In my last post, I ridiculed the idea that the Arrow Impossibility Theorem is somehow underappreciated. Do I have an answer to Tyler Cowen's request for a hard-to-popularize result in economics, then?
Yes, I do: the Put-Call Parity Theorem, and I gave my attempt at explaining it herea while back. It's important because it reminds us that markets can phrase the same transaction in several different ways, making it hard to ban particular ones. This forces you to think carefully about exactly what kind of transaction you want to prohibit when you say that e.g. options trading, fractional reserve banking, etc. should be illegal.
A blog by Silas Barta
Tuesday, October 26, 2010
Setting Arrow's Impossibility Theorem Straight
Okay, by now, you might have noticed the econ blogosphere cooing over how awesome and insightful and useful the Arrow Impossibility Theorem is: Here, here, here, here, and here (in random order).
Um, to put it mildly ... no.
First, a summary of the theorem: let's say you want to convert individual preference rankings over outcomes into a social preference ranking that faithfully reflects these individual preferences as best as possible (i.e., create a voting system). You place a few "obvious" constraints on it that it voting system should meet, and it turns out -- you can't! Boo hoo, democracy sucks. (Well, in many senses, it does ... just not for this reason.)
This issue was discussed almost exactly one year ago on LessWrong. Long story short, the result has much less practical application than you might think. The requirements it asks of an aggregation system are far too strict. For one thing, the "determinism" requirement rules out the use of randomized tie-breakers. Keep in mind, there's always the possibility of some hopeless tangle involving a preference ordering like:
Person 1: A > B > C
Person 2: B > C > A
Person 3: C > A > B
Such preferences are completely intransitive, so no method of aggregation has any hope of being faithful. Normal people react to this by saying, "Okay, in the occasional pathological case, just use some tie-breaker that's not slanted in favor of any option -- in the end, it all averages out, so no problem". But Arrow's Theorem throws up its abstract arms and says, "Gosh, how hopeless. You can never satisfactorily aggregate preferences. Look how insightful I am!"
Needless to say, "We are not impressed."
It gets better though. "Black Belt Bayesian" makes the point that the "independence of irrelevant alternatives" (IIA) requirement is undesirable in the first place. (IIA means basically, if you remove some option, it should not change the aggregated ordering of the remaining options.) Why is it undesirable? Because so-called "irrelevant alternatives" aren't. Rather, they give evidence about the relative _strengths_ of preferences and therefore SHOULD affect the aggregated preference ordering!
Why was the econ blogosphere talking about Arrow's Theorem in the first place? Because someone had asked about underappreciated ideas in economics. Well, I think it's clear by now that this one doesn't suffer from a lack of deserved appreciation.
But what's even worse is that Amartya Sen's celebrated Liberal Paradox is viewed as a corrolary to the Arrow Theorem, and is just as ridiculous. It basically says you can't *both* respect people's rights *and* achieve Pareto optimality. Now, how do you imagine that works out? Well, you cheat by equating rights with obligations -- that is, you eliminate the possibility of people waiving a right when it's infringement would make everyone -- everyone -- weakly better off.
But who cares about that case? Not me. The very reason that rights allow for Pareto-optimality is because people can trade them as necessary when they find welfare-improving opportunities! If you equate "property rights in a specific apple" with "the obligation never to trade the apple away" ... well, you kinda throw a kink in all that.
As I said a year ago, if a transaction really is Pareto-efficient, then rights won't get in the way, because the relevant parties will waive the relevant rights! (Epic tongue-twister, too.)
Reassuringly, the folks on the opposite end of the ideological spectrum from me come to the same conclusion.
So are we set straight now?
Um, to put it mildly ... no.
First, a summary of the theorem: let's say you want to convert individual preference rankings over outcomes into a social preference ranking that faithfully reflects these individual preferences as best as possible (i.e., create a voting system). You place a few "obvious" constraints on it that it voting system should meet, and it turns out -- you can't! Boo hoo, democracy sucks. (Well, in many senses, it does ... just not for this reason.)
This issue was discussed almost exactly one year ago on LessWrong. Long story short, the result has much less practical application than you might think. The requirements it asks of an aggregation system are far too strict. For one thing, the "determinism" requirement rules out the use of randomized tie-breakers. Keep in mind, there's always the possibility of some hopeless tangle involving a preference ordering like:
Person 1: A > B > C
Person 2: B > C > A
Person 3: C > A > B
Such preferences are completely intransitive, so no method of aggregation has any hope of being faithful. Normal people react to this by saying, "Okay, in the occasional pathological case, just use some tie-breaker that's not slanted in favor of any option -- in the end, it all averages out, so no problem". But Arrow's Theorem throws up its abstract arms and says, "Gosh, how hopeless. You can never satisfactorily aggregate preferences. Look how insightful I am!"
Needless to say, "We are not impressed."
It gets better though. "Black Belt Bayesian" makes the point that the "independence of irrelevant alternatives" (IIA) requirement is undesirable in the first place. (IIA means basically, if you remove some option, it should not change the aggregated ordering of the remaining options.) Why is it undesirable? Because so-called "irrelevant alternatives" aren't. Rather, they give evidence about the relative _strengths_ of preferences and therefore SHOULD affect the aggregated preference ordering!
