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17 years ago the Clay Institute announced 7 Millennium problems and offered $1 million for the solution to each.  To date, only one has been solved. It suggests that the supply (of mathematical attention) has not increased to meet demand. Therefore, the value of the prizes are to low. Why might the current value of the  prize prolong the time it takes to obtain a solution? Suppose, two agents, each in possession of an idea that in combination would produce the sought after solution. Neither agent has an incentive to reveal what they know, for fear that the other will build upon this to earn the prize. Pooling their efforts means splitting the prize. Thus, one has a familiar trade-off. Laboring alone delays the reward but it is unshared. Teaming up, accelerates the reward but it must be shared.

 

 

Is a question I thought as dead as a Dodo.  When I came upon it in an undergraduate philosophy of science class  the drums had been muffled and the mourners called. Nevertheless, there are still those who persist in resuscitating the corpse (see here for a recent example) and those, who for noble reasons, indulge them by responding.

There were, and are two good reasons for why this question should be left to rot in peace. The first is that the comparisons made to arrive at a demarcation are problematic. If Science were a country, Physics might be its capital. If one were to ask whether History is a Science, the customary thing to do is to measure the proximity of History to Science’s capital city. Why proximity to the capital and not to one of its outlying settlements like Geology and Archaeology? The second, better reason, is that the question, `is X a science?’ is of interest only if we believe that scientific knowledge should be privileged in some way. Perhaps it alone is valid and useful while nonscientific knowledge is not. If that is the case, the correct question should not be whether X is a science, but whether X produces knowledge that is valid and useful. Now we have something interesting to discuss: what constitutes useful or valid knowledge?

One might point to accurate prediction, but this alone cannot be the touchstone. How would we feel about the laws of Newtonian motion if we came upon them via regression? I suspect many of us would find such a theory to be incomplete, not least because of the concern with out of sample prediction. By the way, if you think this outlandish, I first learnt Newton’s laws by sending little carts down inclines with bits of ticker tape attached to them to so that we might, by induction, learn a linear relationship between velocity and acceleration. Truth be told, the Physics was sometimes lost in the enormous fun of racing the carts when the master’s back was turned. What if prediction is probabilistic rather than deterministic? In earlier posts on this blog you will find lengthy discussions of the problems associated with evaluating the accuracy of such predictions. I mention all this to hint at how difficult it is to pin down precisely what constitutes useful, reliable or valid knowledge.

An unintentionally amusing missive by Marion Fourcade, Etienne Ollion and Yann Algan’s discovers that the Economics profession is a self perpetuating oligarchy. This is as shocking as the discovery of gambling in Casablanca. Economists are human and respond to incentives just as others do (see the Zingales piece that makes this point). Are other disciplines free of such oligarchies? Or is the complaint that the Economist’s oligarchy is just order of magnitudes more efficient than other disciplines?

The abstract lists three points the authors wish to make.

1) We begin by documenting the relative insularity of economics, using bibliometric data.

A former colleague of mine once classified disciplines as sources (of ideas) and sinks (absorbers of them). One could just as well as describe the bibliometric data as showing that Economics is a source of ideas while other social sciences are sinks. if one really wanted to put the boot in, perhaps the sinks should be called back holes, ones from which no good idea ever escapes.
2) Next we analyze the tight management of the field from the top down, which gives economics its characteristic hierarchical structure.

Economists can be likened to the Borg, which are described by Wikipedia as follows:

“….. the Borg force other species into their collective and connect them to “the hive mind”; the act is called assimilation and entails violence, abductions, and injections of microscopic machines called nanoprobes.”

3) Economists also distinguish themselves from other social scientists through their much better material situation (many teach in business schools, have external consulting activities), their more individualist worldviews, and in the confidence they have in their discipline’s ability to fix the world’s problems.

If the authors had known of this recent paper in Science they could have explained all this by pointing out that Economists are wheat people and other social scientists are rice people.

Its not: why haven’t I one won? I have. A sixth form science prize. In my salad days I would day dream about winning the big one (to the sound of Freddy Mercury crooning `We Are The Champions’). But, one ages and comes to term with one’s mediocrity.

