The Function of Prizes

My aunt’s husband, Field Medal winner Atle Selberg, died a few weeks ago.  The Washington Post:

The Fields Medal was awarded to Dr. Selberg for his work on proving a challenging theory about the distribution of prime numbers. For years, mathematicians had believed that it could be proved only by the laborious application of ponderous techniques. In 1949, Dr. Selberg and another celebrated mathematician, Paul Erdos, achieved a proof through techniques of startling simplicity.  Each, it was reported, was to report on his own contribution in the same issue of the same mathematics journal. Because of what has been described as a misunderstanding that led to hurt feelings, Dr. Selberg published first.  His Fields Medal, recognizing him for a variety of accomplishments, followed.

The usual story about such independent discoveries is that they both deserve recognition.  And this makes sense if the point of such prizes is to identify and validate genius.  But if we awarded prizes instead to create incentives for discovery, we should reward neither discoverer.  After all, the marginal contribution to progress of each simultaneous independent discovery is near zero – without that discovery progress would have been nearly the same, since the other sources were available.   

Yes, independent replications can aid progress in experiments and data analysis.  But much less so for math, and few think later replications deserve anywhere near the same reward – so why should simultaneous replications get more?  Yes, rewarding both might reduce their risk in seeking the reward, but we already accept an awful lot of risk in such situations.  The slight additional risk from rewarding only substantial marginal contributions would create important incentives for researchers to coordinate on their research topics. 

Independent simultaneous discovery is a waste, not a triumph.  The fact that we seem to feel otherwise is to me further evidence that academia’s main local function is to validate impressive people.  Relative to the main goals of most participants, research progress is only a side effect. 

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  • Stuart Armstrong

    Set up two prize systems: one for marginal achievement, one validating genius (validating genius prizes are good from the point of view of 1) motivating people to entre the field and 2) promoting more collaboration). We seem wired to prefer “you’re great!” prizes to “you’ve done a lot” prizes, so the first set of prizes should offer more cash than the second.

  • AnĂ³nima

    “But if we awarded prizes instead to create incentives for discovery, we should reward neither discoverer.”

    For inventors filing a patent, the first to file or to invent (depending on the country) gets the patent. I have never heard that solution questioned as a logical solution to the problem of nearly simultaneous inventions in which an inventor files the second application without knowing, because it has not being published, that there is already another application filed.

    Rewarding neither seems really like a good idea for motivating people to cooperate instead of making them compete to be the first to file a patent. And cooperating should be more efficient to speed research results.

    At least that sounds logical to me, but I’m still wondering…

    Thanks anyway for making me think along new lines đŸ™‚

  • http://bizop.ca michael webster

    I would go even further: prizes for solving intellectual puzzles are counter-productive. They are awarded at precisely the wrong time, after the puzzle has been solved instead of before. They are awarded to the wrong parties, individuals instead of the community which bears responsibility for moving the question to the forefront of research.

  • Vladimir Nesov

    But concurrent research provides diversity which helps in evading local minima. Correct solutions may coincide even if original arbitrary research choices were different, so for another problem only one of the projects would have reached the goal.

  • josh

    Who thinks simultaneous discovery is better than individual discovery? I’ve never heard that before. Simultaneous major breakthroughs may be a waste ex poste, but its not as if either party anticipated the other making a major breakthrough. I don’t see how we could use this idea to come with a better allocation of resources. In any case, it may be a bit of a shame that they didn’t make two different breakthroughs, but its still pretty good.

  • michael vassar

    I pretty much agree with Josh here. It’s not a bad incentive.

    Anyway, math seems a more clear example of looking for impressive people than science.

  • http://byrneseyeview.com Byrne

    This would lead to ‘squatting’ on prizes: once one person is reasonably close to finding a solution, everyone else has a disincentive, even if their research involves another avenue of study which could lead to further advances.

  • conchis

    It seems to me that the appropriate incentives will depend on the costs of coordination. If these are prohibitively high, then you may frequently see people diverting into less important, more obscure topics to avoid the possibility of being scooped.

    (No, that wouldn’t be an equilibrium, but I don’t see much reason to expect us to stay in equilibrium here, rather than just perennially over and undershooting. In the absence of co-ordination, it strikes me as pretty analogous to the old El Farol Bar thing.)