Why was the econ blogosphere talking about Arrow's Theorem in the first place? Because someone had asked about underappreciated ideas in economics. Well, I think it's clear by now that this one doesn't suffer from a lack of deserved appreciation.
But what's even worse is that Amartya Sen's celebrated Liberal Paradox is viewed as a corrolary to the Arrow Theorem, and is just as ridiculous. It basically says you can't *both* respect people's rights *and* achieve Pareto optimality. Now, how do you imagine that works out? Well, you cheat by equating rights with obligations -- that is, you eliminate the possibility of people waiving a right when it's infringement would make everyone -- everyone -- weakly better off.
But who cares about that case? Not me. The very reason that rights allow for Pareto-optimality is because people can trade them as necessary when they find welfare-improving opportunities! If you equate "property rights in a specific apple" with "the obligation never to trade the apple away" ... well, you kinda throw a kink in all that.
As I said a year ago, if a transaction really is Pareto-efficient, then rights won't get in the way, because the relevant parties will waive the relevant rights! (Epic tongue-twister, too.)
Reassuringly, the folks on the opposite end of the ideological spectrum from me come to the same conclusion.
So are we set straight now?
Wednesday, October 20, 2010
A great chance to meet Silas in person!
Since I currently live in a small, remote town, I don't get many chances to meet my readers. But I'll be spending my vacation time this year in New York City, from Oct. 30 (my birthday!) to Nov. 21. I'll be staying in an internet friend's apartment in lower Manhattan and visiting a lot of my like-minded internet friends -- for all of them, it will be the first time I meet in person.
So, if you live anywhere in that general vicinity and want to meet me, now's your chance! Give me a shout, either by email or in the comments, and we'll work something out.
Also, advice for a non-NYCer for navigating this rough city will be quite welcome.
So, if you live anywhere in that general vicinity and want to meet me, now's your chance! Give me a shout, either by email or in the comments, and we'll work something out.
Also, advice for a non-NYCer for navigating this rough city will be quite welcome.
Monday, October 11, 2010
Today, I smack myself
An idea occurred to me after reading Bob Murphy's overpromised book on infinite banking, which carries the wonderful insight that if you save a lot, you can "borrow" from yourself on favorable terms -- oh, and that's also true if you save through a whole-life insurance plan.
But the real insight is in how much of your money (if you're a typical debt-carrying mouth-breather) goes to financing costs that could be avoided if you simply saved before a purchase, which was backed by some surprising examples.
Now, that doesn't do much for my finances because I'm a big saver. But it dawned on me: even if I'm not a big borrower, employers are, including and especially mine. So if I'm not living paycheck-to-paycheck, then they and I could work out a deal whereby they defer my salary payments (effectively taking a loan from me) and pay me interest much greater than I could get on savings (0%), but much lower than they would pay the financial markets (all costs considered, probably 30+%). Everyone wins.
But how many workers actually want to do something like that? No, it's too bizarre, so alas, I suffer again from being the rare saver...
And that's when I smacked myself -- they've had a program that lets me do that the whole time! They call it the employee stock purchase program, and it lets you set aside money so that at pre-defined six-month intervals you can buy company stock at a 15% discount to its current value, and yes, you can sell it immediately. I never bothered because I figured there was some catch to it that I never fully researched, even as those who used it assured me there's not.
Using the program, if you set aside money, buy at a discount, and immediately re-sell, you get an effective annual return of 38%! (Actually, higher, because the money wouldn't all be "invested" at the beginning of the six-month period.) I had just never realized what this was for the whole time! Stupid, stupid, stupid...
Oh, and there's a severe thunderstorm going on right now.
But the real insight is in how much of your money (if you're a typical debt-carrying mouth-breather) goes to financing costs that could be avoided if you simply saved before a purchase, which was backed by some surprising examples.
Now, that doesn't do much for my finances because I'm a big saver. But it dawned on me: even if I'm not a big borrower, employers are, including and especially mine. So if I'm not living paycheck-to-paycheck, then they and I could work out a deal whereby they defer my salary payments (effectively taking a loan from me) and pay me interest much greater than I could get on savings (0%), but much lower than they would pay the financial markets (all costs considered, probably 30+%). Everyone wins.
But how many workers actually want to do something like that? No, it's too bizarre, so alas, I suffer again from being the rare saver...
And that's when I smacked myself -- they've had a program that lets me do that the whole time! They call it the employee stock purchase program, and it lets you set aside money so that at pre-defined six-month intervals you can buy company stock at a 15% discount to its current value, and yes, you can sell it immediately. I never bothered because I figured there was some catch to it that I never fully researched, even as those who used it assured me there's not.
Using the program, if you set aside money, buy at a discount, and immediately re-sell, you get an effective annual return of 38%! (Actually, higher, because the money wouldn't all be "invested" at the beginning of the six-month period.) I had just never realized what this was for the whole time! Stupid, stupid, stupid...
Oh, and there's a severe thunderstorm going on right now.
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