Centralization versus Decentralization as a Risk-Return Trade-off
Alessandra Arcuri Giuseppe Dari-Mattiacci
Amsterdam Center for Law & Economics Working Paper No. 2007-06 The complete Amsterdam Center for Law & Economics Working Paper Series is online at: http://ssrn.acle.nl For information on the ACLE go to: http://www.acle.nl
Electronic copy available at: http://ssrn.com/abstract=1013329
Centralization versus Decentralization as a Risk-Return Trade-o¤ Alessandra Arcuriy Erasmus University Rotterdam
Giuseppe Dari-Mattiacciz University of Amsterdam
February 11, 2009
Abstract This paper characterizes the choice between centralization and decentralization as a risk-return trade-o¤ and examines it in a model that integrates ideas from committee-decisionmaking and portfolio theories. Centralization, by pooling expertise, rarely yields erroneous decisions; however, when it fails, the consequences are global. In contrast, in a decentralized system, erroneous decisions are more frequent but their consequences are locally con…ned. We assess the relative desirability of (de-)centralization in various scenarios with independent versus interdependent risks. We further discuss the robustness of the model and the relevance of our results for policymaking. Keywords: centralization, decentralization, federalism, Condorcet Jury Theorem, risk diversi…cation. JEL classi…cation: D72, K00, K33.
We are indebted to the editor, an anonymous referee, Britta Augsburg, Arnoud Boot, Roger Congleton, Bruno Frey, Edward Iacobucci, Jonathan R. Nash, Francesco Parisi, Margherita Saraceno, Jeroen van de Ven, Matthijs van Veelen, Bauke Visser, and Jose…en van Zeben for their invaluable suggestions on how to improve the analysis. We also thank Susan Russell for her skilled editorial assistance. We would also like to thank the participants in the seminars at the University of Zurich and the University of Amsterdam, and the 2007 annual conferences of the International Society for New Institutional Economics at the University of Reykjavik, the Canadian Law and Economics Association at the University of Toronto and the Midwestern Law and Economics Association at the University of Minnesota Law School. This paper was previously circulated as “Multilevel Governance and Risk Diversi…cation”. y Erasmus University Rotterdam, School of Law. Address: Burg. Oudlaan 50, 3062PA Rotterdam, The Netherlands. Email:
[email protected]. z University of Amsterdam (ACLE, CSECLE and Tinbergen Institute). Address: Roetersstraat 11, 1018WB Amsterdam, The Netherlands Email:
[email protected]. The …nancial support provided by the NWO grant 016.075.332 is gratefully acknowledged.
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Electronic copy available at: http://ssrn.com/abstract=1013329
1
Introduction
The formation of law and policy in contemporary societies is often in‡uenced by experts. Expert-driven law is justi…ed by the fact that experts are endowed with specialized knowledge necessary to design e¤ective policies in technically complex domains. These domains include a wide range of policy issues from the regulation of occupational health to the setting of food safety standards, environmental law and policy and the regulation of pharmaceuticals.1 An interesting question raised by the nature of expert-decisionmaking is how the level of governance— centralized versus decentralized— a¤ects the decisions made. The juncture between expert-decisionmaking and the centralization versus decentralization debate is a somewhat unexplored territory in the …eld Law and Economics. The goal of this paper is to chart this area by examining the risk-return trade-o¤s entailed by di¤erent levels of governance. Take, for example, the decision to authorize the marketing of Genetically Modi…ed Organisms (GMOs). Assume that the process can take two forms: either a centralized or a local authority is in charge of the approval decision. Both authorities rely on the opinion of a given number of experts: If the decision is centralized, all experts sit together in one committee, whereas, if the decision is decentralized, the same experts will be distributed among independent local committees. Assuming that there is a superior decision (for example, it is desirable to authorize the GMO in question), we show that centralization, by pooling expertise, rarely yields erroneous decisions (high returns); however, when it fails, the consequences are widespread (high risk). In contrast, in a decentralized system, erroneous decisions are more frequent (low returns) but their consequences are locally con…ned (low risk). As a main insight, our analysis suggests that decentralization, implying the possibility that di¤erent jurisdictions make di¤erent decisions, works as a risk-diversi…cation device, thereby limiting society’s exposure to risk. The perspective introduced by this contribution pushes the centralization versus decentralization debate towards a new frontier: It introduces risk as a dimension of the analysis and it emphasizes the role that decisionmaking processes may play for the generation of desirable outcomes. While our model is built around the expert-decisionmaking case, the number of available experts can be seen as a proxy for the resources devoted to the decisionmaking process. Thus, our conclusions can be generalized to any assembly or committee whose members hold imperfect knowledge about the issues at stake. 1 Institutions relying on technical, economic, and legal expertise can be found both at the local and at the central level. Examples of federal US institutions include: the Occupational Health and Safety Administration (OSHA), created in 1970, the Environmental Protection Agency (EPA), established in the same year and the Food and Drug Administration (FDA), which has existed for over a century. The establishment of administrative agencies and authorities in Europe is more recent. To name just few examples: The European Food and Safety Authority (EFSA) created in 2002 and the European Medicines Agency (EMEA) established in 1995. The di¤erence in timing between US and Europe might be taken as evidence of a European tendency to move to a higher level of centralization of administrative law closer to the one already achieved in the US. These issues are further discussed in section 4.
2
After relating our analysis to the existing body of literature, we address the question concerning the optimal level of governance in section 2, in a model of approval (yes-or-no) decisions, such as in the GMO example. We let the optimal level of governance depend on several parameters— the quality of the available expertise, the total amount of resources devoted to decisionmaking, the degree of society’s risk-aversion and the characteristics of the risks involved (independent versus interdependent risks)— and analyze how changing circumstances a¤ect the optimal level of governance.2 In section 3, we discuss the robustness of our model in light of possible relaxations of our main assumptions. Finally, in section 4, we discuss policy implications, summarize our results and state our conclusions.
