Economic Ideas Not Well Popularized

Arrow Impossibility Theorem popularized:

Three people are on a desert island. and a treasure washes ashore. They are all self interested and untrustworthy. Only raw power thwarts them. However, at any moment any two of them can always force their will on the third.

Is there any stable distribution of the treasure? NO.

I would think efficient markets would be more difficult than Markowitz/Sharpe in the (b) category. Though they are related, they aren't the same, and people (even researchers) think efficient markets mean all kinds of things that they don't.

Thank the gods that most people don't understand "portfolio theory". The optimal portfolio is an abstraction with little connection to reality. Taleb blew it up in Fooled by Randomness.

The covariance between shares are nonstationary and prone to sudden sign changes. Plus returns have undefined variance, the normal density model isn't even close.

I am as democracy-skeptic as the next guy, but I find Arrow's theorem more interesting theoretically than practically. The problems with democratic government don't strike me as having much to do with non-satisfaction of Arrow's criteria.

There are plenty of special cases (e.g. single-peaked preferences) where majority rule satisfies all of Arrow's criteria, but even in those cases democracy still has the same practical problems as it does in the general case.

My own suggestion is for the basic concept that when you buy something, that requires someone else to have sold that thing. So at the end of the purchase, there's still the same amount of money in the economy as a whole.

@ John Goodman

I'm not an economist, so perhaps I'm wrong. But haven't you merely described Condorcet's Paradox, and not Arrow's Impossibility Theorem?

I think this is perhaps the trickiest part about Arrow's Theorem; what is the practical difference between it and Condorcet's Paradox?

@ GU

I was only asked to popularize the theorem. But I think you will find that my example meets all the core requirements of Arrow. It generalizes to as many people as you like.

Of course, the issue set is constrained. One of the things that bothers a lot of people about Arrow's Theorem is that they are not sure what set of issues it applies to. In other words, is the result a curiosity, or a problem to be expected to occur often.

I hope my example shows that the problem is always there whenever you have pure redistribution of income among (narrowly) self interested people.

How about this:

"So long as it is legitimate for government to use force to effect redistribution of material benefits – and this is the heart of socialism – there can be no curb on the rapacious instincts of all groups who want more for themselves."

Re: Arrow's Theorem.

The non-dictatorship assumption is very broad. In fact, too broad. Essentially it says the tipping vote in any election is decisive, and therefore, dictatorial. (This is not quite the same thing as saying the game has no stable core.)

Sen's follow up work on the Impossibility of a Paretian Liberal or "Liberal Paradox" makes similar mistakes.

To say the majority or winning coalition is decisive is not to say it's dictatorial. Of course, it certainly can be, but that's not itself instrinsic to every vote-taking process.

I actually think people implicitly understand portfolio theory. They just don't have the means the implement it themselves, so they use rules of thumb. Some points:
1) Recent work on Bayesian portfolio theories shows how you can start with some prior and take some views on stocks to develop a better allocation
2) Mean-variance optimization is quite sensitive to changes in expected returns. If somebody takes a prior and blends it with a view that stocks 1-5 have a 2% expected monthly return (where the average return in the prior for everything else is say 0.5%), the optimizer will tell him to create a fairly concentrated portfolio.
3) If he incorporates transaction costs or taxes into his analysis, it may (or may not) result in him avoiding the small positions that may generate frequent, unnecessary trading.

As for JPIrving, the input into optimization is expected returns and expected covariances (and there are other more advanced techniques that can take into account tail risk). If you model covariances using GARCH, then the covariances you project forward will take into account time-varying volatility.

No one doubts that a simple implementation of mean-variance optimization based on historical returns is going to create sub-optimal portfolios. After overcoming the problems, I don't think portfolio theory is so bad.

I think lay people and even many economists don't understand the counter-factual nature of most economic statements. If economists understood that they wouldn't for example be trying (like Alan Krueger) to empirically falsify the negative effect of the minimum wage on employment.

More on that here: http://mises.org/journals/jls/17_1/17_1_3.pdf

"My own suggestion is for the basic concept that when you buy something, that requires someone else to have sold that thing. So at the end of the purchase, there's still the same amount of money in the economy as a whole."

That is the simple part.

The more complex part is that the economy as a whole is richer due to every voluntary exchange.

If you sell something, you voluntarily do so only because the price is greater than your utility for that item, thus you gain wealth in the transaction.

If you buy something, you voluntarily do so only because your utility for the item is greater than the price, thus you gain wealth in the transaction.

(Where wealth=item utility+cash).

On a second note, I think that Ricardo's comparative advantage is overused in discussion of free trade, but makes more sense to teach it about specialization in general.

Got Steve? ;')

http://www.thebigquestions.com/2010/10/26/straight-arrow/

Mr. Econotarian, I agree that it's the simple part. It's just that I've run across many people who don't get the simple part when thinking about the economy as a whole.

As for comparative advantage, you might be right there. I once ran across someone who blithely asserted that trade was only good when there was a comparative advantage, if there was an absolute advantage then trade was bad.

I suggest the Miller-Modigliani Theorem and the theory of comparative advantage.

so ...are any of you clever chaps on here going to have a crack at explaining arrow's impossibility.....or are you leaving it to landsburg.