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Phil Ball

Richard Haughton

Philip Ball.

The mathematics of science's broken reward system

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Science has been peculiarly resistant to self-examination. During the ‘science wars' of the 1990s, for instance, scientists disdained sociological studies of their culture. Yet there is now a growing trend for scientists to use the quantitative methods of data analysis and theoretical modelling to try to work out how, and how well, science works — often with depressing conclusions. Why are these kinds of studies being produced, and what is their value?

Take a study published on 10 November1 by psychologists Andrew Higginson of the University of Exeter and Marcus Munafò of the University of Bristol, UK. It considers how scientists can maximize their ‘fitness’, or career success, in a simplified ecosystem that allows them to invest varying amounts of time and effort into exploratory studies. The study finds that in an ecosystem that rewards a constant stream of high-profile claims, researchers will rationally opt for corner-cutting strategies, such as small sample sizes. These save on the effort required for each study, but they raise the danger that new findings will not prove robust or repeatable

A slightly different perspective — but a similar conclusion — comes from work published on 21 September2, by information scientist Paul Smaldino at the University of California, Merced, and evolutionary ecologist Richard McElreath, at the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany. They take an evolutionary view, imagining that laboratories are in competition for rewards, and that the most successful of them produce more 'progeny': new research groups that use the same techniques and strategies. There is generally a trade-off between productivity and rigour: producing more statistically secure, replicated findings takes more time and effort, but generating too many false positives will eventually take its toll on reputations. Under selection for productivity, however, less-rigorous methods spread and false discovery rates increase.

Metric incentives

It is no coincidence that this kind of game-theory approach to modelling science has arisen as researchers worry about the rise of metric-driven management of science’s funding and reward systems. Bibliometric data sets mean that scientific success can be quantified with achievement metrics such as the h-index — a quantitative measure of the number of highly cited papers that an academic produces — or the journal impact factor, which proposes to identify the most visible journals.

Many researchers have warned that the availability of these metrics, which are supposed to make the management of science and funding more systematic and objective, may be changing the nature of science. They are starting to dominate how science is structured and steered and place great pressure on researchers, especially in the earlier stages of their career, to publish often and prominently. As a result, understanding science as a social phenomenon has become a matter of some urgency.

And by quantifying goals and rewards, metrics transform science into the kind of game-theoretical play of utility maximization and cost-benefit analyses with which economists and ecologists have long become familiar. It is only, I think, because science is now so driven by metrics-based incentives that such models and analyses can meaningfully be applied at all.

The models suggest that when researchers apply strategies that boost individual and institutional performance metrics, by publishing papers as often as they can in high-profile journals, scientific research as a whole becomes less efficient and reliable. (Rigorous journals and referees can partly ameliorate the situation).

“Whenever quantitative metrics are used as proxies to evaluate and reward scientists,” write Smaldino and McElreath, “those metrics become open to exploitation if it is easier to do so than to directly improve the quality of research.” That’s basically a statement of Goodhart’s law, familiar to economists: when a measure of success becomes a target, it loses its worth.

Munafò thinks that placing so much emphasis on high-profile publications is a mistake, and that it would relieve the pressure on junior scientists if they were given more opportunity to develop their ideas and to report ‘null’ findings. That fits with a conclusion from a study published last year3 by bioinformaticist Andrey Rzhetsky of the University of Chicago, Illinois, and his colleagues that modelled the rate of scientific discoveries. Using a data set from biomedical chemistry, they suggest that over the past three decades, scientists have been gradually choosing more conservative, low-risk research strategies. They argue that papers reporting replications and null results are important for increasing the efficiency of science, but because they don’t tend to get highly cited, there is little incentive to produce them.

Why models are useful

A question hanging over these studies is whether they really tell us anything we could not already intuit. Don’t we already know that science’s reward schemes encourage ‘safe’ research and encourage corner-cutting?

Perhaps. But relying on what ‘everyone knows’, without inspecting the evidence, has never been a good way to do science. Grumbling about over-assessment and bad incentives is one thing, but if they can be rigorously shown to create problems, then they are harder to ignore.

While the current wave of science models may not yet have told us anything utterly unexpected, studies of game-theoretic competition and complexity in other systems, both social and natural, often turn out to have some counter-intuitive implications; apparently well-motivated incentives can lead to unintended, detrimental outcomes.

The real benefit of mathematical modelling is that it gives you some idea of how the problems arise, and therefore which dials should be turned to ease them. How, for example, do you foster more risk-taking research strategies? By earmarking funding and creating Grand Challenges? By developing teams and institutions that spread the risk? It’s not as obvious as it might seem.