    Of course, if the costs of coordinating are falling, then Robin’s suggestion starts to become more and more relevant. (Though maybe growth in the number of researchers is counteracting technological developments here.)

  • Silas

    Robin_Hanson: I don’t understand how “awarding nothing for simultaneous discoveries” is consistent with creating incentives for discoveries. If a researcher knows that the reward is nothing if someone else discovers it at about the same time, he takes an addtional risk by pursuing the prize. If the prize is a major reason that both are pursing the discovery, both may decide the risk/return profile no longer justifies pursuing it, meaning the discovery never happens.

    It’s true that simultaneous discovery is a sign of greater obviousness, but if the puzzle is challenging enough to merit creating a prize for it, it’s probably not that obvious.

    A while ago I came up with the idea that one way to profit from an invention would be to speculate in the markets that it impacts. (e.g., new orange juice machine bids up orange prices, so buy orange futures and then publicly disclose the invention) The result of simultaneous discovery in that case would be that the inventors enter the market at the same time, bid up factor prices twice as fast, and split the profits that result.

    AnĂ³nima: For inventors filing a patent, the first to file or to invent (depending on the country) gets the patent. I have never heard that solution questioned as a logical solution to the problem of nearly simultaneous inventions in which an inventor files the second application without knowing

    In a sense, the patent system already denies patents to simultaneous discoverers *when there are enough of them*. They refer to this as the “obviousness” standard.

  • http://profile.typekey.com/robinhanson/ Robin Hanson

    In case it wasn’t obvious, I meant to hold constant the total amount of money awarded as prizes. So if in some cases we awarded less, in other cases we would award more.

  • http://acceleratingfuture.com Michael Anissimov

    Happy birthday Robin! Interesting post as always.

  • http://3form.org/blog Alex

    In my opinion, awards currently encourage researchers to spend more time on marketing their research and social networking to make sure the research they work on will be widely known and popular enough in the academic community to be nominated for an award. Awards miss scientists who produced the original work in favor of those who had more academic influence (due to their skills, position, or prior awards) to successfully popularize and market that work. I have no doubt that popularizing is also an important skill and might be a great contribution all by itself worth to be awarded if the prior work is properly cited (ironically, not citing prior work greatly increases the chances of getting an award).

  • Silas

    Okay, I think my previous post responded to the wrong point. I was referring to awards for specific discoveries (i.e. dis/proving P=NP, etc.) rather then general “greatness” awards. But I think my point still stands: if there is such a sharp cutoff for “me-too”s, *and* if the prize money is the driving factor for the researcher, the risk/reward profile is skewed to the point that they may just devote their brain to making money outside of academia.

    I agree that the money *can’t* have much of an incentive effect because of the low probability of getting it (even if you do good research) and how long it will take to be recognized, so the prize is more effective at “validation”.

  • Constant

    The case of math may be somewhat different from the case of science generally. In math, the result is not the only thing that matters. The proof is also important. Finding new proofs of the same result is a worthwhile endeavor. It’s not just the result that is discovered, but the proof as well, and so a new proof of an old result is a genuine discovery.

    Of course, if Erdos and Selberg actually came up with the same proof, then perhaps it was, in hindsight, a waste of effort. However, we do not approach our tasks with hindsight.

    Incidentally, Paul Erdos seems to me quite famous, more so than most any Fields winner. At least, I have often seen him mentioned. If it’s fame people want – and isn’t that a large part of it – then Erdos did well without the Fields medal.

  • http://3form.org/blog Alex

    Here is a relevant article from The New Yorker: http://www.newyorker.com/archive/2006/08/28/060828fa_fact2

  • Math Geek

    As Constant said, the significance of one’s work in mathematics is judged not only by one’s results but by the methods developed therein. Techniques used in a proof often stimulate additional research, sometimes creating entirely new fields of mathematics. Thus a subsequent proof may be more significant than the original one.

  • Anonymous

    In practice, simultaneous co-discoverers do not each receive as much credit as a single person would have: most people downgrade their estimate of the contribution when they hear several people did it independently and at the same time. Furthermore, when prizes are involved, they may be split, or they may be awarded to the one person who is judged to have made the largest contribution, but I’ve never heard of the total prize money being increased so that each co-discoverer gets a full share. So I’m not sure what Robin is complaining about.

    Incidentally, the Erdos-Selberg story is quite a bit more subtle than the Washington Post story indicates. See http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf for the details.

