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One distressing general trend was that people seemed to be more responsive to what they thought others would count as acceptable behaviour than they were to any independent judgements of acceptable behaviour (and so for example, even in one-shot games, whether or not their partner will find out how they choose makes a big difference to way they choose.)

While the results were quite interesting I didn't find them all that disturbing. I'm pretty skeptical in the first place that one has an obligation to divide up money evenly when one is the dictator as you have no reason to believe total utility will be higher if you are fair so long as the opponent doesn't know.

In other words playing so as to live up to social norms is actually quite appropriate as people's negative reactions to being 'treated unfairly' are the only factor which makes this game deviate from a zero-sum game. I mean what else does one have to go by when you don't have good knowledge of the other person's financial state. Or do you think 50/50 split is the best division in any situation.

Moreover, if i remember correctly people were still pretty fair even when they were anonymous. The difference about whether their partner finds out was based upon the value of their chips being tripled and the other person told or not told. However, if your chips are worth 3 times as much it seems to be the morally optimal strategy is to maximize the total profit while not reducing utility by triggering an unfairness response in the other individual.

Of course I don't think this is what is actually motivating people. One way that one could test this is to make the person's chips worth only half as much and see if this makes them more generous (helps them more than helps me).

One thing I did find really interesting about these results is the extent to which it suggests our moral responses to acts and deciscions are heavily shaped by evolutionary accountability. This is why I think we should only take moral intutions from our opinion of what states are better than others and ignore these sort of gut reactions to acts.

Ohh just to share my thoughts on the conference.

I think the highlights for me was kenny's paper and your paper (even though I only caught the comments). Gillies was pretty good too (what can I say I am a math person) and I was really pleased to see Kevin Kelly using recursion theory for epistemology even if I think he is a little quick to dismiss classical methods and the theory needs some work.

I'm sure I'm forgetting some good talks as well.

Crikey, you can share that thought on the conference all you like!

Yes, Kenny's going to be a star. (Anthony Gillies is a star already, of course. I was really tempted to blog about his use of the expression "moneyshot" in the middle of the talk, but I thought it might be a bit Wonkette for this blog.) I also really liked Jason Alexander's tutorials and Lara Buchak's paper. (It's perhaps a sign of my not being quite as much of a math person as you that the tutorials were my some of my favourites.)

I was at lunch with Mike and Darren and Andy today, and Thony's use of the term "moneyshot" definitely came up.

Beyond the papers mentioned here (in particular, yours, Kevin Kelly's, and Lara Buchak's, but also Thony Gillies'), Alison Gopnik's and Andy Egan's seem to be the ones that have given me the most to think about. Even though I had already heard the central ideas of both of those, either at talks at Berkeley or on Brian Weatherson's blog.

Shoot, I was supposed to email one of them because they were going to be in the SF area. Ohh well it is probably too late now. That's what I get for trying to remember things after drinking. Is Hajek in the bay area now or next week?

Back on to the conference I would have rated Gopnik's talks up there as well if I hadn't already seen it. The interesting observation I thought was the central role of intervention in causal reasoning. I think this is strong evidence that the difference between causal laws and constant conjunctions should be defined with interventions as a basic causal nexus. Thus we gain the benefits of the Humean view of causation (we need postulate no special metaphysical status to causal laws nor answer how we could determine this status) without having to take on accidental conjunctions or make the distinction completely arbitrarily. Ever being whose conciousness is embeded in the world 'in a similar manner to ours' is going to share our notion of causation.

Alternatively if you are really wedded to a seperate metaphysical status for causal laws you could insist that conciousness can only be embeded in the world in a way that respects causal laws. (That is brains which functioned sideways in time instead of space are impossible). Then you might be able to answer how we come to know which laws are causal.

In either case I thought that point was really important but i had already heard it and I'm just not that interested in the development of 4 year olds in that sort of heat. It is a fairly interesting subject just not really my cup of tea.

However, I have to disagree about Buchak's paper. While representing risk sensitive agents is an interesting quesiton (though one I think which has been addressed in the economic literature) I wasn't quite sure what she was trying to establish in her paper. She argued that it wasn't irrational for people to be risk-sensitive but I saw no argument why her notion of risk-sensitivity was the right one. Conversly there was no empirical data that suggested this particular model was the right one.

