Monday, October 31, 2011

The murderous philanthropist

Let's put on our Thought Experiment caps and consider the case of the murderous philanthropist.  Here is his MO: He finds people in need, and asks them if they would like a turn in his Strike It Rich machine.  "The machine is simple," he explains.  "You strap yourself in, and press this big red button.  With probability one half, an arm swings down and gives you a million dollars.  Otherwise, though, you are instantly and painlessly executed by the machine."

To be rich or not to be, that is the question.  You may find this horrifying or not, depending on your outlook.  It's certainly far beyond selling organs.  But here's a fact: In the real world, many people would voluntarily take the offer...

  • Perhaps people who are practically on the verge of death anyway.  
  • Perhaps people who have many friends and family members, or a really good cause they value more than their own life, that could really benefit from the money.

Or, perhaps, people who think like this: a minute from now, I will either exist or not.  If I don't exist, I won't experience anything, and I will have no preferences over anything.  I can only care about anything conditional on existing, and conditional on existing, I will be rich.

Buy it?  No?  Here, try these on for size:

  • Maybe, instead of a machine, the philanthropist offers to visit clients in the night, and either dump a million dollars over their bed or kill them quietly in their sleep.  From the perspective of subjective experience, it is true that when they wake up, they will wake up rich.
  • Or maybe the murderous philanthropist is God -- not an inappropriate title for many of his most popular incarnations, by the way -- and He plays this game on everyone's behalf before they yet exist.  In such a world, everyone who comes to exist, lives a very nice existence.  But other "entities" that have not yet attained personhood are deprived of that future.
  • Or maybe someday our civilization gains the power to revive people who died long ago.  (This one is supposed to get rid of the "murderous" part, while maintaining the prior existence of the parties involved).  Does anything change when the (not so murderous) philanthropist works his magic over the decision of who to revive now?    To continue in the vein of the thought experiment, imagine that the potentially revived souls know this will happen in advance, and have signed up for a 50-50 shot at awesome life or continued death.  Is this better or worse than reviving all of them but not giving them awesome lives?

I'm not going to argue about "the right way to think" here.  But if you feel differently about this scenario in its various incarnations, it's probably not a bad idea to think about it.  I know I have mixed feelings.  The second-to-last scenario is empirically indistinguishable from the current state of the world, and I don't know what sort of existence rule I would most prefer such a god to implement.

We care about the quality of life on this planet.  But should we care about something like the sum total of life quality across people, or something more like average life quality conditional on existing?  That is, do we prefer a bunch of people with okay lives, or do we want fewer people with better lives?

When people run a Rawlsian veil of ignorance-type thought experiment of "what kind of world would I want to live in, if I didn't yet know who I'd be," they are implicitly conditioning on existing in that world.  This is inadequate for policy decisions that affect who lives and who doesn't, unless you're comfortable with conditioning on existence.  If you're not comfortable with that, you'll have to broaden your thought experiment to include the probability of existing in the first place.  To me there's something attractive about having more people with lower average wellbeing, but more total wellbeing.  But there's also something compelling about having high wellbeing for anyone who's able to appreciate high wellbeing (i.e. anyone who exists).  In the end I think most people prefer something in between the two extremes, but at the same time, it is easy to forget that a spectrum exists, from issue to issue.  You could easily get stuck at one end by accident, if you weren't careful.

When we talk about cattle treatment, it's so critical to ask whether we'd prefer a world with fewer but happier cows, or more but worse off cows.  Almost everyone seems to condition on existence here, although one gets the sense that they haven't explicitly thought about (or even noticed) the inevitable tradeoff.

Do you have a problem with the Strike It Rich machine, while you feel no sense of obligation to unborn cows or persons?  You're not committing some sort of logical sin if your way of thinking about these things follows very different logic.  But it's something to be aware of, and perhaps curious about.  Where my answers to the above questions differ, I wonder why that is, and whether I'm really okay with it.

(Many people will say that extant people have "rights" that are not shared by nonentities.  But to lexicographically prioritize extant people seems suspicious and too-convenient.  Nor does this path lead to a complete answer, because it provides no way to rank alternatives in which different subsets of potential people exist).

Monday, October 24, 2011

The adventures of collin rose: Don't tase me bro edition!

Tony points me to this article about two tased college football players, as reported by Missoula Police Sgt. Collin Rose.

Please join me in welcoming Sgt. Collin Rose to the cast of characters here at Economonomics.  He will be taking the lead whenever we encounter a dynamic game played against one's future self.

And because I do not wish to anger the Missoula police department, if you are Sgt. Collin Rose, let me dispel any concerns&confusions you may have.  You are an object of interest only because Collin sounds like columns and Rose sounds like rows just go with it it's a game theory thing.

Friday, October 7, 2011

Jeopardy! strategy

Fellow crossworder joon pahk has now won the last 4 nights of Jeopardy! Will he sweep the week?  I will not presume my typical reader is tapped into the crossword scene, but if you were, you would probably know who joon is, and you would probably be tuning in for these nail-biters.  I must say, Jeopardy is a lot more exciting when you have someone to root for!

Anyway, I have been thinking a little bit about the game theory of Final Jeopardy betting.  If you don't know, contestants (1) learn the category of the question, (2) place bets anywhere from $0 up to all of their current money, (3) hear the question and submit their answers, after which they either gain (if correct) or lose (if incorrect) the amount of their bid.  So in FJ, you can accomplish anything from losing all your money to doubling it...and so can the other players.

