I read somewhere that the reason we don't see these people is that they all immediately go to Vegas, where they can easily acquire as many positive value deals as they want.

Here is a simple way to assess your value-of-life (from an article by Howard).

Imagine you have a deadly disease, certain to kill you. The doctor tells you that there is one cure, it works perfectly, and costs you nothing. However, it is very painful, like having wisdom teeth pulled continuously for 24 hours without anesthetic.

However, the doctor says there is one other possible solution. It is experimental, but also certain to work. However, it isn’t free. “How much is it?” you ask. “I forgot,” says the doctor. “So, you write down the most you would pay, ...

214y

Would you accept a 95% chance of death for $36 million?

If it helps, I think this is an example of a problem where they give different answers to the same problem. From Jaynes; see http://bayes.wustl.edu/etj/articles/confidence.pdf , page 22 for the details, and please let me know if I've erred or misinterpreted the example.

Three identical components. You run them through a reliability test and they fail at times 12, 14, and 16 hours. You know that these components fail in a particular way: they last at least X hours, then have a lifetime that you assess as an exponential distribution with an average of 1 hour....

814y

Heh, that's a cheeky example. To explain why it's cheeky, I have to briefly run through it, which I'll do here (using Jaynes's symbols so whoever clicked through and has pages 22-24 open can directly compare my summary with Jaynes's exposition).
Call N the sample size and θ the minimum possible widget lifetime (what bill calls X). Jaynes first builds a frequentist confidence interval around θ by defining the unbiased estimator θ∗, which is the observations' mean minus one. (Subtracting one accounts for the sample mean being >θ.) θ∗'s probability distribution turns out to be y^(N-1) exp(-Ny), where y = θ∗ - θ + 1. Note that y is essentially a measure of how far our estimator θ∗ is from the true θ, so Jaynes now has a pdf for that. Jaynes integrates that pdf to get y's cdf, which he calls F(y). He then makes the 90% CI by computing [y1, y2] such that F(y2) - F(y1) = 0.9. That gives [0.1736, 1.8259]. Substituting in N and θ∗ for the sample and a little algebra (to get a CI corresponding to θ∗ rather than y) gives his θ CI of [12.1471, 13.8264].
For the Bayesian CI, Jaynes takes a constant prior, then jumps straight to the posterior being N exp(N(θ - x1)), where x1's the smallest lifetime in the sample (12 in this case). He then comes up with the smallest interval that encompasses 90% of the posterior probability, and it turns out to be [11.23, 12].
Jaynes rightly observes that the Bayesian CI accords with common sense, and the frequentist CI does not. This comparison is what feels cheeky to me.
Why? Because Jaynes has used different estimators for the two methods [edit: I had previously written here that Jaynes implicitly used different estimators, but this is actually false; when he discusses the example subsequently (see p. 25 of the PDF) he fleshes out this point in terms of sufficient v. non-sufficient statistics.]. For the Bayesian CI, Jaynes effectively uses the minimum lifetime as his estimator for θ (by defining the likelihood to be solely a function of the

014y

excellent paper, thanks for the link.

014y

My intuition would be that the interval should be bounded above by 12 - epsilon, since the probability that we got one component that failed at the theoretically fastest rate seems unlikely (probability zero?).

Logarithmic u-functions have an uncomfortable requirement that you must be indifferent to your current wealth and a 50-50 shot at doubling or halving it (e.g. doubling or halving every paycheck/payment you get for the rest of your life). Most people I know don't like that deal.

014y

That's only a requirement for risk-neutral people. Most people you know are not risk-neutral.

014y

I'm confused about what is uncomfortable about this, or what function of wealth you would measure utility by.
Naively it seems that logarithmic functions would be more risk averse than nth root functions which I have seen Robin Hanson use. How would a u-function be more sensitive to current wealth?

14y5

A similar but different method is calculating your "perfect life probability" (from Howard).

