Cooperating for reasons other than "I expect cooperating to make other people cooperate" gives people a reason to defect and make the total (and your expected) reward lower.

Yes. And I did cooperate because I expected that it would make other people cooperate (acausally). I was explaining why I wanted more people to cooperate, even though it would mean that Yvain would lose more money.

I've done the math elsewhere in this thread, and if at least a third of all respondents decide to cooperate no matter what, the optimal solution is to just defect and take their money.

Good. Then a defector has been enticed to take the survey.