As you know, I normally like Rose and Colin for my rows and columns, but let's use Joon and Franny today.  Joon has $14,200 going into Final Jeopardy, while Franny has $17,600.  To simplify this, let's talk about betting "big" or "small," by which I loosely mean betting quantities that do and don't bridge the gap between their scores.  Yes, this is casual...umm let's say betting small means betting $0 and big means betting everything. Just go with it!

Here's a breakdown of the possible outcomes:
  1. If they both bet big, Joon wins only when he's right and she's wrong.
  2. If they both bet small, Joon will never win.
  3. If Joon bets big and Franny bets small, he will win whenever he's right.
  4. If Joon bets small and Franny bets big, he wins whenever she's wrong.
Oh and we aren't done simplifying, no sir.  Let's say that the probability of getting the question right is p for both of them, and let's say those are independent (see below for more on this tho).  And let's say they only care about winning (i.e. not winnings).  Oh man.  Do you feel the powahhhhh?  You know the drill, game theory types!  We just got ourselves one of these:


What can we see from this diagram other than the fact that it is obviously scratchwork?  It shows the payoffs to Joon and Franny, i.e. their probability of winning, when they play various combinations of betting Big and Small.  [If this is complete gibberish to you and you have a powerful urge to change that...]

Unsurprisingly, the unique equilibrium is a mixed strategy.  If my algebra is correct (and that is a big if), Joon plays Small with probability r=(p^2)/(1-p+p^2), and Franny plays Small with probability q=(1-2p+p^2)/(1-p+p^2).  (Damn you Blogger for not enabling TeX!  Or maybe it is good to disincentivize math in blog posts)

Anyway, if p=.5, this works out to r=q=1/3 (they are each more likely to bet Big) and the probability of Joon winning is 1/3, not bad for someone who is behind going into the finals.  If p=2/3, we have r=4/7, q=1/7, and the probability of Joon winning is 2/7, slightly worse.  As we move toward p=0 or 1, Franny becomes heavily favored; indeed, if p=0 or 1, she can guarantee a win by betting 0 or everything, respectively.

The gameshow determines the difficulty of FJ questions and thus has control over p.  Where do they set it?


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One interesting detail ignored above: whether the contestants' answers are right or wrong is likely to be correlated.  A question can be easy or hard, and if Joon gets the answer right, it's more likely that Franny will get it right as well.  Interestingly, when Joon answered tonight but before Franny's answer had been revealed, the subjective (as perceived by me) probability of him winning momentarily fell even though he got it right!

Why?  If they both bet small, Joon has no chance.  So if Joon bets small, he needs Franny to bet big.  And if she bets big, Joon wins precisely when she answers incorrectly.  But the fact that he got the question right made it much more likely (in my mind) that Franny would get it right too!

Added: Here's an article on the events of the week.

Wednesday, October 5, 2011

Spot the Problem: Answer

The economonomadollars have been claimed; congratulations to T-Bone and TAllen, and I look forward to answering their questions. 

Below is my solution:

When you're evaluating the biological effect of a drug on HIV transmission, what matters is not the HIV transmission rate per 100 person-years.  What matters is the transmission rate per sexual encounter.  For someone deciding whether it's a good idea to take this drug, the question is how much it increases or decreases the probability of HIV transmission per encounter.  That is the fundamental biological property of this drug that the study appears to be targeting. [We might also be interested in the effect of drugs on the spread of disease, but they do not appear to be talking about that here].

The problem with letting rate per year stand in for rate per encounter is, it seems likely that people with a more effective contraceptive might just be having more sex.  Because the overall cost of sex is lower when you're using a drug that more effectively prevents pregnancy, right?  Indeed, even if the transmission rate per encounter is identical, they ought to be transmitting more HIV per person-year.

*
Anyway, this is a serious flaw in either the study or the reporting.  Either the study doesn't address it, or the writer doesn't. It seems like someone should be hired (not necessarily an economist, though an economist would do) to just sit around and point out obvious flaws in research that really matters a whole lot.  The next obvious question is, why isn't that happening?

If the problem is at the NYT (and yes, the NYT has a serious problem in this area, regardless of whether this particular article is an example of it), then it's not too hard to see why they don't hire someone to fix it. Most of their readers don't notice or care, and you can write more sensational articles for those customers if your standards are lower.

And if the problem is in research in other fields...well, it's easy to see why they might not want someone shooting down all their ideas, either...but now we can at least ask where the funding comes from.  Someone who's interested in solving big medical problems in Africa might want to hire a bunch of medical types to study these issues, together with some other guys to keep them in check.

Tuesday, October 4, 2011

Spot the Problem

Here's some excerpts from a recent NYT article.  What's wrong?  You should probably at least suspect it from the very first sentence.
The most popular contraceptive for women in eastern and southern Africa, a hormone shot given every three months, appears to double the risk the women will become infected with H.I.V., according to a large study published Monday.  
...In each couple, either the man or the woman was already infected with H.I.V. Researchers followed most couples for two years, had them report their contraception methods, and tracked whether the uninfected partner contracted H.I.V. from the infected partner, said Dr. Jared Baeten, an author and an epidemiologist and infectious disease specialist.
...The study found that women using hormonal contraception became infected at a rate of 6.61 per 100 person-years, compared with 3.78 for those not using that method. Transmission of H.I.V. to men occurred at a rate of 2.61 per 100 person-years for women using hormonal contraception compared with 1.51 for those who did not.
First person to answer correctly gets one economonomadollar ($1$).  Currently the $$ is not accepted across the US, but every fiat currency has to start somewhere. If nothing else, the American dollar can be used to pay your taxes, so to give the $$ some backing, let's say that I'm currently selling my answer to any question you might have, for $1$ per answer.  [As a disclaimer, please note that I said my answer, not the answer.  This ensures that I can always make good!]