Sequential problem choice and the reward system in Open Science
Introduction
Nelson (1959) and Arrow (1962) first highlighted that the specific characteristics of knowledge considered as a public good result in a default in knowledge creation incentives. Consequently private investment in knowledge creation is below its optimal level. This very well known result appeared as a theoretical justification for public support of research which may (non-exclusively) be undertaken by funding a specific social institution, namely academia. In that respect, modern countries obviously support a network of public laboratories and academic researchers. After having focused on the social returns of public research,1 economists have logically begun to address the issue of the internal organization of the academic institution.
Dasgupta and David (1994) have recently synthesized in an economic fashion the mertonian mechanisms at play within academia. According to Merton (1957), the functioning of the academic institution, he labels Open Science, relies on social norms2 that generate a set of effective rules which stress a specific reward system in which priority is essential. The incentive mechanism at play may be sketched as follows. Peers collectively establish the validity and novelty of knowledge produced (peer review). The attribution of rewards is based on recognition by peers of the “moral property” on the piece of knowledge produced which increases the producer’s reputation within the community (“credit”). Dasgupta and David (1994) highlighted that Open Science functioning has two fundamental and original economic properties that contribute to its efficiency. First of all, it avoids some of the asymmetric-informational problems that might otherwise arise between funding agencies and scientists in public procurement of advanced knowledge: scientists themselves are certainly the most able to carry out verification and evaluation operations in the peer-review like procedures. Secondly, since it is precisely the very action of disclosing knowledge which induces the reward (reputation or credit increase), the reward system thus creates simultaneous incentives both for knowledge creation and for its early disclosure and broad dissemination within the community. That is why this mode of knowledge production has been said to have very interesting efficiency properties (Arrow, 1987) and even to constitute a “first best solution” for the appropriability problem (Dasgupta and David, 1994) as it solves the dilemma between knowledge creation incentives and knowledge disclosure incentives (Stephan, 1996).3
Several modelling exercises have considered specific dimensions of the academic institution. Carmichael (1988) attempts to explain why does the tenure system exist: it is the only reliable employment contract that guaranties scholars will provide correct advises for employing high quality colleagues who might otherwise challenge their own positions. Lazear (1996) models the effects of several funding rules (e.g. weight more past efforts or the quality of the proposal, engage few big or many small awards, favor junior or senior researchers) on the incentives provided to scholars. Windrum and Birchenhall (1998) study the impact of the credibility based funding pattern on the evolution of a population of research units. Brock and Durlauf (1999) introduce a model of discrete choice between scientific theories when agents have an incentive to conform to the opinion of the community. Levin and Stephan (1991) propose a human capital model of knowledge production which fits the usual inverse-U shape of life-cycle scientific productivity. Carayol (2005) proposes a model of scientific competition in which overlapping generations of researchers compete at the different stages of their career while universities also simultaneously compete to hire the best scientists.
In this paper we focus on another dimension of academic organization, namely the sequential determination of research agendas within scientific communities and the subsequent disciplinary knowledge production. Our point of departure is that even though competition between scientists is clearly important (associated with “winner-takes-all” rules and “waiting and racing games” issues, cf. Dasgupta and David, 1987, Reinganum, 1989), it is only second, while the first and most important decision a scientist has to take is the choice of which research area and which problem she or he will investigate. This issue is usually referred to in the sociology of science as the “problem of problem choice” (Merton, 1957, Zuckerman, 1978, Ziman, 1987).4 As a matter of fact, a very consubstantial organizational trait of the Open Science is the significant freedom given to scholars in defining and selecting their own research agendas. More, the selection of good problems is far from being marginal from scholars’ points of view in the academic competition: not all problems are the same in their eyes and in the ones of their peers.
The model introduced in this paper addresses the issue of the impact of the Open Science reward system on the allocation of attention of the community of scientists ex ante, and on the resulting evolution of disciplinary knowledge ex post.5 Scientific disciplines are represented as growing tree-like webs of research areas that are the repository of accumulated knowledge. At each period, researchers allocate their attention responding to academic incentives. It leads to the improvement of knowledge in a given area or to the investigation of a new area. Our main results are that the process exhibits path dependency (David, 1985) especially disciplines that are more specialized have a higher chance to become even more specialized. We also find that there is a decline in the generation of new research areas over time which can be balanced by increasing the rewards for performing pioneering research. We also study how the outcoming disciplines are shaped through tuning the various typical incentives of the Open Science rewarding process. Finally, we propose a welfare criterion which assigns a given social surplus to each new problem addressed. We show and discuss how to balance academic incentives for improving the decentralized allocation of scholars’ attention.
The paper is organized as follows. The next section discusses the issue of modelling problem choice and subsequent evolution of disciplinary knowledge. The technical presentation of the theoretical model is the purpose of the third section. The fourth section is dedicated to the study of the generic properties of the process, while the fifth section studies parameters effects on the dynamics and discusses the characteristics of the outcoming disciplines. The sixth section introduces a welfare criterion and analyzes how the reward system should be tuned for an efficient allocation of attention. The last section concludes.
Section snippets
Modelling problem choice in science
This section aims to ground our model of problem choice on what is known on problem choice in science. We first survey the literature on incentives provided to scholars for choosing problems in science and next expose, in a non-technical manner, the main features of our model of sequential selection of problems and of disciplinary knowledge expansion.
The model
This section is dedicated to the formal presentation of our model. We first define the disciplines, seen as more or less improved research areas organized as nodes in a tree-like web. Next we discuss and show how these disciplines generate a set of problems that can be handled given the present state of knowledge. Thirdly, we introduce an expected reward function which provides the incentives associated with solving each of the available problems. Finally, we present the probabilistic function
Generic properties of the process
Once the model has been presented, we first turn to an exploration of the generic properties of the system, that is the behavior of the dynamic process through time and its limit behavior, while the characteristics of the drawn trees depending on parameters values are described in the next section. As it has been said above, the system is a quite complex one which naturally leads to complex dynamics. To make that point clear, let us consider the following. From Eq. (5), it can
Incentives, motivations and the outcoming disciplines: parameters effects study
Now that the main generic dynamic properties of the system are known, we wonder how various combinations of parameters values (which stress the effective rewarding of problem selection) impact on the outcoming disciplines analyzed mainly by computing the two indexes defined in Eqs. (6) and (7) and discuss the generic features of the typical disciplines generated by opposed values of parameters.
Tuning the academic reward system for improving the decentralized allocation of attention
In the two preceding sections we have focused on the dynamic properties of the process of scientific knowledge generation and have studied how the structural properties of emerging disciplines vary according to the set of incentives/motivations at play within the community. This led to highlighting that some obviously ‘ill’ dynamics may arise when the academic system of incentives is not well balanced. Nevertheless, we did not try to compare the outcoming disciplines in a systematic manner
Conclusion
In this paper we have presented an original model of knowledge production within scientific disciplines. It is a graph theoretical model in which knowledge production is sequential. The main question tackled in the paper is how the specific incentives provided by the academic reward system influence researchers’ problem choice and thus shape the stochastic process of knowledge generation within scientific disciplines. Let us sum up the main results obtained.
We first found that the process
Acknowledgements
The authors are in debt with R.K. Merton who provided them with an unpublished manuscript written with R.C. Merton, and kindly offered very useful and stimulating comments. His work as well as his advice helped us track the sources of the “problem of problem choice in science”. P.A. David should also be acknowledged for his helpful comments at different stages of our work. Two anonymous referees gave us stimulating remarks and criticisms that helped us to improve the paper. A related paper was
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