Let A be a "perfect" life in terms of health and wealth. Say $2M per year, living to 120 years and being a perfectly healthy 120 year old when you instantly and painlessly die.

Let B be your current life.

Let C be instant, painless death right now.

What probability of A versus C makes you indifferent between that deal and B for sure? That is your "perfect life probability" or "PLP." This is a numerical answer to the question &quo...

214y

This is an interesting thought experiment. I submit that for many men, the probability is quite small, say on the order of 15% or 25%, whereas for most women it is 90-95%.
Edited: I originally wrote "for women it approaches unity".

014y

It's not clear to me what B means.
Is it "your health and wealth will always be the same as they are today, and you will die at age 90"? Is it "your life will have the smoothly varying health and wealth that the average person is expected to have from today's statistics"? Is it "the best life you expect to have with at least a 10% confidence interval"? Is it "the world is deterministic, you have some fate B unknown to you, and the only free choice you'll ever make in your life is that between B and A/C"?

Some students started putting zeros on the first assignment or two. However, all they needed was to see a few people get nailed putting 0.001 on the right answer (usually on the famous boy-girl probability problem) and people tended to start spreading their probability assignments. Some people never learn, though, so once in a while people would fail. I can only remember three in eight years.

My professor ran a professional course like this. One year, one of the attendees put 100% on every question on every assignment, and got every single answer correct. ...

15y48

I cannot begin to say how vehemently I disagree with the idea of firing the first attendee. If I found out that your professor had fired them I would fire your professor.

Sure, it *has* to be an expected utility fail if you take the problem literally, because of how little it would have cost to put only 99.99% on each correct answer, and how impossible it would be to be infinitely certain of getting every answer right. But this fails to take into account the out-of-context expected utility of being AWESOME.

Firing the second guy is fine.

I've given those kinds of tests in my decision analysis and my probabilistic analysis courses (for the multiple choice questions). Four choices, logarithmic scoring rule, 100% on the correct answer gives 1 point, 25% on the correct answer gives zero points, and 0% on the correct answer gives negative infinity.

Some students *loved* it. Some hated it. Many hated it until they realized that e.g. they didn't need 90% of the points to get an A (I was generous on the points-to-grades part of grading).

I did have to be careful; minus infinity meant that on one quest...

08y

What does 0.01% on the wrong answer get you?

215y

Good thing with a log score rule is that if the student try to maximize the expected score, they should write in their belief.
For the same reason, when confronted with a set of odds on the outcome of an event, betting on each outcome in proportion to your belief will maximize the log of the expected gain (regardless of what the current odds are)

15y16

minus infinity meant that on one question you could fail the class

...wow. Well, I guess that's one way to teach people to avoid infinite certainty. Reminiscent of Jeffreyssai. Did that happen to a lot of students?

When I teach decision analysis, I don't use the word "utility" for exactly this reason. I separate the "value model" from the "u-curve."

The value model is what translates all the possible outcomes of the world into a number representing value. For example, a business decision analysis might have inputs like volume, price, margin, development costs, etc., and the value model would translate all of those into NPV.

You only use the u-curve when uncertainty is involved. For example, distributions on the inputs lead to a distribu...

015y

Totally. ;)

If you wanted to, we could assess at least a part of your u-curve. That might show you why it isn't an impossibility, and show what it means to test it by intuitions.

Would you, right now, accept a deal with a 50-50 chance of winning $100 versus losing $50?

If you answer yes, then we know something about your u-curve. For example, over a range at least as large as (100, -50), it can be approximated by an exponential curve with a risk tolerance parameter of greater than 100 (if it were less that 100, then you wouldn't accept the above deal).

Here, I have asse...