In the good old days, when men were men and sheep were nervous, prizes were awarded for accomplishing particular tasks. The French academy of sciences, for example, established in 1781, I think, a system of prizes or contests. A committee would set a goal (in 1766 it was to solve the 6 body problem, in 1818 it was explain the properties of light) and submissions judged after a deadline and a prize, if merited, awarded. One sees that today with the X -prize and the Clay prize. The puzzle with these prizes is would the challenge they highlight not be undertaken in their absence? For example, resolving P = NP has been around well before the Clay prize and many a bright young thing had already given it serious thought.

Many prizes are `achievement’ awards, given out in recognition of a great accomplishment after the fact. Some are awarded by learned societies and named in honor of an ancient worthy (Leibniz, Lagrange, Laplace etc.) Others are funded by private individuals (Nobel, Nemmers, Simons etc.).

Some learned societies have a surfeit of prizes (Mathematics) that are concentrated in the hands of a few. Indeed, one might be able to construct a partial order of the prizes and come to the conclusion that some prize X can only be awarded provided prize Y has already been secured. Once again, there is the incentive question. It is hard to imagine the prize winner strives and continues to do so in the anticipation of winning further prizes. If the purpose of the prize is to honor the work (rather than the individual) why give the $$’s to the individual? Perhaps better to take the $$’s, divide them up and hand it to junior researchers in the same area telling them they have received it in honor of X, a pioneer of the field.

Other learned societies have very few prizes (American Economic Association). There is the Clark medal (famous), Walker medal (discontinued after Nobel), Ely Lecture and the Distinguished Fellow (who?). No doubt, this is a great comfort for the members’ status anxiety. Although I have it heard it said that a paucity of awards can adversely affect a discipline in that it lessens its members chances of securing grants. No doubt this is why some learned societies have prizes for every age group and speciality one can imagine: best under 40 in applied nobble nozing theory.

Why do private individuals fund prizes? Nobel is the archetype. Is it a way to purchase reflected glory? The founders of Facebook and Google are famous in their own right, so it is hard to see how a prize will burnish their images. Perhaps they genuinely wish to support research into topic X. One can easily imagine more effective ways to do this via grants, fellowships and conferences. Indeed, both the Kavli and Simons do just this (in addition to handing out prizes). Perhaps its advertising. If one wishes to publicize the importance of some field, does awarding a generous prize buy more publicity than a simple advertisement or cultivating journalists? Unclear. How many have heard of the recent `breakthrough’ prizes?

On August 24th an airplane of a national Chinese carrier came down well short of the runway while attempting a night landing in Yichun airport, northeast China. 42 people were killed, 54 injured. China makes an inquiry about this unfortunate event, and some heads will be cut. But this is not the topic of this post.

Keith Bradsher reports at the New York Times that “China’s top leaders have given aviation regulators a clear mandate to make safety their top priority and told the chief executives of the nation’s airlines that they would be held personally responsible for any crashes, Mr. Harbison [chairman of the Center for Asia Pacific Aviation in Sydney, E.S.] said.”

So, any crash whatsoever is the personal responsibility of the chief executives of the nation’s airlines. The word that made me raise my eyebrow is “ANY” that appears at the beginning of the sentence. Suppose that a mechanic did something which is against regulations, or a pilot played PacMan during flight, even though he knows it is against regulations, or a pilot had a heart attack during flight. Any crash is the personal responsibility of the carrier’s CEO, period.

Suppose that you are a CEO of a national carrier. What will be the effect of this governmental announcement on your performance? And how will this announcement change the quality of people who choose to be CEO’s? Did policymakers in China thought of these issues? Or maybe there is difference in language, and the meaning of “any” in Chinese is different than in English or Hebrew?

