For what it’s worth, at my high school the incidence of (recurrent and/or obvious) cheating was closer to 50%, and even then the majority of the cheating was on homework, where some of it may not technically have been cheating at all.
This may have been due to an unusually high probability of getting caught (private school, small classes, and engaged teachers) and unusually strong punishments, up to and including expulsion.
Based on your observation that your direct evidence for human mortality is limited, you conclude that you will never receive evidence, under some definition, that you are mortal. Do you have any evidence (under the same definition) that I am mortal, or indeed that anybody else is? If yes, could you please explain the difference in conclusions from identical evidence?
And it’s complicated by loss aversion.
Are you banking on subjective quantum immortality?
Both interpretations could be simultaneously true...
Ah, of course, I forgot a prepositional phrase: he actually was less likely to score on that side because it was easier for the goalie to predict which side he would favor.
(Incidentally, this proposition has been empirically tested in G.C. Moschini, Economics Letters 85 (2004) 365–371)
However, we do have to be careful in games of strategy in selecting what we call capability improvements. Increasing my payoff in a single cell can change the relationship between cells, preventing me from credibly committing to a particular strategy and thereby diminishing the outcome of the game.
As an example, imagine we have a game defined as follows:
(U,L) ⇒ (1,1)
(U,R) ⇒ (0,0)
(D,L) ⇒ (0,0.9)
(D,R) ⇒ (1,0)
where the pairs are (x strategy, y strategy) mapped to (payoff to x, payoff to y).
The unique Nash equilibrium is (U,L), so each player receives a payoff of 1.
Now “improve” player y’s capabilities by making (U,R) ⇒ (0,1.1). Now there is no equilibrium in pure strategies, and the unique mixed strategy equilibrium is: Pr(U) = 0.9, Pr(L) = 0.5. Expected payoff to the “improved” player is 0.99, and to the other player 0.5, both down from their previous equilibrium values of 1 each, and the magnitude of the effect damaging player y increases as her payoff to (D,L) decreases (derivations available on request).
Of the top of my head, I suspect your heuristic applies in zero-sum games, but not necessarily elsewhere. Unless the players could read each other’s source code...
If you are interested in those kind of social dynamics, I highly recommend studying game theory—it’s absolutely full of surprising results and predictions.
In one class, we proved that for a certain model of soccer penalty kicks, if a kicker got better at shooting (increased the chance of scoring, ceteris paribus) but only in one direction (left or right), he actually was less likely to score because it was easier for the goalie to predict which side he would favor.
For what it’s worth, I remember a study on Stanford undergrads with what was essentially speed dating; men suggested their interest in a second date with ~90% of the women they met, and simultaneously their top criterion for that choice was attractiveness. Even granting that they had loose definitions caused by the study, I suspect that under Dan’s metric (binary choice) a reasonably large minority might be tagged “pretty.”
I also didn’t get the impression from the photos on the website that anybody in the Knox case was pretty in the sense that you mean it—I think of your criterion as defining “remarkably pretty” rather than “pretty, if I had to choose,” and I’d say you’re probably right on <5% being remarkably pretty.
Hmm… I’ve been thinking about your question the last couple days and I’m really not sure. I haven’t really written up my experiences in the field very much, if that’s what you’re asking. If, on the other hand, you’re looking for stories of games played to illustrate game-theoretic concepts, there are lots of places to point for those.
Perhaps you could expand on the type of stories you’re looking for?
“A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away.”
Always possible, but I wasn’t suggesting that I had an unfair advantage. Quite the opposite: game-theoretically, my opponent was in a vastly preferable position, as long as I didn’t tear up one of my slips.
To see this, imagine there were only two partners per player. One player can make a deal with each partner, where the other player can only make one deal total. The partners of the former player are playing the Nash bargaining game; the partners of the latter are participating in an auction for the right to play the Nash bargaining game.
Since the theoretical/canonical outcome of the bargaining game is that the person in the stronger bargaining position (the person with less to lose from walking away) takes a larger share of the money, it’s not a big leap to see how the outcomes should differ. When I could make a deal with each partner, they were in the stronger bargaining position (not being eligible for the $20 meta-prize). In the other case, they knew that they could only get some money if they were allowed to come to the table, so to speak, and so they competed with each other in essentially a bidding war for that opportunity.
Does that make sense? As further evidence that I wasn’t simply unusually unpopular, I should note that the outcome I described was standard, happening year after year in the class. Indeed, the professor relied on it turning out that way to make a point; he would have looked rather foolish if I had come out on top despite the apparent structural disadvantages.
Based on previous feedback, there are a number of things in this story about which I was unclear, so it may very well have been on my end.
That said, I’m rather honored that you put in that degree of effort!
As a further note, though, if by
doesn’t seem likely that you could actually end up doing worse that those with fewer slips
you mean I should be able even without tearing up a slip or otherwise limiting my own options, then no—I was in a weaker bargaining position at the beginning, and game-theoretically I should have ended up worse than my opponent. That was a key finding of Thomas Schelling’s, though he applied it to nuclear warfare (see The Strategy of Conflict and also the link at the beginning of this post for more info on his bare-knuckle game theory).
You’re right—and as my professor said, since I had a better initial situation, I should have been able to do at least as well as my opponent.
Tearing up two slips would have been unlikely to beat tearing up one—the latter creates the necessary scarcity (and causes the auction) while not diminishing the total number of deals that much. In fact, since my opponent beat five dollars, I couldn’t have won with two torn slips, but I should at least have been even with my opponent, and might (as my reply to CronoDAS notes) have been able to win via a trick.
I could refuse a bad deal, but my partners knew that I was trying to win $20, where they stood to lose at most a dollar relative to agreeing to the deal; they had less to lose, and thereby had a stronger bargaining position (the literature on Nash bargaining is relevant).
A good point. Fixed.
I turned the lights out. Thanks for the suggestions!
Done. Thanks for the input—apparently I haven’t yet internalized de Saint Exupery’s admonition.
As the consensus seems to be that the latter half of the story diminishes the impact of the former, I’ve deleted it.
Thanks for the suggestions—it’s great to have feedback.
It’s true—we discussed that very point afterwards. A fraction of the class was arguing that I should have merely set aside one slip to be unused, made the deals, and then reversed myself and used the final one.
The argument was over whether that was a credible action—and I like your strategy better.
Assuming that there is, in fact, a correct way to specify the predictions. It’s possible that you weren’t actually disagreeing and that you both assign substantial probability to (world is made worse off but not destroyed | non-FAI is created) while still having a low probability for (non-FAI is created in the next decade).