1.1
Relation to the literature
The question we address in this paper— whether decisions should be centralized or decentralized— has long been the focus of scholarly attention from the conventional economic theory of federalism (Tiebout 1956; Stigler 1957) to the theory of the …rm (Coase 1937) and the study of hierarchy (Sah and Stigliz 1986). Advocates of centralization mainly base their claims on the detrimental consequences of heterogeneity and lack of coordination that might result from decentralized decisionmaking: most prominently, the externality problem.3 One instantiation of the externality problem is the race to the bottom.4 In the 1933 case Louis K. Liggett Co. v. Lee, (288 U.S. 517 [1933], 558-559), judge Brandeis warned against the risk that di¤erent jurisdictions might ine¢ ciently lower their standards in order to attract individuals or …rms precisely on these grounds. The above opinion presents a di¤erent side of the coin from that given a year earlier in New State Ice Company v. Liebmann (285 U.S. 262 [1932], 311), in which decentralization was described as a laboratory of democracy, insofar as jurisdictions use their discretion to develop solutions to common problems that can then spread to other states. This view on the pros of decentralization formed the basis for later theories emphasizing that decentralization enhances the government’s proximity to local preferences and conditions (Tiebout 1956; 2 Formal
proofs of the propositions are available with the authors. interesting perspective on this topics can be found in Ellet (1839) who noted that decentralized ownership of lines of transportation could result in excessive pricing, and hence suboptimal use, due to what is known in di¤erent strands of literature as complementary monopoly (Cournot [1838] 1897), double marginalization (Spengler 1950) or the anticommons problem (Heller 1998). Ellet advised the US government to centralize ownership in order to solve this problem. Although from di¤erent perspectives, Bentham (1817) and Weber ([1925] 1954) also prized the virtues of centralized decisionmaking by maintaining that codi…cation as opposed to common law reduces the uncertainty of the law and fosters economic and social development. 4 In the speci…c …eld of environmental law, Oates and Schwab (1988) and Revesz (1992) cast doubts on the race-to-the-bottom hypothesis concerning environmental standards. To the same e¤ect, by studying the history of the US Clean Air Act, Revesz (1996) argues that federal regulation (a form of centralized decisionmaking) does not solve problems of transboundary externalities. 3 One
3
Oates 1972), hence o¤ering citizens a way to choose the community which is closest to their characteristics. In turn, the ability of citizens to move to other states or regions fosters a race to the top, inducing di¤erent jurisdictions to improve their production of goods and services (Breton 1996) such as, for example, their corporate laws (Romano 1985).5 Despite the expansion of the literature on the economics of federalism, no study has attempted to show the implications entailed by the risk dimensions inherent to many decisions. We accordingly enrich this analytical framework by integrating …ndings from the literature on the Condorcet Jury Theorem (henceforth CJT; Condorcet [1785] 1994)6 with insights from portfolio theory (Markowitz 1952). From the CJT we take the idea that agencies with more experts are more accurate than agencies with fewer experts. Thus, according to the CJT, centralization has the advantage that, by pooling experts, it yields the right decision more often than decentralization. In contrast, portfolio theory suggests that decentralizing decisions allows for risk-diversi…cation, thus casting a vote in favor of decentralization. There are many important contributions that apply the CJT to the study of decisionmaking by juries, committees and legislative bodies.7 However, none of these contributions has employed the CJT to consider issues of centralization versus decentralization.
2
The optimal level of governance
In this section, we analyze binary yes-or-no decisions, such as the decision whether to approve a new GMO. The decision can be made at a centralized or decentralized level. In the following sections, we build a model that allows us to measure the performance of centralized versus decentralized decisionmaking in terms of returns and risk. We assume that, at the outset, it is not clear whether the GMO should be approved or banned.8 The right decision— 5 Decentralization has also been associated with reduced rent-seeking (Brennan and Buchanan 1980), lower corruption (Fisman and Gatti 2002), improved accountability (Tommasi and Weinschelbaum 2007), less strategic delegation (Besley and Coate 2003), broader political participation (Inman and Rubinfeld 2000), better communication between local divisions (Alonso, Dessein and Matouschek 2008), learning (Nelson and Winter 1982; March 1991) a feeling of participation among citizens (Frey and Stutzer 2002) and a terrorist-proof di¤usion of power (Frey 2004). In a more general spirit, Shumpeter (1934) and Hayek (1978) emphasize the virtues of competition in fostering economic development and information acquisition. 6 See also Grofman, Owen and Feld (1983); Black (1958); Grofman (1975 and 1978); Miller (1986); Young (1988); Ben-Yashar and Nitzan (1997). 7 Kornhauser and Sager (1986); Grofman and Feld (1988); Estlund et al. (1989); AustenSmith and Banks (1996); Feddersen and Pesendorfer (1998); McLennan (1998); Coughlan (2000); List and Goodin (2001); Levmore (2002); Dharmapala and McAdams (2003); AustenSmith and Feddersen (2006); McGinnis and Rappaport (2008). 8 This situation can be modeled by employing an information-aggregation model of approval decisions by a group of individuals with common preferences but diverse information (Edelman 2002, pp. 333, 338-339). There are only two states of the world, A and B, with the same prior probability of 50%. Only two decisions are possible: approve, A, or ban, B, the new GMO. The outcome ( ; ) depends on the state of the world and the decision taken, with A; A = B; B = G > 0 and A; B = B; A = 0. This formulation also implies an assumption of symmetry in the cost and likelihood of errors on either side.
4
correctly approving or banning— yields a positive payo¤ of G, while the wrong decision— banning a GMO that should be approved or approving a GMO that should be banned— yields a (normalized) payo¤ equal to zero.9 Thus, G is the value at stake. The decision is made by a regulatory agency relying on the opinion of a committee of n identical experts, where n represents the amount of resources devoted to decisionmaking. For the purpose of the analysis, we assume that agencies always follow the advice of their committees and, hence, we use the words committee and agency interchangeably. Reliance on expert committees is justi…ed by the technical nature of the decisions. Laymen and politicians do not possess the necessary knowledge to make an informed assessment: their choices would be guesses with a 50% probability of being correct. However, as is often the case, the state of the art is such that not even experts are always able to pick the right outcome, although their assessments are better than those by laymen. Unlike laymen, each expert collects some information (a signal) about the problem. This information allows the expert to make an assessment of the situation— whether the GMO should be banned or approved— which is correct in p > 50% of the cases. In this sense, decisions by experts are better than decisions by laymen.10 The probability p indicates the quality of the scienti…c knowledge available and suggests that all experts possess an identical level of expertise. When experts gather together, each of them brings in some information on whether approving or banning is more desirable. After a possibly lengthy discussion, the committee produces a deliberation that is then adopted by the regulatory agency. We are interested in the probability Pn (p) that a committee of n experts with expertise p makes the right decision. This probability is in fact equal to the probability that a simple majority of the experts in the committee makes the right assessment.11 Intuitively, we expect the committee decision to improve if there are more experts— who bring in more information— 9 We do not imply that wrong decisions have no negative e¤ect. This formulation simply indicates that the di¤erence between the outcome of a good decision and the outcome of a bad decision is G. 1 0 It is assumed that each expert i 2 f1; :::; ng independently receives a private signal i 2 fa; bg, which is correlated with the state of the world. In particular, for each expert i, we have Pr ( i = aj A) = Pr ( i = bj B) = p > 50%. Thus, p is the probability that an expert is correct in his assessment of the state of the world. 1 1 Experts have identical utility functions U ( ; ), and derive disutility from wrong decisions: U A; A = U B; B = 0 and U A; B = U B; A = 12 . The committee takes two votes. The …rst round is a non-binding communication round in which experts simultaneously reveal their signals. In the second round, a formal vote determines the …nal decision. Since experts have a common interest, it is a subgame perfect Nash equilibrium for the experts sincerely to reveal their signals in the communication round (Coughlan 2000, proposition 6). Given sincere revelation, in the formal voting round all experts vote for the alternative that collected more votes in the …rst round, irrespective of the formal voting rule employed (Coughlan 2000, 382). Thus, this framework supports the CJT. Alternatively, with formal voting without previous communication, voting according to one’s signal results as a Nash equilibrium if the optimal voting rule— in this case, a simple majority— is used (Ben-Yashar 2006). This framework also supports the CJT. See also McLennan (1998). For a recent contribution on voting behavior in committees see Visser and Swank (2007).