In fact I think there are strong reasons why not to accept her notion of risk-sensitivity. It has the unfortunate property of being linear in the vector of stakes for a fixed bet. That is the deseriability of betting 1 million dollars on the flip of a fair coin is a million times the desierability of betting 1 dollar on the same outcome. If rationality allows risk aversion should we really expect people who will bet a dollar on something to bet a million dollars on the same event? This certainly is not observered in practice.

Of course one might claim that desireability isn't proportional to monetary wealth. However, if you take this line you now need to demonstrate that people are risk averse in actual utilities. Arguably utilities are so defined so that people aren't risk averse but even if not it seems very hard to verify that we are risk averse in utility. Certainly there are results like the Allias paradox but in light of results like the conjunction fallicy even in carefully controlled better situations might this not simply be a failure of proper probabilitic reasoning. I mean it seems wrong to incorporate the willingness of people to assign lower probability to one conjunct than the whole conjunction and choose the whole conjunction to bet into our theory of rationality so how do we know this isn't the same thing?

I don't mean to say the paper wasn't good. I think if she was more specific about what notion of rationality she was trying to capture (clearly the word has several different meanings) and gave arguments the show people are truly risk averse in utility it could be pretty good. But I think the linearish risk function needs to go.

Ohh yah and the crazy moneyshot comment really stunned me. I didn't say anything because I thought moneyshot might also have a non-sexual meaning but I don't really think so.

Maybe this isn't surprising--informal fellow that I am--but I found James Pryor's talk particularly intriguing. I didn't really understand exactly how the system he was talking about works, but it looks like an interesting way to try to formalize some more of the topics that are of particular interest to more traditional epistemologists.

I missed Lara's talk, but from her paper it seemed like one of the things she was trying to do was to show that risk-sensitivity can't be refuted by the sort of Dutch book argument that is often used to support the Savage axioms. If that's what she meant to do, maybe she doesn't need an empirically supported account of risk-sensitivity; she just needs to show that there is some way to be risk-sensitive without being Dutch-bookable.

Unfortunatly I believe I missed pryor's talk. That was on sunday right?

Anyway I thought it was already well known that risk aversion did not force you to run afoul of Dutch-books. I mean real people are risk averse and philosophers haven't become rich making bizarre sequences of bets. So we already knew there was some way to be risk averse that didn't fall afoul of Dutch book arguments. In fact this is hardly a difficult burden for a theory of risk aversion to meet at all. Any theory which accepts strictly less bets than the standard theory will not be subject to a butch book argument (formulated as a sequence of bets you accept but guarantees you lose money).

This brings up another difficulty with her theory. The utility of bets is not additive. Two opposite bets on a coin cancel each other out but the sum of their desierabilities on her theory will be negative. Moreover in this case the sell and buy price are the same on her theory (the bets are symetric) so if she is to avoid a dutch book she can't just sum the utilities together. What I believe she does (or at least could do) is simply stipulate that you evaluate a collection of bets by simplifying it into one complex bet. Yet if this is her solution she hasn't shown she avoids dutch book so much as stipulated it. ANY theory of betting which demands that you evaluate complex bets by simplifying them and gives at leat n utils to a bet guaranteed to give you n utils and at most m utils to a bet guaranteed to give you less than m utils (i.e. the bet I give you 5 if heads 7 if tails has value at least 5) will avoid dutch book. This is for the simple reason that you are just putting your bets together and asking if they form a dutch book and rejecting those which do.

Moreover, the lack of any nice way to sum bets makes the theory very unwieldy in a practical sense. Sure simple examples like a coin flip which will be independent from everything else aren't a problem but as soon as an agent is taking bets on more complex effects (like most uncertain events in real life) one has to factor in ALL of the agents other 'bets' to value the bet for the agent. In fact this means you also need to factor in the possibility of future bets on the same object (If I think Johnny might make me a bet which lets me hedge the risk on yours it might change my value of it). We don't even know if her theory will converge in these cases much less have any idea how to actually calculate utilities.

Moreover, while she may simply stipulate avoidance of Dutch book in the simple sense violating the sure thing principle seems just as bad. Certainly prefering an outcome which is worsein all possible outcomes is a violation of rationality if anything is. In fact this seems central to the very notion of rationality.