215y

I think this greatly oversimplifies the issue. Whatever my response to the query is, it is only an estimation as to my preferences. It also assumes that my predicted risk will, upon the enactment of an actual deal, stay the same; if only for the life of the deal.
A model like this, even if correct for right now, could be significantly different tomorrow or the next day. It could be argued that some risk measurements do not change at intervals so fast as would technically prohibit recalculation. Giving a fixed metric puts absolutes on behaviors which are not fixed, or which unpredictably change. Today, because I have lots of money in my account, I might agree to your deal. Tomorrow I may not. This is what I mean by intuitions - I may think I want the deal but I may in reality be significantly underestimating the chance of -50 or any other number of factors which may skew my perception.
I know of quite a few examples of people getting stuck in high load mutual funds or other investments because their risk preferences significantly changed over a much shorter time period than they expected because they really didn't want to take that much risk in their portfolio but could not cognitively comprehend the probability as most people cannot.
This in no way advocates going further to correcting for these mistakes after the fact - however the tendencies for economists and policy makers is to suggest modeling such as this. In fact most consequentialists make the case that modeling this way is accurate however I have yet to see a true epistemic study of a model which reliably demonstrates accurate "utility" or valuation. The closest to accurate models I have seen take stated and reveled preferences together and work towards a micro estimation which still has moderate error variability where not observed (http://ideas.repec.org/a/wly/hlthec/v13y2004i6p563-573.html). Even with observed behavior applied it is still terribly difficult and unreliable to apply broadly - even to an

Example of the "unappealingness" of constant absolute risk aversion. Say my u-curve were u(x) = 1-exp(-x/400K) over all ranges. What is my value for a 50-50 shot at 10M?

Answer: around $277K. (Note that it is the same for a 50-50 shot at $100M)

Given the choice, I would certainly choose a 50-50 shot at $10M over $277K. This is why over larger ranges, I don't use an exponential u-curve.

However, it is a good approximation over a range that contains almost all the decisions I have to make. Only for huge decisions to I need to drag out a more complicated u-curve, and they are rare.

As I said in my original post, for larger ranges, I like logarithmic-type u-curves better than exponential, esp. for gains. The problem with e.g. u(x)=ln(x) where x is your total wealth is that you must be indifferent between your current wealth and a 50-50 shot of doubling vs. halving your wealth. I don't like that deal, so I must not have that curve.

Note that a logarithmic curve can be approximated by a straight line for some small range around your current wealth. It can also be approximated by an exponential for a larger range. So even if I were purely...

015y

Unfortunately the better parts of my post were lost - or rather more of the main point.
I posit that the utility valuation is an impossibility currently. I was not really challenging whether your function was exponential or logarithmic - but questioning how you came to the conclusion; how you decide, for instance where exactly the function changes especially having not experienced the second state. The "logarithmic" point I was making was designed to demonstrate that true utility may differ significantly from expected utility once you are actually at point 2 and thus may not be truly representative.
Mainly I am curious as to what value you place on "intuition" and why.

215y

Further to this, it's also worth pointing out that, to the extent that Andew's biographies and rich acquaintances are talking about a logarithmic experienced utility function that maps wealth into a mind state something like "satisfaction", this doesn't directly imply anything about the shape of the decision utility function they should use to represent their preferences over gambles.
It's only if they're also risk neutral with respect to experienced utility that the implied decision utility function needs to be log(x). If they're risk averse with respect to experienced utility then their decision utility function will be a concave function of log(x), while if they're risk loving it will be a convex function of it.
P.S. For more on the distinction between experienced and decision utility (which I seem constantly to be harping on about) see: Kahneman, Wakker and Sarin (1997) "Back to Bentham? Explorations of Experienced Utility"

For the specific quote: I know that, for a small enough change in wealth, I don't need to re-evaluate all the deals I own. They all remain pretty much the same. For example, if you told me a had $100 more in my bank account, I would be happy, but it wouldn't significantly change any of my decisions involving risk. For a utility curve over money, you can prove that that implies an exponential curve. Intuitively, some range of my utility curve can be approximated by an exponential curve.