5
or if the experts have better expertise— that is, if the information brought in is more accurate. These results are known as the CJT. The probability that the committee makes the right decision can be expressed as follows:12 Pn (p) =
n X
n i p (1 i
i= n+1 2
n i
p)
where the right-hand side is simply the probability that more than half of the experts receive a correct signal. The CJT enables us to rely on an array of standard results. In fact, we have Pn (p) > p, that is, the probability that a committee makes the right decision is greater than the probability that a single expert makes the right decision; moreover, Pn (p) increases at a decreasing rate both in n and in p and asymptotically approaches 1 as n grows to in…nity or p approaches 1. This means that the agency’s decision improves if more resources are devoted to the decisionmaking process, in terms of the number of experts n, or if their expertise p improves. Given a total number N of available experts— a resource constraint imposed on the decisionmaking process (Sah 1991, 68)— the question we address here is whether decisions should be made at a centralized or decentralized level. At a centralized level decisions are made by one regulatory agency with global jurisdiction over the entire planet and pooling all N experts. Instead, at a decentralized level decisions are made by N di¤erent agencies, each having local jurisdiction in one of N (identical) regions in which the planet is divided13 and relying on the advice of a single expert per agency. It is useful to begin the analysis by posing the problem in such dichotomous terms; later on we will account for intermediate levels of decentralization, allowing each local agency to rely on more than one expert. The fact that the state of the world cannot be perfectly observed gives rise to two di¤erent problems. One is how to maximize the expected return on the decision; the other is how to reduce the risk due to the variance of the outcome.14 This trade-o¤ can be expressed by the following formulation for 1 2 This formulation refers to n as being odd. If n is even and ties are randomly attributed to either decision and there is an easy transformation rule to bring the analysis back to n being odd: Pn (p) = Pn 1 (p) (Miller 1996, p. 175). 1 3 We use the notions of “planet” and “region” simply to denote the geographical unit of analysis and its local subdivisions, respectively. Thus, depending on the context, “planet” might refer to the US or the EU as a whole and “region“ to each of the (member) states, or “planet” might be the entire world and “region” a country, or else “planet” might indicate a county and “region” one of its municipalities. 1 4 It is easy to verify that the risks that we consider cannot always be ranked according to stochastic dominance criteria. A mean-variance approach to the problem allows for more general comparisons, which depend on the degree of individuals’aversion to risk.
6
society’s welfare:15 W =R
V
where R is the expected return on a decision, V is its variance, and the riskaversion index > 0 measures individuals’willingness to accept lower returns in exchange for less risk. The balance between expected returns and riskiness of decisions will be shown to depend on the level of governance at which those decisions are made. In the next subsections, we will discuss the issue of centralization versus decentralization. Initially, we consider independent risks. Risks are said to be independent when a decision made by a local agency has no impact on other regions— that is, there are no externalities across regions. Risks are interdependent if the opposite holds true,16 a scenario that we will consider in section 2.3.
2.1
Centralization
When decisionmaking is centralized, all of the N experts are pooled together in one agency. Since the probability that a committee makes the right decision increases with the number of experts, employing all of the experts in one committee (n = N ) gives the most accurate decision possible, denoted by PN (p). For a decision with stakes G, the expected return and the variance of centralization are easily calculated as follows: R1 V1
= PN (p) G = PN (p) (1
PN (p)) G2
We will examine the performance of decentralized decisionmaking against this benchmark.17
2.2
Decentralization
Decentralized decisionmaking employs N agencies consisting of one expert each. In this scenario, the probability that the agency makes the right decision is trivially the same as the probability that the expert decides correctly, P1 (p) = p. 1 5 In turn, assuming that all individuals are identical, the social welfare function can be supported by a utilitarian summation of individual utility functions of the following form: Yj = 1 (R V ), for j = 1; :::; M . It should not come as a surprise that, unlike individuals’utility M functions, experts’ utility functions were assumed to be consistent with the maximization of the expected return but do not include concerns about the variance. Experts, in fact, operate at a local level, while the variance is a concern only if one takes a global perspective. 1 6 Note that local outcomes may be dependent on each other for other reasons. For instance, local agencies might in‡uence each other’s decisions. In this paper, we assume that agencies decide independently of each other. 1 7 Our model is based on an assumption of no decision costs. That is, increasing the size of the committee does not trigger any additional cost due to more lengthy or cumbersome decisionmaking processes. In a number of circumstances it might be more plausible to assume positive decision costs that increase as the committee size increases. Should this be the case, the advantage of centralization in terms of better decisions will be constrained by concerns about the costs of decisions.
7
Because local outcomes are independent of each other, expected return and variance of the decision are simple sums over the N local expected returns and G variances. Moreover, as each region is N1 of the planet, the local payo¤ is N , that is the stakes of the decision at the global level divided by the number of regions. Accordingly, expected return and variance are as follows: RN VN
= pG 1 = p (1 N
p) G2
Centralization has a clear advantage over decentralization: it yields larger expected returns (R1 > RN ). This result occurs because the decision made by a centralized agency is more accurate than the decisions made by each of the local agencies (PN (p) > p). This is true for any level of expertise but is more pronounced for interior values of p. In fact, when p approaches 21 (complete lack of expertise) or 1 (very accurate expertise), PN (p) approaches p and hence the returns to centralized and decentralized decisions are the same (see …gure 1).
