I teach a course on Analytic Methods for Lawyers. The idea is that there are a number of subjects, such as statistics, accounting, and economics, that lawyers cannot expect to be competent in but should be familiar with. We spend a week or two on each.
Wednesday I gave a midterm. The first question was on decision theory. Such questions usually deal with an attorney trying to decide whether to settle a case or go to court, whether to hire an expert witness, and similar issues, but I decided to do something a little more interesting. And topical.
If any of you would like to take the course virtually, you will find on the course web page recordings of the lectures, power points from the last time I taught it (I'm not using them this year), and related materials.
Wednesday I gave a midterm. The first question was on decision theory. Such questions usually deal with an attorney trying to decide whether to settle a case or go to court, whether to hire an expert witness, and similar issues, but I decided to do something a little more interesting. And topical.
If any of you would like to take the course virtually, you will find on the course web page recordings of the lectures, power points from the last time I taught it (I'm not using them this year), and related materials.
13 comments:
I love it; although one dynamic that both you and Mencius Moldbug missed in your analysis of Libya is that the armed forces aren't magically or universally loyal.
Whilst being bombed from a MiG may effectively disperse a riot, there's a line between "appropriate" and "excessive" force, the crossing of which may stir dissent amongst the soldiers. Soldiers who would not hesitate to lead a cavalry charge into a riot, or fire a machine gun into a riot, would hesitate before dropping a couple of pounds of high explosive on one.
Awesome! Thank you very much, I'll have a look at your game theory presentations.
Alternative one is worth 675 million dollars if I've read the probabilities right. Holding an election and risking a coup is worth 1,500 millions. Trying to shoot the head of security services and then holding the election is worth $ 1,650 millions. (The relevant probabilities are: 25% Abdul shoots you; 45%, you shoot and win the election; 30%, you shoot Abdul, lose the election and retire.) [1]
Finally, attempting to suppress the demonstrators yields $1,100,000,000.
Thus, the optimal choice under the circumstances is to shoot Mr. al-Hakkar and subsequently hold an election.
[1] This only holds if we can retire safely after holding an election and surviving the attempted coup: but if retirement is risky (as in the first alternative) then holding an election and risking a coup is worth 1,402.5 million dollars, whereas trying to shoot the head of security is worth $ 1,552.5 millions. This doesnt change the decision, actually.
As an exercise in reading text and multiplying probabilities, it seems like a reasonable question.
As an attempt to use statistics to answer a practical question the question writer gets an F. Variance plays a huge role in these outcomes, and given that these events you cite are unlikely to be normally distributed, just multiplying out the probabilities will generate the wrong answer.
The "F" goes to neolibertarian. The questions does not deal with statistics, but with probabilities (as applied to decision theory). The concepts of variance or underlying distribution play no role.
@Gordon. As someone who works in this exact field, I'll just thank you for your wonderfully unique perspective. It's always a joy to see such unabashed enthusiasm for things one is clearly ignorant of.
Neolibertarian--could you explain your criticism of the question more precisely? I specified risk neutrality and I gave the one case where one decision (shooting Abdul) affected the probability of a subsequent event.
It's not clear to me what normal or non-normal probability distributions have to do with dichotomous events. Can you give an example of probability distributions consistent with the information provided that would change the conclusion?
"although one dynamic that both you and Mencius Moldbug missed in your analysis of Libya is that the armed forces aren't magically or universally loyal."
I don't think I mentioned the armed forces at all in the question, only the Security Services--which, so far, do seem to have remained loyal.
And I certainly did not assume that the security services were magically loyal--as you can see from the question. On the contrary.
@anonymous, I think you have a math error. Here's my take:
E[fight]=1b+100=1.1b
E[retire]=0.1*0+0.25*0.1+0.65*1b=0.675b
E[dont shoot,election]=0.5*3+0.5*(0.5*0 +0.5*1b)=1.5b+0.25b=1.75b
E[shoot,election]=0.75*(0.6*3b+0.4*1b)+0.25*0=0.75*(1.8b+0.4b)=0.75(2.2b)=1.65b
Highest is don't shoot then hold election. (Also assumed for calculations that on safe retirement after losing election)
@Neolibertarian:
here risk-neutrality is assumed, so variance is irrelevant. Another unstated assumption is EXPECTED UTILITY maximization, as opposed to non-EU framework (minimizing regret, preference for flexibility, preference for commitment etc).
Normal distribution is also irrelevant because this question uses Bernoulli distributions (obviously!).
If you're working in this field, you should be a prime candidate for taking the virtual course, unless you were an admin assistant or paralegal.
Looking over the question here are the biggest problems:
1) No standard error values which can be used to measure confidence in the estimated probabilities. This is most particularly problematic with the polling organization which *should* be providing you with at least MoE values.
2) A non-continuous set of outcomes. In the real world, you're probably going have some non-normal distribution of outcomes instead of $1B, $100K, $0.
3) The tree for this "game" is exceedingly small, and any solution is going to be biased strongly towards the "known knowns" as opposed to the "known unknowns" and the "unknown unkowns". For example, there estimate for "Win election/get killed" scenario, which in this heated situation clearly needs to be accounted for at least implicitly by using some sort of "shit happens" outcome, but preferably explicitly.
As I said originally, it's a fine exercise in multiplying out probabilies. As a basis for approaching a real world problem, it doesn't even come close to being even a valuable toy game. It has too many irrelevant details, and not enough relevant ones.
As for what I do, I develop and maintain game theory models and solvers.
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