Now that I know it is exponential over some range, I needed to figure o...

015y

It makes sense however you mention that you test it against your intuitions. My first reaction would be to say that this is introducing a biased variable which is not based on a reasonable calculation.
That may not be the case as you may have done so many complicated calculations such that your unconscious "intuitions" may give your conscious the right answer. However from the millionaires biographies I have read and rich people I have talked to a better representation of money and utility according to them is logarithmic rather than exponential. This would indicate to me that the relationship between utility and money would be counter-intuitive for those who have not experienced those levels which are being compared.
I have not had the fortune to experience anything more than a 5 figure income so I cannot reasonably say how my preferences would be modeled. I can reasonably believe that I would be better off at 500K than 50K through simple comparison of lifestyle between myself and a millionaire. I cannot make an accurate enough estimation of my utility and as a result I would not be prepared to make a estimation of what model would best represent it because the probability of that being accurate is likely the same as coin flipping.
Ed: I had a much better written post but an errant click lost the whole thing - time didn't allow the repetition of the better post.

15y6

Here's one data point. Some guidelines have been helpful for me when thinking about my utility curve over dollars. This has been helpful to me in business and medical decisions. It would also work, I think, for things that you can treat as equivalent to money (e.g. willingness-to-pay or willingness-to-be-paid).

Over a small range, I am approximately risk neutral. For example, a 50-50 shot at $1 is worth just about $0.50, since the range we are talking about is only between $0 and $1. One way to think about this is that, over a small enough range, there is

115y

How have you come to these conclusions?
For example:
Is that because there have been points in time when you have made 200K and 400K respectively and found that your preferences didn't change much. Or is that simply expected utility?

When I've taught ethics in the past, we always discuss the Nazi era. Not because the Nazis acted unethically, but because of how everyone else acted.

For example, we read about the vans that carried Jewish prisoners that had the exhaust system designed to empty into the van. The point is not how awful that is, but that there must have been an engineer somewhere who figured out the best way to design and build such a thing. And that engineer wasn't a Nazi soldier, he or she was probably no different from anyone else at that time, with kids and a family and f...

15y75

Interesting illustration of mental imagery (from Dennett):

Picture a 3 by 3 grid. Then picture the words "gas", "oil", and "dry" spelled downwards in the columns left to right in that order. Looking at the picture in your mind, read the words across on the grid.

I can figure out what the words are of course, but it is very hard for me to read them off the grid. I should be able to if I could actually picture it. It was fascinating for me to think that this isn't true for everyone.

118d

I think of myself as a good visualiser, but I found this task quite hard. I had to visualise reading each of the words about. 5 times before the whole 3x3 grid became stable and I could read it horizontally,

21y

I think my inability to image form like this is why I've always been so bad at chess.
I can really only hold an image of one word in my mind. If I want to read "God" on the top, I completely lose the second and third rows. I can also write in "Gas" in the first column and read it (barely), but the second I add the second word, everything gets blurred (abstractly). The information just... isn't there.
Despite this, I'm extremely good at mental rotations... which seems strange because it's also visual imagery. Somehow, I'm a lot better at holding a shape in my mind and rotating it, than I am at holding a grid in my mind and writing on it.
Growing up always being told how smart I was, it was kind of jarring to be so bad at a simple intelligence task like visual imagery. Chess gave me the hint - in every other game, I'd be trivially top 20% or so after just learning the rules, but in chess, I had to grind for like a 1500 ELO, and just auto-piloting, I can't even play at a 1200 level consistently.
Good life lesson I guess though.

311y

I can't, at all. And I find this extremely odd, as I've always thought of myself as someone with extremely good visual-spatial skills, and can picture and rotate quite complex objects in my mind. I can also do it if, instead of those words, they are a series of 9 numbers. I would speculate as to what's going on here, but I have no idea whatsoever.
It's been 36 hours since I last slept, so that may also have something to do with it. I'll see if I can do it after I sleep (it might have something to do with working memory, which is currently not operating at full capacity).