R
1.0
0.9
0.8
0.7
0.6
0.5 0.5
0.6
0.7
0.8
0.9
1.0
p
Figure 1 : Expected returns of decisions under centralization (dashed curve) versus decentralization (solid line) with G = 1 and N = 9. With respect to risk, however, there are two countervailing e¤ects. On the one hand, centralized decisions are more tightly clustered around the right decision than decentralized ones— in fact, PN (p) (1 PN (p)) is less than p (1 p)— to the e¤ect that the variance tends to be lower under centralization. On the other hand, the outcome is the same for all regions in centralized decisionmaking while it may vary under decentralization. The possibility for di¤erent local decisions realizes a spreading of the risk, which in turn allows for lower variance under decentralization— re‡ected by the term N1 . Which of these two e¤ects prevails depends on the total number of experts N and their expertise p.
8
V
0.25
0.20
0.15
0.10
0.05
0.00 0.5
0.6
0.7
0.8
0.9
1.0
p
Figure 2 : Variance of decisions under centralization (dashed curves) versus decentralization (solid curves) with G = 1 and N = 9 (thick curves) or N = 15 (thin curves). Figure 2 depicts the variance of decisions when there are N = 9 experts. With decentralization the variance is hill-shaped, while centralized decisionmaking yields a bell-shaped function. The …gure only depicts the halves of those functions that apply to our setting (p > 21 ). There is a level of expertise p^ at which the solid curves cross (^ p is about 0:8 in the …gure). When the available expertise is poor (p < p^), decentralization attains a lower variance; in contrast, with advanced expertise (p > p^) centralization performs better. This result suggests that decentralization is a substitute for lack of expertise in terms of reducing the riskiness of decisions. Is this also the case with respect to N ? When N increases, the variance of decentralized decisions decreases because there are more regions and hence spreading risk is easier; the variance of centralized decisions also decreases because the accuracy PN (p) of decisions increases. Both (dashed) curves move downwards and to the left, crossing at a point p^0 < p^ (^ p0 is about 0:76 in the …gure). Thus, centralization becomes desirable for a broader range of expertise, suggesting that decentralization is also a substitute for a lack of experts as it is for a lack of expertise. We can now draw some implications for social welfare based on the choice between centralization and decentralization. When the available expertise is advanced, centralization is to be preferred as it yields more accurate and less risky decisions. With poor expertise, decisions under centralization, although more accurate, are also more risky than under decentralization. The choice then depends on how much weight is given to riskiness. In turn, this depends not only on the risk-aversion index, which obviously makes decentralization more desirable, but also on the stakes of the decisionmaking process G, which appears as a simple term in the expected return but is squared in the calculus of the variance. Hence, when the stakes are higher— that is, when the right decision is very valuable compared to the wrong decision— decentralization is again more 9
desirable. Finally, the number of available experts in‡uences this balance by lowering the threshold of expertise above which centralization dominates, thus undermining the scope of decentralization. The following proposition summarizes these results. Proposition 1 With independent risks, if p p^, centralization is preferable to complete decentralization. If p < p^, centralization is preferable for a low degree of risk-aversion or small stakes G; otherwise complete decentralization is preferable. The threshold p^ decreases in the number of experts N .
2.3
Governance with interdependent risks
Although some risks might be independent, other risks are not. A bad decision made in one region might well a¤ect neighboring regions or even the entire planet. It is not super‡uous to stress once more that, although we are analyzing the case of interdependency, this only refers to outcomes and not to decisions, which we still assume to be made independently in each region. There are various ways in which interdependencies could play a role in this analysis, but there is something all formulations will have in common. When the outcomes are more dependent on one another, the advantage of decentralization in terms of risk-diversi…cation tends to fade away. To show that decentralization may still play a role, let us examine an extreme scenario in which the decisions made by di¤erent agencies are aggregated to produce a unique global outcome that applies to all regions; that is, the riskdiversi…cation advantage is completely lost. Let us de…ne interdependency to mean that if some regions make the right decision, this converts into a good outcome for the entire planet irrespective of the decisions other regions made.18 Note that in this case there is no advantage in diversifying risk as the outcome is either good or bad for all regions. Accordingly, the problem in this scenario is merely how to maximize the likelihood of a good outcome. In order to clarify the role played by interdependent risks, we will examine three stereotypical cases. 2.3.1
Best-shot risks
With best-shot risks, such as the risk that an endangered species will become extinct, local policies are perfect substitutes in the achievement of the global policy and, thus, success at the local level results in success at the global level. Here, making the right decision in any of the regions means that the outcome will be good for the whole planet, irrespective of whether other regions have 1 8 Using terminology borrowed from reliability theory (Harrison 1965), the problem is one of determining the reliability of an r-out-of-N system: the system works if at least r components work. The di¤erent types of risks analyzed below can be interpreted as follows: best-shot risks describe a 1-out-of-N system (a parallel system), majority risks describe a N2+1 -out-of-N system and weakest-link risks describe a N -out-of-N system (a series system). The probability P N i that at least r regions take the right decision is thus given by: Qr = N p)N i . i=r i p (1 Accordingly, expected return and variance with interdependent risks are as follows: RN = Qr G and VN = Qr (1 Qr ) G2 .
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also made the right decision. The formula governing these types of risks can be written as 1 minus the probability that all regions make the wrong decision: N Q1 = 1 (1 p) > PN (p). The probability of success in best-shot risks is greater with decentralization than with centralization. There are two forces at work. Although decentralization triggers a negative e¤ect, as its accuracy is less than that of a centralized agency, the likelihood that all regions make the bad decision is small and turns out to be less than the probability that the centralized agency makes the wrong decision. Thus the likelihood of a good outcome can be improved by decentralizing decisionmaking. 2.3.2
Majority risks
In the intermediate case of majority risks, success or failure depends on what the majority of the local agencies decide. The situation described corresponds to a risk that can be avoided if, at the local levels, there are more right decisions than wrong ones. The probability of success in majority risks is the same whether decisions are centralized or decentralized. This is due to the fact that decisions by local agencies in a decentralized system are aggregated in the same way as the votes of individual experts in a centralized agency: Q N +1 = PN (p).19 2
2.3.3
Weakest-link risks
With weakest-link risks, such as the risk of a viral epidemic, local policies are strict complements for the achievement of the global policy and, hence, local failure results in global failure. Here, a wrong decision in any of the regions entails a bad outcome for the whole planet. The formula governing these types of risks can be written as the probability that all regions make the right decision: QN = pN < PN (p). Here increasing decentralization has two negative e¤ects. The …rst negative e¤ect is that a local agency is less accurate than a centralized one; the …rst negative e¤ect is that for the outcome to be good all agencies have to make the right decision, which further lowers the odds that the outcome will be good. The combined e¤ect is that the likelihood of success decreases with decentralization. To summarize, the result of the decisionmaking process heavily depends on the type of risk. Decentralization has two countervailing e¤ects. On the one hand, it entails a lesser degree of accuracy in each of the regions, thus potentially reducing the expected return on the decision. On the other hand, it makes it more likely that at least some regions will adopt the right decision. Whether one e¤ect dominates the other depends on the proportion of regions that need to make the right decision for the global outcome to be good. The following proposition follows directly from the previous analysis. 1 9 Formally,
Q N +1 = 2
PN
+1 i= N2
N i
pi (1
p)N
11
i
= PN (p).
