Public Choice 113: 251–263, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.
251
Jurisdiction size, political participation, and the allocation of resources RAINALD BORCK DIW Berlin, Königin-Luise-Str. 5, 14195 Berlin, Germany; e-mail:
[email protected] Accepted 18 October 2001 Abstract. This paper analyzes the effect of population size on political participation and allocative efficiency. Increasing population is generally found to reduce political participation. However, since participation is not evenly spread throughout the population, this will have consequences for allocation. Namely, we argue that increasing population size shifts power to the rich. We discuss the consequences for the optimal size of jurisdictions, the size of government, and the measurement of publicness.
1. Introduction Economic theories of federalism, local public goods and club goods have, for some time, studied the optimal size of jurisdictions. In local public goods models (Tiebout, 1956), the optimal jurisdiction size is found by trading off benefits from cost sharing against congestion costs. Theories of federalism argue that small governments can better satisfy diverse preferences, while running the risk of leaving scale economies unexploited and spillover externalities uninternalized (Oates, 1972). Whereas economists concentrate on the effects of jurisdiction size on the allocation of resources, political scientists have long been concerned with other functions of jurisdictions. In summarizing some of these political theories, Inman and Rubinfeld (1997b) argue that an optimal federalism should allocate decision rights to achieve economic efficiency, protect individual rights, and ensure political participation by citizens. In particular, while large jurisdictions may be more efficient in dealing with public goods provision, political participation may be more widespread in smaller jurisdictions. They discuss possible benefits from political participation, including instrumental, educative, and consumptive benefits. In arguing that optimal federalism should trade off participation and efficiency, they implicitly concentrate on the consumptive and educative benefits of participation. This paper, on the other hand, concentrates on the instrumental benefit of voting. Namely, we argue that political participation affects the allocation of resources and should therefore be included in the traditional economic
252 analysis of federalism. The reason is the well-documented fact that political participation is not uniform throughout the population. In particular, turnout in elections has been shown to increase with income and decrease with the size of the constituency.1 We take these observations as starting points for the analysis of the effect of group size on political participation and allocation. To this end, we assume that the political process yields the outcome desired by the median voter. However, since individuals may abstain, this need not be the population median. In particular, we argue that since participation increases with income, the median of the voters will lie above the population median. We then describe the effect of population size on turnout and, hence, the voting outcome. We show that definite results can be obtained if the distribution change can be characterized with the concept of first-order dominance. We thus link the study of optimal jurisdiction size – as it appears in models of club goods and local public goods, and fiscal federalism – with the problem of political participation. Downs (1957) argued that in large two-candidate elections, the probability of being decisive was essentially zero and, given positive costs of voting, rational individuals should therefore abstain, unless they derive some non-monetary benefit from voting. Later on, game theoretic models have criticized this approach, since it ignores strategic interaction: If any one individual thought no one else voted, he or she would be decisive with probability one, and should therefore vote if the costs were not too large (Ledyard, 1984). Hence, no one voting may not be an equilibrium either, at least with low costs of voting. Some game-theoretic models have found equilibria with positive turnout (see, e.g., Aldrich, 1997, for a survey). However, with some exceptions, the literature has been rather silent on the effect of turnout on allocation. Among the first to study this issue, Ledyard (1984) analysed turnout and voting outcomes in large two-candidate elections. Feddersen and Pesendorfer (1996) argue that uninformed voters may rationally abstain, since this increases the probability of the “right” candidate being elected. Abstention then has obvious consequences for the voting outcome. Osborne, Rosenthal, and Turner (1999) study participation in regulatory meetings. They show that moderates are likely to abstain. They also show that participation falls with population size. A similar model was presented by Larcinese (1999). He shows that richer voters have a higher incentive to be informed on political issues. Party competition in his model leads to candidates adopting positions corresponding to the ideal point of the expected median voter. Since information increases with income, the expected median has income larger than the population median. There are also some recent empirical studies which have examined the link between turnout and voting outcomes. Rothenberg and Sanders (1999) exam-
253 ine congressional voting and find that on several important votes, abstentions altered the outcome. Lindert (1996) and Mueller and Stratmann (1999) found that voter turnout increases social spending. This is compatible with the idea that high turnout gives more power to the poor who benefit from spending on social programs. Thus, the idea that turnout can affect voting outcomes is not only reasonable but seems to be supported by evidence. By implication, the effect of different institutions on voter participation and, hence, on allocation, should be taken into account. The paper proceeds as follows. Section 2 describes how political participation affects the optimal size of jurisdictions. In Section 3, we outline the reasons why political participation should vary systematically with income and constituency size. The empirical evidence on these effects is also discussed. In Section 4, we characterize the link between population size, participation, and allocation. Sections 5 and 6 study the model’s implication for the size of government, and the measurement of publicness. The last section concludes the paper.