15y21

Picture a 3 by 3 grid. Then picture the words "gas", "oil", and "dry" spelled downwards in the columns left to right in that order. Looking at the picture in your mind, read the words across on the grid.

Interestingly, I find the task much easier if I do it the other way: visualizing the words spelled *across*, and then reading off the words going down the grid.

If mental images consist of replayed saccades, this makes perfect sense. To generate the downward images of words and then read across would reasonably be harder than ...

215y

I wonder if the ability to play blindfold chess is related to the ability to perform with exercise.

9[anonymous]15y

That is interesting. Any attempt I make to read off the grid seems to involve recreating the grid about nine times. On the other hand I have no particular difficulty mentally enumerating rapidly over character arrays.

Intelligent theists who commit to rationality also seem to say that their "revelatory experience" is less robust than scientific, historical, or logical knowledge/experience.

For example, if they interpret their revelation to say that God created all animal species separately, then scientific evidence proves beyond reasonable doubt that that is untrue, then they must have misinterpreted their revelatory experience (I believe this is the Catholic Church's current position, for example). Similarly if their interpretation of their revelation contradi...

15y0

I am struggling with the general point, but I think in some situations it is clear that one is in a "bad" state and needs improvement. Here is an example (similar to Chris Argyris's XY case).

A: "I don't think I'm being effective. How can I be of more help to X?"

B: "Well, just stop being so negative and pointing out others' faults. That just doesn't work and tends to make you look bad."

Here, B is giving advice on how to act, while at the same time acting contrary to that advice. The values B wants to follow are clearly not the ...

-115y

I don't think hypocrisy is so fundamentally different as you think. If it interferes with your other goals (e.g. by making you less rational than you need to be) then work on it, but if hypocrisy gives you warm fuzzies (which it seems do for many people) then go ahead, although you shouldn't be surprised if other people judge you (or don't trust you) because of it.

When dealing with health and safety decisions, people often need to deal with one-in-a-million types of risks.

In nuclear safety, I hear, they use a measure called "nanomelts" or a one-in-a-billion risk of a meltdown. They then can rank risks based on cost-to-fix per nanomelt, for example.

In both of these, though, it might be more based on data and then scaled down to different timescales (e.g. if there were 250 deaths per year in the US from car accidents = about 1 in a million per day risk of death from driving; use statistical techniques to adjust this number for age, drunkenness, etc.)

I've used that as a numerical answer to the question "How are you doing today?"

A: Perfect life (health and wealth) B: Instant painless death C: Current life.

What probability p of A (and 1-p of B) makes you indifferent between that deal (p of A, 1-p of B) and C? That probability p, represents an answer to the question "How are you doing?"

Almost nothing that happens to me changes that probability by much, so I've learned not to sweat most ups and downs in life. Things that change that probability (disabling injury or other tragedy) are what to worry about.

15y3

I want to be a good citizen of Less Wrong. Any advice?

1) For example, should I vote on everything I read?

2) Is it okay for me to get into back and forth discussions on comment threads? (e.g. A comments on B, B comments on A's comment, A comments on B's new comment, times 5-10) Or should I simply make one comment and leave it at that.

I am asking out of pure ignorance. not judging anything I've seen here, I just want to get advice.

315y

1) Upvoting anything unusually good or downvoting anything unusually bad is a public service, but I don't think there's a need to do it for everything.
2) No problem, that's part of the point of moving to threaded comments.

In Newcomb, before knowing the box contents, you should one-box. If you know the contents, you should two-box (or am I wrong?)

In Prisoner, before knowing the opponent's choice, you should cooperate. After knowing the opponent's choice, you should defect (or am I wrong?).

If I'm right in the above two cases, doesn't Omega look more like the "after knowing" situations above? If so, then I must be wrong about the above two cases...