Proposition 2 With best-shot risks, complete decentralization is preferable to centralization; with majority risks, complete decentralization and centralization are equivalent; …nally, with weakest-link risks, centralization is preferable.
2.4
Intermediate levels of governance
In the preceding subsections we have sought the optimal level of governance in a dichotomous fashion, only allowing for complete centralization or complete decentralization. In this section we extend the analysis to intermediate levels of governance in between these two extremes. We thus employ a more general framework, which encompasses centralization and complete decentralization as special cases. The planet is partitioned into k regions of equal size, so that in each region decisions are independently made by a local agency. The N experts will be accordingly distributed among the k local committees, so that each committee is composed of N k experts. By varying the parameter k, one can describe centralization (k = 1) and varying degrees of decentralization (1 < k N ). As the number of regions k grows, we have an increasing degree of decentralization and a decreasing number of experts per agency; the limit case (k = N ) corresponds to complete decentralization, which was examined in the above section. It is also possible in this framework to show that, with independent risks, if expertise is better than a certain threshold (p > p), making decisions at a central level yields both less risk and greater accuracy. Therefore, centralization is preferable and the optimal partitioning of the planet would be in one all-encompassing region (k = 1). However, if expertise is poor (p < p), there is a trade-o¤ to be addressed. While decentralization progressively lowers accuracy, it also yields better risk spreading; thus, some level of decentralization might be optimal (k < N ), but not necessarily complete decentralization as in the dichotomous case of the previous section. As in the previous case, the optimal balance between risk and expected returns and, hence, the optimal level of decentralization k depend on the parameters of the model. Finally, with interdependent risks, allowing for intermediate levels of decentralization does not change the results obtained in the dichotomous case, since either centralization or complete decentralization is optimal.
3
Discussion
In the previous sections, we have made a number of assumptions. Here we discuss four of them, which have particular relevance for the interpretation and the domain of application of our analysis.
3.1
Right and wrong decisions
We base our analysis on the idea that there is a “right”decision, one that most bene…ts society. Such a right decision exists in those cases in which mankind
12
share a common goal, even if the right decision is generally not known ex ante— in fact, identifying the right decision ex ante is the problem we address in this paper. This is a limitation of our approach, because individuals may di¤er in their goals; in such cases, unanimous consent cannot be reached. Consequently, the notion of a “right decision”necessarily rests on a previous choice of a social welfare function that aggregates individual preferences.20 However, the formulation of a social welfare function is a well-known and more general problem in welfare economics, which is not speci…c to our framework and we do not address it here. Thereby, our analysis is necessarily based on the assumption that society’s goal has been set.
3.2
Decentralized knowledge
In the model we assume that scienti…c knowledge is exogenously given and does not depend on the level of governance. However, one could entertain the idea that there might be some inherent informational advantages in going local. If this is true, the expertise would increase with decentralized decisionmaking; in other words, p would become endogenous to the model. Let us consider two plausible instances. The …rst is that local decisionmakers might better know the preferences of their constituencies. The main point is that what is considered an acceptable risk by one constituency may not be considered so by another.21 Second, even with homogenous preferences, local conditions or exposure to risk may vary. To illustrate, take two di¤erent standards commonly used by regulatory food agencies: the acceptable daily intakes (ADI) and the maximum residue levels (MRLs) of potentially harmful compounds present in food. The optimal ADI may di¤er across regions because preferences concerning acceptable risks vary; with the same preferences, the optimal ADI standards should in theory be the same. In contrast, optimal MRLs might vary even with homogeneous preferences, because of local variations in food consumption behavior. Local experts are likely to better evaluate both local preferences and local conditions, such as exposure to risks, which translates into an increase in p when decentralizing. Ceteris paribus, decentralization becomes more desirable. In our model this would imply a larger p in the case of decentralization and quantitatively (but not qualitatively) bias the results away from centralization.
3.3
Centralized diversi…cation
Knowledge acquired by a centralized agency could be spread to local agencies or else the central government could directly implement di¤erent policies in di¤erent regions. Apparently, in this way one could escape the risk-return 2 0 Miller (1986) tackles this problem by considering as correct the alternative that would receive a majority of votes ex post, when all information is available. See also Ladha (1992, 620). 2 1 There are many examples of geographical di¤erences in risk perceptions and risk-aversion towards food safety; see Schroeder et al. (2007) and Gaskell et al. (2004). For the seminal studies on risk perceptions, see Slovic, Fishho¤ and Lichtenstein (1980) and Slovic (1987).
13
trade-o¤ and achieve the characteristic high returns of centralization and the risk-diversi…cation typical of decentralization. However, this scenario might be problematic in some cases. In fact, assume that the centralized committee of experts has deliberated in favor of policy A. If this advice is transmitted to local agencies, the likely result is that all local agencies will implement policy A, thus risk-diversi…cation will not be achieved. Should a central agency try to diversify by implementing the superior policy A in some regions and the inferior policy B in other regions, this approach would likely encounter strong political opposition of the not-in-my-backyard type. Again, once policy A is found to be the superior policy, it will probably be implemented across the board. We concede that in some cases it is possible that a central agency might locally diversify its policies, but our main observation that decentralization generates risk-diversi…cation remains qualitatively valid, even though the results might be quantitatively a¤ected.
3.4
Individual mobility
The analysis of the previous sections is based on an implicit assumption that individuals care about global and not only local outcomes. This approach in turn implies that individuals can move from one region to another should the wrong policy be implemented in their region.22 Instead, if individuals cannot move or else they only care about local outcomes, the analysis changes. In this case, in fact, there would be no advantage in having di¤erent regions make di¤erent decisions, because all individuals care about is the outcome in their own region. Paradoxically, when individuals are only concerned about local outcomes, they favor centralization, as this is the level of governance that guarantees the highest probability of making the right decision overall.
