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Comment author: army1987 26 January 2014 01:26:49AM 11 points [-]

Also, it's well possible that your utility function doesn't evaluate to +10000 for any value of its argument, i.e. it's bounded above.

Comment author: Matt_Simpson 31 January 2014 05:14:58AM 0 points [-]

Since utility functions are only unique up to affine transformation, I don't know what to make of this comment. Do you have some sort of canonical representation in mind or something?

Comment author: Oscar_Cunningham 27 January 2014 12:27:29PM *  3 points [-]

There are versions of the VNM theorem that allow infinitely many possible outcomes, but they either

1) require additional continuity assumptions so strong that they force your utility function to be bounded

or

2) they apply only to some subset of the possible lotteries (i.e. there will be some lotteries for which your agent is not obliged to define a utility).

I might look it up on the original paper when I have time.

The original statement and proof given by VNM are messy and complicated. They have since been neatened up a lot. If you have access to it, try "Follmer H., and Schied A., Stochastic Finance: An Introduction in Discrete Time, de Gruyter, Berlin, 2004"

EDIT: It's online.

Comment author: Matt_Simpson 31 January 2014 05:13:47AM 0 points [-]

See also Kreps, Notes on the Theory of Choice. Note that one of these two restrictions are required in order to specifically prevent infinite expected utility. So if a lottery spits out infinite expected utility, you broke something in the VNM axioms.

For anyone who's interested, a quick and dirty explanation is that the preference relation is primitive, and we're trying to come up with an index (a utility function) that reproduces the preference relation. In the case of certainty, we want a function U:O->R where O is the outcome space and R is the real numbers such that U(o1) > U(o2) if and only if o1 is preferred to o2. In the case of uncertainty, U is defined on the set of probability distributions over O, i.e. U:M(O) -> R. With the VNM axioms, we get U(L) = E_L[u(o)] where L is some lottery (i.e. a probability distribution over O). U is strictly prohibited from taking the value of infinity in these definition. Now you probably could extend them a little bit to allow for such infinities (at the cost of VNM utility perhaps), but you would need every lottery with infinite expected value to be tied for the best lottery according to the preference relation.

Comment author: somervta 09 October 2013 01:26:51AM 1 point [-]

I bite my pills into thirds.

Comment author: Matt_Simpson 14 October 2013 02:07:25AM 0 points [-]

I do this too, though in smaller bites. fitfths? fourths? I'm not sure, actually, but it seems to work.

Comment author: army1987 31 July 2013 05:26:23PM *  9 points [-]

I dunno, in the context it sounds clearly tongue-in-cheek -- though you usually can't countersignal to people who don't know you (see also).

Comment author: Matt_Simpson 01 August 2013 07:42:55PM 0 points [-]

Good point.

Comment author: Prismattic 31 July 2013 02:02:38AM 30 points [-]

Ugh. I am generally in the unsympathetic-to-PUA thinking camp, so I offer the following not to bring up a controversial subject again, but because I think publicly acknowledging when one encounters inconvenient evidence for one's priors is a healthy habit to be in...

Recently I added the following (truthful) text to my OkCupid! profile:

Note, July 2013 -- I can't claim to be in a relationship yet, but I have had a couple of dates with a someone who had me totally enthralled within 30 minutes of meeting her. I'm flattered by the wave of other letters that have come in the past month, but I've put responding to anyone else on hold while I devote myself to worshiping the ground she walks on.

Having noted that I am a)unavailable and b)getting lots of competing offers, a high status combination, the result is... in three days, the number of women rating my profile highly has gone from 61 to 113.

Comment author: Matt_Simpson 31 July 2013 04:57:19PM 6 points [-]

Funny, I read your post and my initial reaction was that this evidence cuts against PUA. (Now I'm not sure whether it supports PUA or not, but I lean towards support).

PUA would predict that this phrase

...while I devote myself to worshiping the ground she walks on.

is unattractive.

Comment author: gwern 27 July 2013 09:27:32PM 8 points [-]

I took an hour to draw up a list of personal bets I've made or tried to make with people. The list turns out to be surprisingly short and have resulted in next to no bets, implying that for all that people talk about bets, actual bets are far rarer than I had realized. This is a bit of a pity - so much cheap talk...

Comment author: Matt_Simpson 28 July 2013 08:10:37PM 2 points [-]

Well based on your track record there, it seems like a prudent move to avoid making bets with you ;)

(Though I agree with you and should be shaming them rather than defending them.)

Comment author: cousin_it 24 July 2013 09:18:45PM 0 points [-]

Yeah. The idea came when I was lying in a hammock half asleep after dinner, it really woke me up :-) Now I wonder what approach could overcome such problems, even in principle.

Comment author: Matt_Simpson 24 July 2013 10:41:51PM 0 points [-]

If the basilisk is correct* it seems any indirect approach is doomed, but I don't see how it prevents a direct approach. But that has it's own set of probably-insurmountable problems, I'd wager.

* I remain highly uncertain about that, but it's not something I can claim to have a good grasp on or to have thought a lot about.

Comment author: Matt_Simpson 24 July 2013 08:47:00PM *  1 point [-]

I think I understand X, and it seems like a legitimate problem, but the comment I think you're referring to here seems to contain (nearly) all of X and not just half of it. So I'm confused and think I don't completely understand X.

Edit: I think I found the missing part of X. Ouch.

Comment author: falenas108 22 July 2013 12:56:55PM 4 points [-]

Somewhat frequently while talking, either public speaking or just talking to a friend, my mind will suddenly go blank. I won't be able to remember what I'm talking about, and I have to retrace my thoughts to get back to where I was.

Is this something that dual n-back will help with?

(Isomorphic question: Is this a problem of working memory, or something else?)

Comment author: Matt_Simpson 22 July 2013 02:40:10PM 1 point [-]

I also have this problem and would like to know how to fix it / if dual n-back might help.

Comment author: Prismattic 05 June 2013 11:09:11PM 1 point [-]

I think this Noah Smith disquisition on "derp" might be a useful thing to refer people to when one gets tired of referring them to PITMK. It crystalizes for me why I find a lot of political commentary unbearable to read/listen to.

Comment author: Matt_Simpson 22 July 2013 01:57:32PM 1 point [-]

Politics is the mind killer for a variety of reasons besides ridiculously strong priors that are never swayed by evidence. Strong priors isn't even the entirety of the phenomena to be explained (though it is a big part), let alone a fundamental explanation.

Also, I really like Noah's post (and was about to post it in the current open thread before I found your post). Not only did Noah attach a word to a pretty commonly occurring phenomenon, the word seems to have a great set of connotations attached to it, given some goals about improving discourse.

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