Message in a Bottle

Friday, December 01, 2006

Mesage in a Bottle is dead

Obviously. My new blog is Yet another Sheep.

Tuesday, July 20, 2004

Yet another Probability Paradox

Brian Weatherson from Thoughts, Arguments and Rants has just reminded us of the wonderful Monty Hall Problem. Here is a even stranger problem, taken from Raymon Smullyians wonderful Satan, Cantor and infinity: The Two Envelope Paradox. It goes like this: There are two envelopes, one contains twice as much as the other envelope. You see no difference between them from the outside. You choose one envelope and open it, it contains X>>0 dollars. Now you can either keep the money in that envelope or take the money from the other envelope. You are assumed to be risk averse, only caring for the expected amount of money you can get from a decision.

According to one train of thought, you should choose the other envelope since it contains 2X$ with a probability of 0.5 and 0.5X$ with the same probability. That gives you an expected net gain of 3/4X$, a strictly positive sum. Maybe you are convinced now, but there is another train of thought. Suppose you would have chosen the other envelope. You still would want to choose another envelope according to the argument above. But that means the new information you got doesn't influence your decision in any way. So why is that different from the initial position, where you could have chosen any envelope? So it doesn't matter whether you choose the other envelope or not.

The Baysian solution is very simple: You must first have a (subjective) probability distribution and calculate the expected gain of changing afterwards, which will probably lead to other probablities of the higher amount being in the other envelope than 0.5. A analysis for people with a background in basic probability heory can be found here.

Sunday, July 04, 2004

On the Popularity of Verificationism

Verificationism is generally believed to be dead, but is it? Samir Okasha thinks not. Here is a quote from his paper Verificationism, Realism And Scepticism, Erkenntnis Volume 55, Issue 3, Dec 2001, p 371-385:

According to the standard textbook account, verificationism is a doctrine that was popular back in the days of logical positivism. The positivists promised us a ‘verifiability criterion of meaningfulness’ which would help to distinguish ‘cognitively significant’ discourse from nonsense, but despite their best efforts, no workable criterion was ever produced. This led to verificationism being thoroughly discredited and consigned to the philosophical scrap-heap, along with most of the other doctrines characteristic of logical positivism.

Now this story is only partially accurate. For it ignores the fact that verificationist ideas, in one form or another, continue to find adherents among contemporary philosophers. Quine, Putnam and Dummett, to pick the three best-known cases, are all openly sympathetic to the basic verificationist idea that the content of a statement is closely tied to what would count as evidence for its truth. None of these philosophers believes in the ‘criterion of meaningfulness’ that the positivists hankered after, but the spirit of verificationism lives on in their work. Due in large part to the interest generated by Putnam’s and Dummett’s writings, verificationist ideas have enjoyed something of a resurgence in recent years, though not always under that name. In this paper, I examine one of the factors that lies behind the continued appeal of verificationism.

In contemporary discussions, verificationist ideas usually surface byway of opposition to some form of realism. Putnam explicitly contrasts his version of verificationism – which he calls ‘internal realism’ – with a position called ‘metaphysical realism’. Metaphysical realism holds that truth is a ‘radically non-epistemic’ notion, with no conceptual connection to justification or warranted assertion, while internal realism holds that truth is warranted assertibility in the ideal limit. Similarly Dummett contrasts the realist view that meaning is to explained in terms of ‘evidence transcendent’ truth-conditions, with his own anti-realist view that meaning should be explained in terms of verification-conditions, which cannot transcend our ability to detect them. For Putnam, Dummett and others, realism provides the foil for the development of their verificationist viewpoints.

Sunday, June 27, 2004

What is the argument for free trade?

What does it mean, in the language of theory, to say that free trade plus transfers pareto dominates autarky? I guess the formal proof would simply employ the following steps:

1. Assume that the aggregate production of the "world economy" is the sum of the individual aggregate production sets, so that the technological possibilities remain the same.

2. Since the autarky production and consumption plans are still feasible, one can simply employ one of the standard proofs for the existence of individual rational pareto efficient allocations, that is allocations where nobody would lose.

3. By the second welfare theorem we can support such an allocation by a price system.

Voila!

I'm pretty sure this is the correct formulation of the standard view found in undergrad microeconomics textbooks. But isn't it widely agreed that it is impossible to actually do the lump sum transfers required by the second welfare theorem? So what is the real case for free trade, if there is one?

Saturday, June 26, 2004

Will the real John Rawls please stand up?

Brad de Long thinks that Rawls somewhat contractarian argument doesn't work:
Indeed. I never understood the cult of Rawls. His arguments seemed to me to have only one thing going for them at Harvard around 1980: they were less sloppy, more careful, and informed by a much less niggardly will than those of Robert "Anarchy, State, and Utopia" Nozick. I didn't understand why Rawls's arguments were supposed to be so powerful. And the thought of majoring in political philosophy in Rawls's shadow seemed distinctly unappetizing.

Perhaps my problem was that I read Hume's "Of the Original Contract" when I was too young. I found Hume's arguments unanswerable: given that the questions of whether one has an obligation to fulfill various political and personal contracts are so knotty, it seemed simply absurd to try to base all political obligation on one's being a supposed party to a contract that one never even made. I could never even figure out how Rawls could flower in the shadow of Hume.