4
Summary and conclusions
The issue of whether to allocate regulatory powers to a central or local agencies remains disputed in the context of European and American administrative law as well as in the international arena, where an increasing number of international bodies is setting world-wide harmonized standards. Within the European context, the number of expert agencies has boomed in the recent past: ten agencies were created in only …ve years (1990-1995).23 2 2 Moving to another jurisdiction generates congestion costs— more individuals have to share in the same pie— but allows individuals to overcome some of the e¤ects of a bad decision in their jurisdiction by participating in the bene…t of a good decision in another jurisdiction. 2 3 These agencies are: the European Environmental Agency (EEA); the European Training Foundation (EFT); the European Monitoring Centre of Drugs and Drug Addiction (EMCDDA); the European Agency for the Evaluation of Medicinal Products, renamed in 2004 European Medicines Agency (EMEA); the O¢ ce for Harmonization in the Internal Market (OHIM); the European Agency for Safety and Health at Work (EU-OSHA); the Translation Centre for Bodies of the European Union (TC); the Community Plant Variety O¢ ce (CPVO); the European Foundation for the Improvement of Living and Working Conditions (EFILWC); and the European Centre for the Development of Vocational Training (CEDEFOP). These
14
The creation of several agencies in a relatively short period of time could be seen as an evidence of increasing centralization.24 An interesting example of the shift towards more centralization is provided by the regulation of pharmaceuticals and the creation of the European Medicines Agency (EMEA). Before the establishment of the EMEA, pharmaceuticals were approved by national authorities of various Member States. Under the new system, applications for the authorization of marketing of innovative medicines must be submitted to the EMEA.25 It is interesting to note that, like in our model, the new centralized system relies on a wide number of experts— there are currently over four thousand experts— pooled from the Member States.26 Notwithstanding the creation of several agencies, the allocation of regulatory powers between European and Member States institutions is not always clear cut and the debate over whether to centralize or decentralize is still very intense. Insights from our model could help the European regulator assess the e¤ects of granting more or less regulatory powers to existing (and future) regulatory agencies. In this sense, notice that the jurisprudence of the European Court of Justice, which has tended to allow more decentralization in the presence of high scienti…c uncertainty (Vos 1999, 47), is in line with our results. Our analysis may be similarly applied to the US context. While federal agencies are an older phenomenon in the US, issues of risk-diversi…cation or of advantages generated by pooling experts never entered the debate on environmental federalism or other analyses of attribution of regulatory powers to federal versus national agencies (Revesz 1992, 1996 and 2000; Esty and Geradin 2000). Additionally, it is worth emphasizing that the harmonization of various types of standards is also taking place at the international level where a number of standard-setting institutions are directly or indirectly gaining regulatory power, to the extent that some scholars speak of global administrative law.27 One ilbodies are commonly referred to as European agencies, even if in the o¢ cial name they are called authorities or foundations. Today there are twenty-four agencies in Europe; while not all these agencies perform regulatory tasks, most have an important in‡uence on the regulatory process. For an analysis of the functions performed by these agencies see Chiti (2000). 2 4 The jargon used in some European legal texts may be confusing as decentralization is not only used to denote the allocation of (regulatory) powers at the local level but also to denote the functional division of powers (for example, the creation of specialized bodies to deal with speci…c issues). 2 5 EMEA became operational in 1995. Under the previous system a process of “automatic” mutual recognition was established by law; however, it never worked well in practice, leading to a de facto highly decentralized system. It should be noted that under the new centralized system, the decision is technically adopted by the Commission; despite that, the Commission’s decision is generally in accordance with the Agency’s opinion. Additionally, it is worth remembering that the centralized authorization procedure is compulsory only for biotechnological medicines and it remains optional for other highly-technological medicines. Moreover a decentralized market authorization procedure remains; however, the EMEA still plays an important role under this more decentralized system. For a more detailed description of these processes see Vos (1999, 206-50). 2 6 EMEA operates through various technical committees, including the Committee for Medicinal Products for Human Use (CHMP) and the Committee for Veterinary Medicinal Products (CVMP), both counting on experts from the Member States. The CHMP, for example, is mainly composed by 54 members, two for each each of the 27 EU Member States. 2 7 For a seminal work in this area see Kingsbury, Krisch and Stewart (2005). Institutions
15
lustrative example is the Codex Alimentarius Commission, created in 1963 as a joint organ of the Food and Agriculture Organization (FAO) and the World Health Organization (WHO). The food safety standards established by Codex— while mainly of a non-binding nature— are gradually acquiring more force due to the interplay of risk law with WTO law (Charnovitz 2005; Masson-Matthee 2007). If centralization of expert-driven law is also taking place at a global level, it is crucial to investigate whether and to what extent this process is desirable. Our model provides an analytical framework to begin research in this relatively unexplored area. Furthermore, our analysis has bearing on a vast array of regulatory processes that are performed by technical bodies. While our contribution is most directly applicable in the …eld of risk regulation (by which we refer to health, safety and environmental regulation), its results may be considered generally applicable because risk is virtually present in any decision and information is rarely perfect. What are the determinants in favor of more or less centralization of regulatory powers into a single agency? Cutting horizontally through di¤erent strands of literature, we have argued that decentralization can function as a risk-diversi…cation device. Our analysis has re-conceptualized the notion of optimal level of governance by unveiling a risk-return trade-o¤. Most prominently, we have characterized decentralization as a substitute for scienti…c expertise. We have shown that with independent risks— such as local pollution problems— the choice between centralization and decentralization crucially depends on the level of scienti…c expertise available. If advanced expertise is available, centralization guarantees both more accurate decisions and less risk. Instead, with poor expertise, while centralization yields more accurate decisions, decentralization lowers risk. The balance is in favor of decentralization if the degree of risk-aversion is su¢ ciently large and stakes are high. This result suggests that decentralization is a desirable solution for decisions that are important to society, a¤ected by serious scienti…c uncertainty and for which society is riskaverse. If resources devoted to the decisionmaking process are increased— an increase in the number of available experts, in our model— the critical threshold for the expertise is reduced, making centralization desirable at lower levels of expertise. Thus, a better-funded decisionmaking process is more e¢ ciently centralized than a comparable process relying on less resources. We have also analyzed interdependent risks, showing that decentralization plays a role in a subset of cases, namely, best-shot risks. Our model has considered a clean set of cases in which scienti…c uncertainty plagues the decisionmaking process concerning balanced issues, where it is important to make the right decision but errors on either side have the same functioning as global regulators include the Organisation for Economic Co-operation and Development (OECD) network of committees, the World Trade Organization (WTO) committees, the World Intellectual Property Rights Organization (WIPO), the World Health Organization (WHO), the International Standards Organization (ISO), and the International Labour Organization (ILO). It is beyond the scope of this paper to discuss the extent to which these institutions perform a role of centralized regulatory decisionmaking. For such an analysis see the Global Administrative Law project: http://www.iilj.org/GAL/default.asp.
