me:
The prisoner's dilemma is resolved only when the off-diagonal outcomes of the dilemma are known to be impossible.
The "off-diagonal outcomes" are the "(Defect, Cooperate)" and the "(Cooperate, Defect)" squares where one person walks away with all the benefit and the other has none:
Facing an identical (or near identical) copy of yourself? Then the off-diagonal outcomes are impossible, because you're going to choose the same thing. Facing Tit-for-tat in an iterated prisoner's dilemma? Well, the off-diagonal squares cannot be reached consistently. Is the other prisoner a Mafia don? Then the off-diagonal outcomes don't exist as written: there's a hidden negative term (you being horribly murdered) that isn't taken into account in that matrix. Various agents with open code are essentially publicly declaring the conditions under which they will not reach for the off-diagonal. The point of many contracts and agreements is to make the off-diagonal outcome impossible or expensive.
As I said, nothing fundamentally new, but I find the perspective interesting. To my mind, it suggests that when resolving the prisoner's dilemma with probabilistic outcomes allowed, I should be thinking "blocking off possible outcomes", rather than "reaching agreement".