  • http://www.scottaaronson.com Scott Aaronson

    Relative to the main goals of most participants, research progress is only a side effect.

    Robin, this strikes me as both true and obvious. “It is not from the benevolence of the physicist, the chemist, or the mathematician that we expect our journal articles, but from their regard to their own glory.” I thought economists liked mechanisms that induce selfish agents to work toward socially desirable outcomes… đŸ™‚

  • http://hanson.gmu.edu Robin Hanson

    Scott, the part that might not be obvious to some is that those paying for research are included in the “participants” for whom research progress is only a side effect.

    Anony, yes, co-discoverers must split credit, but that is still much more than being given near zero credit.

    Math and Constant, if one wants to reward new interesting proofs of old results, one can simply use that language when defining “discoveries.”

    Conchis, if the average prize awarded is held constant, I don’t see why people would avoid the research topic.

  • Stuart Armstrong

    In case it wasn’t obvious, I meant to hold constant the total amount of money awarded as prizes. So if in some cases we awarded less, in other cases we would award more.

    Prizes bestowing fame and prestige could work with very little money. “Genius” prizes seem more suited for this than “genuine achievement” ones.

    Ah, what would we not give for a time machine, so that future generations could reward researchers today…

  • Douglas Knight

    Stuart Armstrong: the Fields Medal is a prize with little money attached. But that doesn’t mean it’s cheap. It probably required lots of other resources to establish it as a serious open-ended award. I think this is relevant to Constant’s comment; this was only the second time the Fields Medals were awarded and it probably wasn’t well-established.

  • Tom Breton

    After all, the marginal contribution to progress of each simultaneous independent discovery is near zero – without that discovery progress would have been nearly the same, since the other sources were available.

    Sorry, Robin, I think that’s funny counting.

    Let’s say arguendo that there are no side benefits from discovery.
    If discovery A’s marginal contribution to progress is near zero, since there is no quarrel about the total value of discoveries A+B, that means that discovery B contributes nearly the entire value of A+B. Similarly, if we fix B’s value near zero, A contributes nearly A+B. So ISTM you can’t make the marginal value argument for both A and B simultaneously.

    You might treat the fact of simultaneity as a proxy measure for how easy it was to make the discovery. Others have pointed out problems with that.

  • http://profile.typekey.com/robinhanson/ Robin Hanson

    Tom, you need to learn some economics.

  • http://www.hopeanon.typepad.com Hopefully Anonymous

    Stuart, cryonics, a trust fund for oneself, and a published request to future generation to compensate you (via your trust fund) for your work for them.

  • Tom Breton

    Tom, you need to learn some economics.

    I admit that I do, and if I had I would probably have seen the nature
    of your argument sooner and not made a muddled answer that both
    accepted and denied the premiss that one discovery equals one
    unit.

    You are arguing, if I understand correctly now, along the lines that
    the prize-giver is a consumer of discoveries or solutions and has
    bought more units than he needs, and ought to reduce his bid at least
    to the point where he receives only one solution.

    I think that argument doesn’t work. The case of two simultaneous
    discoveries is compatible with the prize amount being just right or
    even too small, as well as too large.

    My argument: I see no reason to assume that the expected distribution
    of number of solutions is a point. ISTM the number of solutions is
    affected by both the prize amount and by random factors beyond the
    control of both prize-giver and contestants. I expect the random
    factors to be significant, because the contestants do. If they
    didn’t, they would co-ordinate so that only one contestant incurred
    the cost of pursuing the prize.

    Since there’s a significant random factor, for no combination of set
    prize amount and expected difficulty is the expected distribution of
    number of solutions exactly one. The distribution might both zero and
    one, both one and two or more, or all three.

    So reducing the prize amount to the point where there is no risk of
    two solutions increases the risk of no solution. If the random factor
    is large enough, the risk of no solution can matter even at the same
    time that there is a significant risk of two or more solutions.

    Nature has in effect packaged solutions in units of unpredictable
    size. Both the prize-giver and the contestants would like to make the
    unit size predictable, so that one solution equals one transaction. The
    prize-giver would avoid the situation at hand and the contestants
    would avoid the risk being the second discoverer. But they can’t. If
    they could, they would have already done so, and the situation would
    already be more like wages or purchases than prizes.