16
impact. Future research might enrich this framework by considering di¤erent likelihoods and costs for type I and type II errors, introducing some form of status-quo bias, considering regulatory capture, and including learning explicitly in the model.
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21
Appendix (not in published article) Here we provide a formal proof of propositions 1 and 2 in the paper and of the results concerning intermediate levels of governance. The following results will be used in the proofs. From Mood (1950, p. 235): Pn (p)
n X
=
n i p (1 i
i= n+1 2
n
= n
Z
1
n 1 2
p
x
n i
p) n
1 2
(1
x)
n
1 2
dx
(1)
0
with the following …rst and second derivatives: 0
Pn (p) 00
Pn (p)
= n = =
n
1
2p 2
(n
1
n 1 2
p
n
n (n
1 2
(1
1)
p) n
n
1
>0
2
1
n 1 2
p
n
3 2
(1
p)
n
3 2
1) (1 2p) 0 Pn (p) < 0 2p (1 p)
This formulation refers to n odd. If n is even, ties are randomly attributed to either decision and there is an easy transformation rule to bring the analysis back to n odd: Pn (p) = Pn 1 (p) (Miller, 1996, p. 175). From Boland (1989, p. 181): 1 Pn (p) = Pn (1 p) (2) Finally, from Berg (1997, p. 564): Pnk (p) > Pk (Pn (p))
(3)
Remark 3 The variance of a decision Vk decreases in p. For k = N , Vk decreases at an increasing rate; for 1 k < N , Vk decreases at an initially increasing and then decreasing rate. Proof. Since k cannot take all integer values between 1 and N , let us …rst N de…ne a set of feasible odd values for k and n k . Let T = ft1 ; :::; tT g be a non-empty set of T prime numbers greater than 2 and let Tn and T Qk be two subsets of T such that T [ T = T and T \ T = ?. Let N = n k n k i ti 2 T, Q Q n = i ti 2 Tn if Tn 6= ? (n = 1 otherwise), and k = i ti 2 Tk if Tk 6= ? (k = 1 otherwise). Note that nk = N . Let us now consider 1 k < N . The variance is Vk =
1 Pn (p) (1 k 22
Pn (p)) G2
with 0
Vk =
1 (1 k
0
2Pn (p)) Pn (p) G2 < 0
and, using (1), 00
Vk
= =
00 1h (1 2Pn (p)) Pn (p) k 0 1 Pn (p) ( ) G2 k 2p (1 p)
i 02 2Pn (p) G2
where: = = 00
Note that sign Vk
(2p
1) (2Pn (p)
1) (n
1) > 0
0
4p (1
p) Pn (p) > 0
= sign (
); since
is zero at p =
1 2
and increases
00
in p, while is zero at p = 1 and decreases in p, Vk changes sign from negative to positive as p increases. Thus Vk decreases in p at a rate that is initially increasing and then decreasing, as in …gure 2.2. Instead, for k = N we have VN = N1 p (1 p) G2 , which is a strictly concave function of p with 0 00 VN = N1 (1 2p) G2 < 0 and VN = N2 G2 < 0. Lemma 4 There exists a unique p^k : Vk = VN and
1 2
< p^k < 1 .
Proof. Vk = VN implies 1 1 Pn (p) + p (1 k N
1 2 Pn (p) k and
1 1 Pn (p) = + 2 2
r
4 p (1 n
1
p) = 0
p)
(4)
Fn (p)
(5)
Note that p^k is a solution to (4) i¤ it satis…es the condition in (5). It has been shown above that Pn (p) is a concave function of p and it is easy to show that Fn (p) is a convex function of p: Fn0 (p)
= n
Fn00 (p)
q
(n =
2
2p 1 n
1
(n
4p (1 q 1) n1 (n (n
4p (1
>0 p)) 4p (1 2
p))
p)) >0
Thus, Pn (p) crosses Fn (p) at most twice. Note that Pn (p) crosses Fn (p) 0 from above at p = 1, since we have Pn (1) = Fn (1) = 1 and 0 = Pn (1) < 0 Fn (1) = n1 . Moreover, Pn 21 < Fn 12 . Thus, there exists one and only 23
one p^k such that Pn (p) < Fn (p) for 12 < p < p^ and Pn (p) > Fn (p) for p^k < p < 1. Since the discriminant is positive, the left-hand side of (4) is negative (Vk > VN ) for p < p^k and positive (Vk < VN ) for p > p^k . It follows that any variance function Vk for a level of decentralization 1 k < N (note that k = 1 corresponds to centralization) crosses the variance function VN (k = N , complete decentralization) from above at p^k . Remark 5 p^k increases in k and decreases in N . ^k increases in k Proof. First note from (5) that p^k is a function of n = N k . Thus p (for a given N ) and decreases in N (for a given k) i¤ p^k decreases in n, which we need to show here. We have calculated the value of p^k using Pn (p) Fn (p) = 0 for n taking odd values between 3 and 35. The plot is shown below. Such values of n cover situations with N 35 and any feasible 1 k N . Scienti…c committees are likely to be small in size, hence this simulations are a su¢ cient proof of our results. We conjecture that these results are also valid for any k and N greater than 35.
P(p)-F(p)
0.006
0.005
0.004
0.003
0.002
0.001
n=35
n=3
0.000
0.75
0.80
0.85
0.90
0.95
1.00
p
-0.001
Figure 4: Values of p^k for n between 3 and 35. The …gure above shows the results of our numerical calculations. Proof of proposition 1. Let p^ p^1 . From lemma 4 it follows that V1 > VN for p < p^ and V1 < VN for p > p^. Thus, for p > p^, we have R1 > RN and V1 < VN ; hence, social welfare in (??) is maximized by centralization. In contrast, for p < p^, we have R1 > RN and V1 > VN . In this case, social welfare is maximized by centralization if the weight given to the variance is small, that
24
is if or G are small. Otherwise complete decentralization is desirable. From remark 5 it follows that p^ decreases in N . Proof of proposition 2. With best-shot risks, the inequality 1 PN (p) can be rewritten as: N
(1
p)
(6)
Using (2), we can write: 1
PN (p)
= PN (1 =
p) N
(1
p) +
N X1
i= N2+1
N N p i
i
(1
i
p) > (1
N
p)
which shows that (6) always holds true. The claims concerning majority risks and weakest-link risks are self-evident. Lemma 6 There exists a unique p^hk : Vk = Vh , with 1
k < h < N and
1 2
< p^hk < 1 .