Didn't she show that violating the sure thing principle might sometimes be reasonable? Not at all as her example rested on an equivocation between utility and money. Her example rested on the fact that your utility was very non-linear in money (must exceed this threshold otherwise broken legs etc..) and thus says nothing about the real sure thing principle. If you insist on substituting money for utility you can create utterly absurd situations that even violate monotonicity (everyone who has more tha $50 in their wallet gets shot).

Ultimately though this is besides the point. My real objection, and the reason I think it might have promise if cleaned up, is that her paper had no identifiable thesis. I don't know if that is how people actually do act, how they should act, or a useful (but incorrect) theoretical tool. In philosophy it just doesn't cut it to just 'do stuff' you should be making a point or at least surprising and interesting observations.

In the end I think the differences in our reactions reflect our backgrounds. Like teddy (who didn't seem too impressed) my background in utility and deciscion theory is from economics where they consider tons of different axioms for preference (to the absurd) and have already made attempts to account for risk aversion. So most of the issues she raised were not new to me and may have been to philosophers.

As an aside I really think commentary might better be done in this sort of blog format than a paper. So once a talk is done (keep the commentor but perhaps more time for questions) a blog goes up and people comment and critique then a month or two later the commentator is responsible for amalgmating the good points into a responding paper.

Pryor's talk was Saturday morning, between Alexander part II and Kelly part II. (I missed all of Sunday, hélas.)

I don't think the broken-legs example was in Lara's paper on the website. My take is that, since most people do violate the sure-thing principle and continue to do so even when the arguments for the sure-thing principle are explained to them--in fact, when arguments for and against the Allais choice are given I believe more people switch to the Allais choice than vice-versa--the presumption should be that it's rational, unless we can come up with an argument that it's not. Risk-sensitivity can cause you to miss a sure gain when you're offered two bets in a row on opposite flips of a coin, if you don't know you'll be offered the second bet when you get the first--but that's forgoing a sure gain rather than incurring a sure loss, and a risk-sensitive person probably wouldn't want to count on the next bet coming along.


About the blog--when Branden was talking about posting it on a web I thought that it would be great to have it be a blog with heavily moderated comments. Maybe I should pass that along to him?

Matt, I think your example is somewhat confused. Either the second bet is guaranteed to occur (in which case risk sensitivity has nothing to do with it) or you aren't passing up a sure gain (as the second bet might not happen). Anyway the situation I am worried about is that violating the sure thing principle means a person who currently holds gamble A and is offered the choice to switch to gamble B which is better in every outcome can rationally refuse to do so.

You suggest that we should accord deliberative choice the status of rationality unless we have a compelling argument otherwise. Sure, this seems reasonable. However, would you say accepting a dutch book is rational if we showed that people would do this after deliberation. I think not because the argument that this guarantees a sure loss is more than compelling enough to override this presumption. Yet this is the same argument I deploy in the sure thing principle so if it is good in one case it should be good in another.

Of course you are likely to respond that the dutch book example is irrelevant as we actually don't see people accept dutch books. However, if you fairly apply the same standard to both dutch books and the sure thing principle you will see we don't have any reason to believe people violate the sure thing principle either.

In particular the Allais paradox only involves an implicit violation of the sure thing principle. The very reason that the Allais result is interesting is because people don't violate the sure thing principle in simple head to head comparisons. It's quite possible that similar reasoning might be used to show implicit violations of dutch books.

I mean in the Allais paradox we see a rule (the sure thing principle) which is followed (when arguments are presented) in every direct comparison violated implicitly. I suspect that this means it is the other assumptions we use to derive a violation of the sure thing principle from the choices which are at fault. However, if you aren't willing to give up any of these other assumptions I don't see how you could claim this isn't irrational. We have a principle that is followed in every transparent (i.e. head to head) case but broken once the situation becomes complicated. If this isn't evidence for irrationality what ever could be?

However, this is all besides the point. Even if you take people's behavior after arguments are explained to be very strong evidence for rationality Lara's paper still fails to capture this notion. Her notion of comparing bets can't both account for the Allais choice and people's failure to violate the sure thing principle (after deliberation) in head to head comparison. I personally think a better approach would be to factor in the extra pain with losing knowing you could have won and winning knowing you could have lost. This can explain the Allais paradox without giving the wrong results in head-to-head comparisons.

Yah suggest the blog thing to branden.