I want to be someone who in situation Y does X, but when Y&Z happens, I don't necessarily want to do X. Here, Z is the extra information that I lost (in Omega), the opponent has chosen (in Prisoner) or that both boxes have money in them (in Newcomb). What am I missing?

115y

No - in the prisoners' dilemma, you should always defect (presuming the payoff matrix represents utility), unless you can somehow collectively pre-commit to co-operating, or it is iterative. This distinction you're thinking of only applies when reverse causation comes into play.

15y8

I convinced myself to one-box in Newcomb by simply treating it as if the contents of the boxes magically change when I made my decision. Simply draw the decision tree and maximize u-value.

I convinced myself to cooperate in the Prisoner's Dilemma by treating it as if whatever decision I made the other person would magically make too. Simply draw the decision tree and maximize u-value.

It seems that Omega is different because I actually have the information, where in the others I don't.

For example, In Newcomb, if we could see the contents of both boxes, then...

815y

Yes, the objective in designing this puzzle was to construct an example where according to my understanding of the correct way to make decision, the correct decision looks like losing. In other cases you may say that you close your eyes, pretend that your decision determines the past or other agents' actions, and just make the decision that gives the best outcome. In this case, you choose the worst outcome. The argument is that on reflection it still looks like the best outcome, and you are given an opportunity to think about what's the correct perspective from which it's the best outcome. It binds the state of reality to your subjective perspective, where in many other thought experiments you may dispense with this connection and focus solely on the reality, without paying any special attention to the decision-maker.

15y5

Here is a (very paraphrased, non-spoiler) snippet from the beginning of "Margin of Profit" by Poul Anderson. The problem is that the evil space aliens are blockading a trade route, capturing the ships and crew of the trading ships. The Traders are meeting and deciding what to do.

Trader 1: Why don't we just send in our space fleet and destroy them?

Trader 2: Revenge and violence are un-Christian thoughts. Also, they don't pay very well, as it is hard to sell anything to a corpse. Anyway, getting that done would take a long time, and our customers w...

115y

Good idea - I actually didn't think of them until I read this, but many of Anderson's Nicholas van Rijn and David Falkayn short stories would be good choices.

15y2

Short Story: "Margin of Profit" by Poul Anderson, along with most of the other Van Rijn / Falkayn stories (also liked "The Man who Counts"). I read them at age 14 or so, but good at any age. Fun, space adventure, puzzle/mystery. Heroes use logic and economic reasoning instead of brute force to solve "standard" space adventure problems. A great deal of humor also.

15y36

One way to train this: in my number theory class, there was a type of problem called a PODASIP. This stood for Prove Or Disprove And Salvage If Possible. The instructor would give us a theorem to prove, without telling us if it was true or false. If it was true, we were to prove it. If it was false, then we had to disprove it and then come up with the "most general" theorem similar to it (e.g. prove it for Zp after coming up with a counterexample in Zm).

This trained us to be on the lookout for problems with the theorem, but then seeing the "least convenient possible world" in which it was true.

"Act as if" might work.

For example, I act as if people are nicer than they are (because it gets me better outcomes than other possible strategies I've tried).

This also has the benefit of clearly separating action (what we can do) from information (what we know) and preferences (what we want).

From Spetzler and Stael von Holstein (1975), there is a variation of Bet On It that doesn't require risk neutrality.

Say we are going to flip a thumbtack, and it can land heads (so you can see the head of the tack), or tails (so that the point sticks up like a tail). If we want to assess your probability of heads, we can construct two deals.

Deal 1: You win $10,000 if we flip a thumbtack and it comes up heads ($0 otherwise, you won't lose anything). Deal 2: You win $10,000 if we spin a roulette-like wheel labeled with numbers 1,2,3, ..., 100, and the wheel c... (read more)

Who are "professional decision analysts?" Where do they come from, and who are their clients/employers? Do they go by any other names? This sounds fascinating.