2. Optimal jurisdiction size What is the optimal size of jurisdictions? To answer this question, we compare the approach in this paper to that of other models. Denote economic efficiency by E, political participation by P, and population by N. Let W (E, P) be the social welfare function, defined over political participation and efficiency. Since both E and P are functions of N,2 the optimal jurisdiction size solves max W(E(N, P(N)), P(N)). N
The first order condition for a maximum is:3 WE EN + WP P + WE EP P = 0.
(1)
Very roughly, traditional economic theories have concentrated on the first term in this expression: the optimal jurisdiction size should weigh the benefits and costs of increasing population, measured in the usual welfare economic sense. Let N∗ be the jurisdiction size where the first term of (1) is zero. Inman and Rubinfeld (1997a) assume WP > 0 > P : Political participation is a valued good, and participation falls with population size. They would therefore argue that the welfare economic rule would lead to jurisdictions which are too ˜ be the jurisdiction size large, other things equal, since WP P |N∗ < 0. Let N where the first two terms are zero i.e., the jurisdiction size which trades off benefits and costs in terms of economic efficiency and political participation.
254 In this paper, we emphasize that the third term in (1) should not be overlooked. In particular, ignoring this term might produce erroneous conclusions if participation is not distributed evenly throughout the population. Call the ˆ Assuming political participation to be jurisdiction size which satisfies (1) N. positively valued (aside from its allocative consequences), we would then conclude that disregarding the third term would lead to jurisdictions which are too small (large) as EP |N˜ < (>)0. The sign of this term depends on the particular model at hand. As an example, consider voting on pure public goods with head taxes. Then, as Bowen (1943) has shown, voting will produce a Pareto efficient allocation if and only if the median voter’s marginal rate of substitution equals the average ˜ and assume that MRS. Suppose we take the Inman-Rubinfeld solution, N, the collective choice would correspond to that of the “average voter”. Now introduce political participation: When less than 100% vote, at any population size, we would get a decisive voter with higher than average income, and, hence a public good level which is larger than optimal. Moreover, increasing population would increase the distance between the median and average voter and therefore lower welfare, other things equal. In other words, in this ex˜ > N. ˆ 4 Conversely, when voting gives ample, the last term is negative, and N too much power to the poor, increasing population might remedy negative allocative consequences by reducing participation and thus shifting power to the rich.
3. Political participation 3.1. Theory Why should political participation vary with individual characteristics, most notably, income? Participation should be broadly interpreted to include voting, lobbying, campaign contributions, bribes, demonstrations, etc. We will mostly talk about voting for expositional simplicity. Following the classic approach to voting (Downs, 1957; Riker and Ordeshook, 1968), the literature has argued that an individual should vote if pB + D − c > 0,
(2)
where p is the probability of being decisive, B the differential benefit obtained when one’s favorite position wins because of the voting decision, c is the cost of participation, and D any intrinsic benefit derived from political action per se. Most of the literature has argued that in large elections, the p term is minuscule, and hence, political participation – at least in large elections – is rational only if the intrinsic benefits outweigh the costs. In small electorates,
255 however, the probability of being decisive may not be that low, and thus, given a sizeable benefit B, voting or participation can be rational even without any intrinsic benefit. We now discuss possible reasons for why turnout varies systematically with income. First, the benefit of voting (the B term) may increase with income. Whether or not this is the case clearly depends on the incidence of the benefits from the issues to be decided. Second, the probability of being decisive may increase with income. This would seem plausible, for instance, in the case of campaign contributions. Individuals with higher incomes will donate more to politicians and thus wield more influence in the political process. Third, the costs of voting may vary with income. On the one hand, richer individuals may have a higher opportunity cost of time, which might lead them to participate less. On the other, they may also have lower costs of collecting and processing information.5 Finally, if voting is a good, then we might expect it to be a normal good (D increases with income), i.e., richer individuals may be more willing to bear a certain cost in order to vote, irrespective of the outcome.6 The effect of changing population, in terms of (2), is to reduce the individual’s perceived probability of being decisive: The more people there are in the polity, the lower each individual’s chances of influencing political outcomes. Hence, the rational voter hypothesis predicts that political participation will fall when the eligible population gets larger. 