Scientists have nothing to fear, and much to gain, from having the lens of science turned back on its own conduct. It’s the old injunction: physician, heal thyself.

Journal name:
Nature
DOI:
doi:10.1038/nature.2016.20987

References

  1. Higginson, A. D. & Munafò, M. R. PLoS Biol. 14, e2000995 (2016).

  2. Smaldino, P. E. & McElreath, R. R Soc. Open Sci. 3, 160384 (2016).

  3. Rzhetsky, A., Foster, J. G., Foster, I. T. & Evans, J. A. Proc. Natl Acad. Sci. USA 112, 14569 (2015).

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  1. Avatar for Young Scientist
    Young Scientist
    Fixing science is not difficult, because most companies work as similar groups of individuals with different roles and objectives. Today science is very naive, imperfect, superficial version of rewarding performance. It would be interesting if models examined reviewers and journals, too. Even without mathematics one can say that optimal reviewer should harm competitors, steal ideas and invest minimal time into reviewing (for example push reviewing to students). Reviewers should be rewarded, checked and punished, too, because of their important role in the system.
  2. Avatar for Pentcho Valev
    Pentcho Valev
    "Science has been peculiarly resistant to self-examination." Self-examination is nonsense, like introspection. Science can only be aesthetically evaluated by the outside public, in the way in which works of art are evaluated. Otherwise we have this: http://www.everythingimportant.org/Einstein_worship/DivineEinstein.jpg https://www.youtube.com/watch?v=9lE-I2I4i00 "No-one's as dee-vine as Albert Einstein not Maxwell, Curie, or Bohr! His fame went glo-bell, he won the Nobel - He should have been given four! No-one's as dee-vine as Albert Einstein, Professor with brains galore! No-one could outshine Professor Einstein! He gave us special relativity, That's always made him a hero to me! No-one's as dee-vine as Albert Einstein, Professor in overdrive!" http://www.youtube.com/watch?v=5PkLLXhONvQ "We all believe in relativity, relativity, relativity. Yes we all believe in relativity, relativity, relativity. Everything is relative, even simultaneity, and soon Einstein's become a de facto physics deity. 'cos we all believe in relativity, relativity, relativity. We all believe in relativity, relativity, relativity. Yes we all believe in relativity, relativity, relativity." https://www.youtube.com/watch?v=BuxFXHircaI Michio Kaku, Brian Cox, Neil deGrasse Tyson, Brian Greene, Lisa Randall: "Light travels at the same speed no matter how you look at it. No matter how I move relative to you light travels at the same speed. No matter who is doing the measurement and no matter what direction you are moving the speed of light is the same. The speed of light is the same no matter what direction or how fast. As you travel faster time slows down. Everything slows down. Everything slows down. Time slows down when you move. Time passes at a different rate. Clocks run slow. It's a monumental shift in how we see the world. It's a beautiful piece of science. It's a beautifully elegant theory. It's a beautiful piece of science. It's a beautiful piece..." http://www.krugozormagazine.com/main/content/9-2009_Enshtein-3.jpg "The Riverside Church in New York, west portal - upper line, second of right. In 1930, during a stay in New York, Albert Einstein and his wife visited the Riverside Church, too. During the detailed guided tour through the church Einstein was also shown the sculptures at the west portal. He was told that only one of the sculptures there represented a living person, and that was he himself. What Einstein is supposed to have thought in that moment when he heard that information and saw himself immortalized in stone? Contemporaries reported that he looked at the sculpture calmly and thoughtfully." Pentcho Valev
  3. Avatar for Sam Regenbogen
    Sam Regenbogen
    While I think there could be an argument made for your initial point (i.e., 'If there's a fire you're trying to douse, you can't put it out from inside the house'), the examples you gave pretty much make the opposite point. Yeah, there's definitely a cult of worship around Einstein, but songs and music videos created by physics teachers and popular science communicators don't exactly count as inward-facing examples of the scientific process. And if your point is that the scrutiny and opinion of the outside public is required to prevent the rise of uncritical hero-worship within science, the example of a sculpture inside of a church is about the most potent piece of contradictory evidence I can imagine.
  4. Avatar for Pentcho Valev
    Pentcho Valev
