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WalMart does not issue loyalty’ cards. Why not? Other retailers, like Safeway, do. They are not literally loyalty cards since they do not induce holders to concentrate their purchases with a particular retailer. They do allow the retailer to track purchases by household. Why would WalMart choose to forgo that information?

Racial and ethnic profiling of airline passengers is back in the news again. The argument in favor  is that it would be costly to mount a careful examination of all airline passengers. Assuming that such profiling is effective, it means that the costs of the acquired safety benefits are borne by a subset of the population. There is a way to redress this inequity. A profiling tax charged to all passengers. Proceeds from such a tax are paid to those who are profiled. Clearly, there are implementation issues but………..

I take it as self-evident and undisputed that when a group of eminent economists sign a letter endorsing the health care bill, the subtext of their message is that the issue is part of their scientific expertise and that they have studied the details sufficiently to deliver their professional opinion: This is the only way to interpret the fact that the undersigned are all economists, and that their academic position is mentioned in the letter. This is why their advice should carry more weight than the advice of an unknown blogger. If this advice is followed and the bill passes, then some of their professional reputation is tied with its success.

What is perhaps more disputable, but still true in my view, is that even this group of most distinguished economists don’t have individual reputations, and that they are drawing from and contributing to a collective reputation pool of the entire profession. The people of this (or any other) country, who are the audience of this letter, don’t distinguish between different scholars of the same discipline. Public trust in the entire profession is determined by the success of the predictions and policy advices of its members.

Following the death of Paul Samuelson, I looked at his seminal paper Proof that properly anticipated prices fluctuate randomly’. I found it intriguingly related to my beloved puzzlement about the meaning of probability, and I have something to say about it. Since I didn’t look at the forty-five years of literature that followed this paper I am probably going to flaunt my ignorance in public, but this is just a blog so what harm can it do.

The purpose of Samuelson’s paper is to formalize the intuition that competitive prices must, in some sense, look like random walk: Let ${\dots,X_{t-1},X_t,X_{t+1},\dots}$ be a stochastic process that represents the spot price of some product, say wheat: ${X_t}$ is the price in which you can buy wheat at day ${t}$. Fix a day ${T^\ast}$ and let ${Z(t)}$, for ${t\leq T^\ast}$, be the price at day ${t}$ of a contract that requires the delivery of wheat at day ${T^\ast}$. Samuelson proves the following theorem:

Paul Krugman breaks down his hate-mail box

Nothing gets me as many crazed emails and comments as any reference to climate change. The anti-global-warming people are just filled with hate for anyone who suggests that maybe, just maybe, the vast majority of scientists are right.

Since Krugman doesn’t read this blog I can safely offer him a challenge — Give me one example in which your writing about global warming suggested that maybe, just maybe’ the vast majority of scientists are right.
More likely whatever you have ever written about this issue suggests that for certainty, real certainty, the vast majority of scientists are right about human-made global warming and its long-run consequences and that everybody who says differently  is a flat-earther idiot.

Just got to Paul Krugman’s criticism of Economics in the Sunday New York Times magazine. Members of the profession are excoriated for being beguiled beyond the bounds of decency by mathematics. Groan! Why do mid-life crisis always lead to proclamations that theory is dead? The militantly middle of the road columnist David Brooks has also joined in while promoting the behavioral cause. I suppose being middle of the road is hard since one has to avoid oncoming traffic in both directions.

These and other criticisms brought to mind Capra’s series of WWII films, Why We Fight.’ They were conceived to convince an isolationist nation about the need to fight the Nazis. No, I’m not comparing the atheoretical unwashed to the Nazi’s. But it did inspire a desire to take up my puny cudgels in defence of mathematical modeling. Herewith, 3 of the usual objections to quantitative models and responses.

Objection #1: Not everything can be reduced to numbers.

True. But a great deal of importance can.

Objection #2: Workable Quantitative models cannot capture the complexities of real life.

So what? The question is not whether a particular quantitative model accurately represents reality but whether there is an alternative model that is more accurate. How do we know that a decision arrived at by what we are pleased to call instinct, intuition or experience has really acknowledged all the complexities of reality? Indeed, one of the beauties of quantitative models is their explicitness. Like Cromwell’s portrait they appear warts and all.

Simple quantitative models frequently provide profound qualitative insights into the process being modeled. Thus, one may wish to build a model not so much to decide what to do, but to test and refine ones intuition about what is going on.

Objection #3: Quantitative models ignore the context.

Yes. However, there is no law that obliges one to follow the recommendations of a quantitative model that is not appropriate to the context. Second, ignoring the context can be a good thing because the context of the decision is irrelevant. A quantitative model often captures the essence of a decision, say, the choice between a gamble and a sure thing. It does not matter whether the context is the stock market, a medical diagnosis or wildcatting. This allows for the transfer of insight from one setting to another.

One of my favorite game theoretic insights is that rational players should not play chess: The outcome is already determined at the beginning of the game. This is what’s usually called Zermelo’s Theorem, but it is a common rant among game theorists that this is a misattribute. Zamir, Maschler and Solan, for example, in their recent game theory textbook credit the theorem to von-Neumann, citing his minimax paper. Following a conversation with David Schmeidler, who suggested that Zermelo might have used this theorem but didn’t make a fuss over it because it’s so trivial, I decided to look at Zermelo’s paper myself. This is possible thanks to translation from German by Ulrich Schwalbe and Paul Walker.