He follows by "quoting" the complete text by Hume. The impatient reader may consult this shortened version of the somewhat lengthy argument: "What contract? I haven't signed anything!". The problem isn't that Brad de Long read Hume, his problem is not having read Rawls. What Rawls did was essentially desingning a clever counterfactual thought experiment in which people would choose, not biased in any way, moral out of being rational, not out of being nice. A contract made under such circumstances would serve as good moral system and can therefore be used to justify moral rules. The details of the experiment are explained here by Fred D'Agostino.

Thursday, June 24, 2004

How to measure media bias?

Tim Groseclose and Jeff Milyo have a paper on media bias. Their way of measuring media bias goes as follows. They used a ranking of the voting records by a liberal lobbying group, ADA, to measure how liberal the members of house and senate are. Then they looked at what think tanks were cited by these persons and used that information to grade how liberal these think tanks are. Now they looked for what media outlet cites what think tank how often and get their measure of media bias that way. Robert Barro has written a popular article on the findings. Patterico thinks the paper gives support to his prejudices. Sadly, the very conservative Hoover Institution, where Barro is a senior fellow, wasn´t ranked.
I personally have another interpretation for this media bias: Bushs economic policies are horrible, so that liberals have good reasons to quote moderate think tanks like the Center on Budget and Policy Priorities to make a point...


Sunday, June 20, 2004

Terry Jones wouldn't torture his Son

Python Terry Jones shows his relief that he wasn't torturing his son when he tried a lot of stuff to find out what his son does after choir practice:
GuardianUlimited:I tried starving him, serving him only cold meals and shaving his facial hair off, keeping him in stress positions, not turning his light off, playing loud music outside his cell door - all the usual stuff that any concerned parent will do to find out where their child is going after choir practice. But it was all to no avail.

I hesitated to gravitate to harsher interrogation methods because, after all, he is my son. Then Donald Rumsfeld came to my rescue.

I read in the New York Times last week that a memo had been prepared for the defence secretary on March 6 2003. It laid down the strictest guidelines as to what is and what is not torture. Because, let's face it, none of us want to actually torture our children, in case the police get to hear about it.

The March 6 memo, prepared for Mr Rumsfeld explained that what may look like torture is not really torture at all. It states that: if someone "knows that severe pain will result from his actions, if causing such harm is not his objective, he lacks the requisite specific intent even though the defendant did not act in good faith".

What this means in understandable English is that if a parent, in his anxiety to know where his son goes after choir practice, does something that will cause severe pain to his son, it is only "torture" if the causing of that severe pain is his objective. If his objective is something else - such as finding out where his son goes after choir practice - then it is not torture.

Who would have thought that Rummy would revolutionize pedagogy?

Saturday, June 19, 2004

Teach your Kids Macro!

No matter wether you want to raise your kids to be keynsians or new classical macroeconomists, lack of appropriate resources is no excuse:

Paul Krugman 1998, Baby-Sitting the Economy

Rober Lucas 1988, What Economists do

Monday, June 14, 2004

The Good, The Bad and The Ugly

Foreign Policy and the Center for Glogal Development have made an index of how much rich nations do for the poorer parts of the world:
The second annual CGD/FP Commitment to Development Index ranks 21 rich nations on how their aid, trade, investment, migration, environment, security, and technology policies help poor countries. Find out who’s up, who’s down, why Denmark and the Netherlands earn the top spots, and why Japan—once again—finishes last.

The article can be found here.

Tuesday, June 08, 2004

Reagan, Volcker and lots of Inflation

Brad De Long reminds us that Reagans policies weren´t exactly making Volckers job easier
The dominant opinion among macroeconomists is (and for two and a half decades has been: see Sargent and Wallace, "Some Unpleasant Monetarist Arithmetic") that Reagan made Volcker's task of reducing inflation not easier but harder and more costly: the Reagan budget deficits made people worry that the U.S. government might decide to inflate away America's rapidly growing debt, and made it more difficult and expensive for the Federal Reserve to earn the necessary confidence that its low-inflation policies were for real and would be sustained.

Here is what Sargent and Wallace say in their paper:
On the other hand, imagine that fiscal policy dominates monetary policy. The fiscal authority independently sets its budgets, announcing all current and future deficits and surpluses and thus determining the amount of revenue that must be raised through bond sales and seignorage. Under this second coordination scheme, the monetary authority faces the constraints imposed by the demand for government bonds, for it must try to finance with seignorage any discrepancy between the revenue demanded by the fiscal authority and the amount of bonds that can be sold to the public. Although such a monetary authority might still be able to control inflation permanently, it is less powerful than a monetary authority under the first coordination scheme. If the fiscal authority's deficits cannot be financed solely by new bonds, then the monetary authority is forced to create money and tolerate additional inflation.

Sunday, June 06, 2004

Who cares about Plagiarism?

I just stumbled over this wonderful post by Kieran Healy on the various types of plagiarizing, familiar to anyone to have ever graded term papers and essays. What I wonder is wether people with no intent to ever go to work in academia see plagiarism as something to be condemned. Plagiarism is a basically a threat to a system most students don´t feel to be a part of. It seems like in academia too the modes of production bring their own superstructure...

Added: Here is another good reference on plagiarism by Mark Steen.

Can there be nonsense in mathematics?

One might think that in the area of mathematics people don´t make any absurd claims. But there seems to be a group of people, many of them employed in academia, that is attacking the simplest theorems of set theory. Not out of some philosophical view on what kind of proof methods are legitimate, but a belief that set theory is simply wrong. So they write papers "proving" that no infite set is countable or that the reals are countable. How do such people manage to avoid contact with logic?