Proof. Vk = Vh implies 1 1 Pn (p) = + 2 2
r 1
4
m Pm (p) (1 n
Pm (p))
Fn (Pm (p))
where N n>m N k h . To prove the lemma, let us rewrite Pn (p) as a function of Pm (p): G (Pm (p)) Pn (p) and formulate the problem in a similar fashion 0 as in lemma 4, which we will then be able to apply. Using @G @p = Pn (p) we have @G (Pm (p)) @p
=
0 @G (Pm (p)) 0 Pm (p) = Pn (p) @Pm (p) 0
) Likewise, using @ 2 G (Pm (p)) @p2
@2G @p2
=
@G (Pm (p)) P (p) = n0 >0 @Pm (p) Pm (p)
00
= Pn (p), we have 00 @ 2 G (Pm (p)) 0 @G (Pm (p)) 00 Pm (p) + Pm (p) = Pn (p) 2 (p) @Pm @Pm (p) 00
0
P (p)
00
)
Pn (p) P n0 (p) Pm (p) @ 2 G (Pm (p)) m = 0 2 (p) @Pm Pm (p)
=
1 2p Pn (p) (n 0 2p (1 p) Pm (p)
0
25
m) < 0
Thus, G (Pm (p)) is a concave function of Pm (p). Moreover, we have G (1) = 0 0 Fn (1), G (1) < Fn (1) and G 21 < Fn 12 , which all follow from straightfor0 ward calculations. Let us now remark that we can calculate G (1) as follows 0
lim G (Pm (p))
p!1
0
P (p) = lim n0 p!1 Pm (p) =
lim
p!1
n
n 1
m
m 1
n
1 2
p
n
m 2
(1
p)
n
m 2
=0
m 1 2
It follows, as in lemma 4, that there exists a unique value of Pm (p) such that G (Pm (p)) = F N (Pm (p)). Since P N (p) is monotone increasing in p, there k h exists a unique p^hk that satis…es the former condition. Lemma 7 If Vh and Vk , with h > k, cross at p^hk , then Vg , with g > h, crosses Vk at p^gk and Vh at p^gh with p^hk > p^gk > p^gh . Proof. The proof follows trivially from lemma 4 and remark 5. Note that this result implies that Vk decreases in k for p < p^ and any 1 k N . Proposition 8 With independent risks, if p p^ the optimal level of governance is k = 1 (centralization). If p < p^ the optimal level of governance k increases towards decentralization in the degree of risk aversion and the stakes G, and decreases towards centralization in the number of experts N and in the expertise p. Proof of proposition 8. It follows from lemma 7 that, the variance function V1 crosses the variance function VN from above at p^ after having crossed all other variance functions Vk with 1 < k < N . For p p^, the lowest variance function is V1 ; thus, centralization is optimal (k = 1) for any levels of the parameters, since it yields both greater expected returns and lower variance than any other level of k. It also follows from lemma 7 that all variance functions Vk cross VN from above after p^. Thus, for p < p^ the lowest variance function is VN . In this case, centralization maximizes the expected return, while complete decentralization minimizes the variance. The expected return Rk decreases in k; from lemma 7 we know that also the variance Vk decreases in k if p < p^. Thus, by reducing k we have greater expected returns at the price of greater risk and, vice versa, by increasing k we have lower risk at the price of lower expected returns. The socially optimal level of k depends on the weight given to Vk in terms of and G; hence, k increases in and G. Finally, we know that for any k and for p p^, the variance Vk decreases in p and— as a direct consequence of from lemma 7— in N . It follows that when p or N increases, the same expected return corresponds to lower variance and hence k can be further increased to attain greater expected returns. Thus, k increases in p and N .
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Proposition 9 The results of proposition 2 also apply to the case of intermediate levels of governance Proof. If we allow for intermediate levels of governance, the probability of a good outcome in the case of k agencies is Qr (p; k) =
k X N i P N (p) 1 k i i=r
k i
P N (p)
(7)
k
With best-shot risks, (7) becomes k
Q1 (p; k) = 1
P N (p)
1
k
The level of k that maximizes Q1 (p; k) is k = N , complete decentralization. k
This is the case if 1
1
P N (p) k
N
(1 p) , which is always satis…ed by virtue of (??). Thus, even when intermediate levels of decentralization are feasible, it remains optimal to decentralize governance completely. With majority risks, (7) becomes Q k+1 (p; k) = 2
k X
i= k+1 2
k i P N (p) 1 k i
k i
P N (p) k
(8)
Note that Q k+1 (p; k) in (8) can be written as Pk P N (p) , which is the k 2 same as the probability that a committee of k members takes the right decision, where the probability that each member of the committee votes for the right decision is given by P N (p). This is in turn the probability that a committee of k N k experts takes the right decision, given a probability p that each expert takes the right decision. From the perspective of calculating the probability that a good outcome results, majority risks are analogous to an indirect majority system. The inequality in (3) suggests that one (direct majority) committee of nk members has a larger probability to take the right decision that a two-step procedure in which …rst k di¤erent committees of n members decide independently and then they each send a delegate to a an assembly of the k delegates, who vote again and take the …nal decision. Applying this result to our setting imN +1 plies Qk p; k 2 < Q1 p; N2+1 = PN (p), that is, any intermediate level of decentralization achieves a lower probability of a good outcome than complete decentralization and centralization. With weakest-link risks, (7) becomes k
Qk (p; k) = P N (p) k
It is easy to see that by reducing k to 1 the former probability improves, suggesting that centralization fares better than any level of decentralization. 27
References [1] Berg, S. (1997), “Indirect Voting Systems: Banzhaf Numbers, Majority Functions and Collective Competence,” 13 European Journal of Political Economy, 557-573. [2] Boland P. J. (1989), “Majority Systems and the Condorcet Jury Theorem,” 38 The Statistician, 181-189. [3] Miller, N. R. (1986), “Information, Electorates, and Democracy: Some Extensions and Interpretations of the Condorcet Jury Theorem,” in Grofman, B. and Owen, G. (eds.), Information Pooling and Group Decision Making, Greenwich, CT: JAI Press. [4] Mood, A. M. (1950), Introduction to the Theory of Statistics, New York: McGraw-Hill.
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