    I think my initial point is generally correct and the examples contradict it only apparently. The outside public could be brainwashed sometimes - then worship becomes its "normal" reaction: http://plus.maths.org/issue37/features/Einstein/index.html John Barrow FRS: "Einstein restored faith in the unintelligibility of science. Everyone knew that Einstein had done something important in 1905 (and again in 1915) but almost nobody could tell you exactly what it was. When Einstein was interviewed for a Dutch newspaper in 1921, he attributed his mass appeal to the mystery of his work for the ordinary person: "Does it make a silly impression on me, here and yonder, about my theories of which they cannot understand a word? I think it is funny and also interesting to observe. I am sure that it is the mystery of non-understanding that appeals to them...it impresses them, it has the colour and the appeal of the mysterious." Relativity was a fashionable notion. It promised to sweep away old absolutist notions and refurbish science with modern ideas. In art and literature too, revolutionary changes were doing away with old conventions and standards. All things were being made new. Einstein's relativity suited the mood. Nobody got very excited about Einstein's brownian motion or his photoelectric effect but relativity promised to turn the world inside out." Even theoreticians can be brainwashed. For instance, nowadays they reject, explicitly or implicitly, the consequence, Einstein's spacetime, but continue to worship the underlying premise, Einstein's constant-speed-of-light postulate (logic forbids the combination "wrong consequence, true premise"): https://www.edge.org/response-detail/26563 Nobel Laureate David Gross observed, "Everyone in string theory is convinced...that spacetime is doomed. But we don't know what it's replaced by." https://www.youtube.com/watch?v=U47kyV4TMnE Nima Arkani-Hamed (06:09): "Almost all of us believe that space-time doesn't really exist, space-time is doomed and has to be replaced by some more primitive building blocks." https://edge.org/response-detail/25477 What scientific idea is ready for retirement? Steve Giddings: "Spacetime. Physics has always been regarded as playing out on an underlying stage of space and time. Special relativity joined these into spacetime... [...] The apparent need to retire classical spacetime as a fundamental concept is profound..." http://www.newscientist.com/article/mg20727721.200-rethinking-einstein-the-end-of-spacetime.html "Rethinking Einstein: The end of space-time [...] The stumbling block lies with their conflicting views of space and time. As seen by quantum theory, space and time are a static backdrop against which particles move. In Einstein's theories, by contrast, not only are space and time inextricably linked, but the resulting space-time is moulded by the bodies within it. [...] Something has to give in this tussle between general relativity and quantum mechanics, and the smart money says that it's relativity that will be the loser." Spacetime is an "immediate consequence" of Einstein's 1905 false constant-speed-of-light postulate: http://community.bowdoin.edu/news/2015/04/professor-baumgarte-describes-100-years-of-gravity/ "Special relativity is based on the observation that the speed of light is always the same, independently of who measures it, or how fast the source of the light is moving with respect to the observer. Einstein demonstrated that as an immediate consequence, space and time can no longer be independent, but should rather be considered a new joint entity called "spacetime." Pentcho Valev
  5. Avatar for Pentcho Valev
    Pentcho Valev
    The speed of light is variable, not constant - any correct interpretation of the Doppler effect proves, explicitly or implicitly, that the speed of light relative to the observer varies with the speed of the observer, in violation of Einstein's relativity. Here is the paradigmatic scenario: The observer walks along the fence. Relative to him, the posts have speed c, and the frequency he measures is f=c/λ, where λ is the distance between the posts. Now the observer starts running along the fence and his speed increases by v. Relative to him, the speed of the posts shifts from c to c' = c+v This shift in the speed of the posts (relative to the observer) causes the frequency he measures to shift from f=c/λ to f' = c'/λ = (c+v)/λ = f(1+v/c) Exactly the same argument is used to calculate the Doppler frequency shift for light: http://rockpile.phys.virginia.edu/mod04/mod34.pdf "Now let's see what this does to the frequency of the light. We know that even without special relativity, observers moving at different velocities measure different frequencies. (This is the reason the pitch of an ambulance changes as it passes you it doesn't change if you're on the ambulance). This is called the Doppler shift, and for small relative velocity v it is easy to show that the frequency shifts from f to f(1+v/c) (it goes up heading toward you, down away from you). There are relativistic corrections, but these are negligible here." http://www.hep.man.ac.uk/u/roger/PHYS10302/lecture18.pdf "The Doppler effect - changes in frequencies when sources or observers are in motion - is familiar to anyone who has stood at the roadside and watched (and listened) to the cars go by. It applies to all types of wave, not just sound. [...] Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/λ waves pass a fixed point. A moving point adds another vt/λ. So f'=(c+v)/λ." Note that the frequency shift f' = c'/λ = (c+v)/λ = f(1+v/c) is a consequence of the fact that the speed of light (relative to the observer) varies with the speed of the observer, in accordance with the equation c' = c+v and in violation of Einstein's relativity. Pentcho Valev

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