MOJO3 results (Common Entries)

The idea of resonant defection was described by Douglas Hofstadter in 'Metamagical Themas.' The idea is this. Perhaps your first response to this situation is to think that of course everyone should pick 'C.' After all, then we all do better, and everyone can see that. But then you think that at least one of the ten people might be at least briefly considering pressing 'D'. But then it occurs to you that if you're thinking this, so must all of the other nine, which must makes you seriously consider pressing 'D' yourself. And it then occurs to you that if they other nine are as smart as you, they must all be seriously considering pressing 'D', which means you should almost definitely press 'D'. So now you feel that you should probably press 'D', and it occurs to everyone else must be thinking the same thing. So you decide to definitely press 'D', and think that everyone else must be doing the same thing.

But this contest is more complicated, because you aren't trying to say what you would do IRL, but only predict what a majority of people will do ITC. So think more formally about how you would decide IRL. You would estimate p_d, the percentage of people who will press 'D' IRL. If p_d is too high, then you feel you are unlikely to get the $1000, so press 'D' yourself. If your utility is linear in dollars, and you are risk neutral, the cutoff is at p_d such that 100=1000(1-p_d)^9, which gives p_d=23%. So if p_d<0.23, you do 'C' IRL, but if p_d>0.23, you do 'D' IRL. Of course, depending on your personal preferences for risk and dollars (which are neither rational nor irrational), your cutoff may vary, but it's certainly below 0.50, since essentially everyone will prefer a certain $100 to a 1/512 chance of $1000. For simplicity, we will call the cutoff 23%, but it can of course

I didn't give even a moment's consideration to what I would do in real life, either in considering this question, or even in considering the earlier version of the question. It's all about guessing what other people are going to say, no?

Jonathan Dushoff

As Hofstadter repeatedly points out, this is to a certain extent a misunderstanding, based on the concept of 'whatever other people do'. If you assume any percentage possibility that someone will press D then you are best off pressing D yourself, so you are definitely better off pressing D. But if everyone went with this logic then they would do less well (scoring 100) than if they all went against the logic and pressed C (and all scored 1000). As Hofstadter points out, there is a scary analogy with the Nuclear arms race here (thankfully less imminent now than it seemed when he wrote), whereby if other people have a nuclear stockpile, then you are misguided not to have one yourself, but that way *everyone* loses out.

So - I vote for unilateral C myself