Currently, most research institutions and universities demand their scientific staff to acquire external funds for research. Unfortunately, the structure of a project proposal, which most funding agencies promote, is not suited for theoretical research: theorists struggle to predict their future discoveries month by month, and explain how to prove theorems without actually proving them. This seemingly absurd activity, without a clear value or purpose beyond mere evaluation, requires countless hours, which are subtracted from actual scientific research. Is there hope for a change?
In their paper, Navascués and Budroni propose a research funding scheme by which each research unit (be it a single scientist, a group leader or a whole institute) applies for funding, but does not specify how much. The decision of how much funds must be awarded to each unit is taken by the funding agency, based on the recent scientific activity of the unit and the prior funding which such a unit was enjoying.
Assuming the existence of an agreed measure of scientific productivity, Navascués and Budroni model the research system as a collection of research units, each of which possesses a “scientific productivity function”, relating how much science a given research unit can produce with the funds it holds to conduct research. The ultimate goal of the funding agency is to distribute the whole science budget over the units in such a way that the expected total scientific production is maximized. There is an inconvenient, though: productivity functions are unknown, i.e., neither the research agency nor the scientists themselves can tell how they look like. On top of that, they are probabilistic, and might change with time.
Despite these cons, Navascués and Budroni devise systematic procedures to decide the budget distribution at each grant call, with the property that the total scientific production of the research community will be frequently not far off its maximum possible value. The simplest of such procedures is “the rule of three”, by which the funds that each research unit receives after a grant call are proportional to the research output of the unit during the previous grant term. It can be proven that, under the rule of three, a scientific community will generate science at a rate of (at least) half of its maximum limit. Moreover, the rule of three is secure under dishonest research units.
The returns of the rule of three must be compared with those of “excellence” schemes, whereby, under equal research outcomes, researchers which were funded in the past have a greater chance of receiving further funds. Such policies can converge to configurations where the total scientific productivity is an arbitrarily small fraction of the maximum achievable by the research system. In view of the existence of alternative methods with proven better performance, Navascués and Budroni discourage the use of excellence schemes in scientific policy.
 M. Navascués and C. Budroni, Theoretical Research without Projects, PLoS ONE 14(3): e0214026 (2019).
 M. Navascués and C. Budroni, Cómo mejorar la financiación de la investigación teórica, Investigación y Ciencia (2019).