Part One: Least Unique-Bid Auctions

In recent years a new auction method became widely used on the internet. This method is called Least Unique-Bid Auction, and it goes as follows. An object is offered for sale, say an iPhone or a car. The bids are made in cents. Each participant can make as many bids as he or she wishes, paying 50 cents for each bid. So if I bid on the numbers 1, 2, 5 and 12 (all in units of cents), I pay 2 dollars for the participation. Once the time runs out and all bidders placed their bids, one counts the number of bidders who bid on each number. The winning bid is the minimal number that was bid by a single bidder. This bidder is the winner, and he pays his bid (in cents). So, if Anne bid on the numbers {1,2,3,6,12}, Bill bid on the numbers {1,2,3,4,5,6,7}, and Catherine bid on the numbers {3,4,5,7,13, 14,15,16}, then the number 12 wins, and Anne gets the object. The auctioneer gets 2.5 dollars from Anne for her 5 bids plus 12 cents which is her winning bid, he gets 3.5 dollars from Bill, and 4 dollars from Catherine.

In practice the auction is dynamic and not static; for each bid that you place, you know at each time period whether (a) it is currently the winner (no one else bid the same number, and there is no lower number that was bid by a single bidder), (b) it is a potential winner (no one else bid the same number, but there is at least one lower number that was bid by a single bidder), or (c) not a potential winner (somebody else also bid on that number).
One must admit that this type of auction is ingenious. The selling price is extremely low, usually less than 2% of the object’s market value, so people are drawn to participate. The names of the winners are listed on the site; there are recurring names. So people realize that there are strategies that profit. One can actually think of such strategies: for example, randomly choose numbers, and when you find a potential winner bid on all numbers below it, trying to kill all lower potential winning numbers. So why not participate and make money?
Bottom line: the auctioneer makes a lot of money.

Part Two: LUBA and the court

A couple of months ago a lawyer called me. He wants to sue a company that operates a certain type of LUBA in Israel on a class action, on the ground that this is a lottery, a gambling game, and not an ability game. By law, in Israel only the state can run lotteries. He asked me to provide an expert opinion that LUBA is a lottery. I apologized. I cannot do that. I believe that strategic bidders can make money in LUBA, and therefore, just as black-jack, LUBA is not a lottery. In fact, I write a paper with Marco Scarsini and Nicolas Vieille arguing that LUBA is not a lottery. Having said that, I believe that LUBA is worse that a lottery: in a lottery, all participants have the same probability of winning. This is not the case with LUBA: the presence of strategic bidders essentially kills the chance of non-strategic bidders, or partially strategic bidders, to win the auction.

Part Three: Moral

So LUBA may not be illegal, but it seems that there is something wrong with it. I discussed this issue with Zvika Neeman yesterday. Just like a pyramid scheme or day trading by non professionals, LUBA is a method to get money out of people who may not realize the strategic complexity of the situation that they face.

Part Four: Complexity Fraud

Merriam-Webster defines fraud as:

“a : Intentional perversion of truth in order to induce another to part with something of value or to surrender a legal right. b : An act of deceiving or misrepresenting.”

Dictionary.com defines it as:
“Deceit, trickery, sharp practice, or breach of confidence, perpetrated for profit or to gain some unfair or dishonest advantage.”

There are many types of fraud. I argue that there should be one additional type: complexity fraud. Sometimes people are asked to participate in complex interactions, paying some amount for participation in the hope of getting a reward at the end. The rules are all set in advance, so nobody can later argue that he or she did not know the rules. But most people are not well versed in game theory, and we have all bounded computational capacity. Therefore, when the interaction is complex, people cannot analyze it and rationally decide whether they want to participate or not. People tend to be optimistic, they over-estimate their ability and smartness. If the strategic analysis of the method was explained to them, and if they were faced by statistics, they would turn away from the method. If this is the case, then hiding the strategic analysis and the complexity of the situation is, in my view, as deceptive as any other fraud.

I am not a lawyer, and I do not know what the court will think of my arguments. I hope that congressmen and parliament members worldwide will look into them, and change the law accordingly.

Richard Dawkins has a new book, in which he sets out to prove, once and for all, that evolution is a fact `in the same sense as it is a fact that Paris is in the northern hemisphere’, or, as he calls it, a Theorum.

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