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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, I’ll find out the cost, and if the cost is less than you are willing... (read more)
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. What is the shortest 90% confidence interval / probability interval for X, the time of guaranteed safe operation?
Frequentist 90% confidence interval: 12.1 hours - 13.8 hours
Bayesian 90% probability interval: 11.2 hours - 12.0 hours
Note: the frequentist interval has the strange property that we know for sure that the 90% confidence interval does not contain X (from the data we know that X <= 12). The Bayesian interval seems to match our common sense better.
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.
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 "How are you doing today?" For example, mine is 93% right now, as I would be indifferent between B for sure and a... (read more)
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. The next year, someone attended from the same company, and decided he was going to do the same thing. Quite early, he got minus infinity. My professor's response? "They both should be fired."
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 question you could fail the class. I did have to be sure that it wasn't a mistake, that they actually meant to put a zero on the correct answer.
If you want to try, you might want to try the Brier scoring rule instead of the logarithmic; it has a similar flavor without the minus infinity hassle.
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 distribution on NPV, and the u-curve would determine how to assign a value that represents the distribution. Some companies are more risk averse than others,... (read more)
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 assessed something about your u-curve by asking you... (read more)
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 comes up between 1 and 50. ($0... (read more)