3.2. Empirical evidence We now briefly review the empirical evidence on the two building blocks of the model: that political participation increases with income, and decreases with population size.7 Among the studies that have examined the effect of income on participation, most have found a positive relationship. For instance, Ashenfelter and Kelley (1975), Durden and Gaynor (1987), and Greene and Nikolaev (1999) all found that election turnout increases with income. There are exceptions, for instance, Darvish and Rosenberg (1988) who find that turnout decreases with income. They interpret this finding to support the hypothesis that the costs of voting increase with income. Moreover, it may be that what is driving the results is education rather than income per se (Ashenfelter and Kelley, 1975; Powell, 1986). Moving beyond voting, political scientists have tried to measure the level of political participation, broadly defined to include voting, protests, campaign work, local board membership and campaign contributions. Verba, Schlozman, Brady and Nie (1993) found that across the various activities, the ‘socio-economically disadvantaged’ are underrepresented. See also Lijphart (1997) and the references therein. Thus, while not unequivocal,
256 the finding of the majority of studies is that richer (or, at least, more educated) voters participate more in the political process. The question whether population size influences participation has also been tested by numerous researchers. Among the first, Barzel and Silberberg (1973) found that turnout in U.S. gubernatorial elections was lower the lower the fraction of voters that are registered. Similar results were obtained, e.g., by Hansen, Palfrey, and Rosenthal (1987), Darvish and Rosenberg (1988), Durden and Gaynor (1987), and Capron and Kruseman (1988). Some studies have found insignificant effects, for instance, Kirchgässner and Meyer zu Himmern (1997). Kirchgässner and Schimmelpfennig (1992) found that population size and the electoral margin had the predicted negative effect when it counts for electoral victory, but not for elections in “subelectorates”, where the constituency size has no influence on the probability of being decisive. This finding then supports the rational voter hypothesis. However, Matsusaka and Palda (1993) find a negative effect of population on turnout in aggregate data, but not in individual turnout data. They interpret this as an instance of an ecological fallacy. Clearly, more studies on individual data are needed to settle this issue. However, it seems that a majority of the studies have generally supported the idea that the size of the constituency does affect political participation in the way predicted by the rational voter theory.
4. Population size, participation, and allocation The public choice literature has, with a few exceptions, assumed that all eligible voters go to the polls. Under the assumption that the issue space is unidimensional and voters’ preferences are single peaked, it then follows that a voting equilibrium exists and corresponds to the median voter’s ideal point (both in direct voting and in representative two-party democracy with vote maximizing parties). Suppose voters’ ideal points vary monotonically with their characteristics (say, demand for public goods is increasing in income). Since everyone is assumed to vote, the median voter is then identical to the voter with the median income in the population. However, if not everyone votes, policy will not generally correspond to the population median. We will assume that the properties of the issue to be decided are still such that the median voter theorem hold – i.e., one dimensional issue and single peaked preferences. Let us suppose that voters rationally decide whether or not to vote, and, once at the polls, which proposition to vote for. Suppose further that the issue selected will be the ideal point of the median voter, that is, the voter with median income among the voters. Let income be distributed on the interval [0, 1] according to the distribution function F(y) with density f(y) = F (y). Suppose further that voter
257 turnout is described by the function φ(y), which gives the fraction of voters which have income y. The corresponding cumulative distribution is (y). The population median is defined by F(y) = 12 , while the median voter is defined by8 F(y)(y) = 12 . How does reduced participation affect the allocation of political resources? In some cases, not at all. For instance, Osborne et al. (1999) show that, if the distribution is symmetric, there is an equilibrium where voters at the edges of the distribution vote, while those in the middle abstain. Since the distribution is symmetric, this implies that the median voter will be in the middle of the distribution independently of population size. However, this is obviously a special case, and also one which seems to be contradicted by the data. We assume in the following that population size is N, and φ (y) > 0 for all y. This implies that the median voter, Mφ , is larger than the population median, M. Consider now an increase of population to some N > N. Let us assume that the support of the distribution remains the same, and the new distribution is simply a larger replication of the old one, so the population median remains at M. Denote the distribution of voters associated with N by (y) with ψ(y) = (y). The median voter is now Mψ with F(Mψ ) (Mψ ) = 12 . A definite result can be obtained by using the concept of first order dominance. Formally first-order dominates if (y) ≤ (y) for all y ∈ [0, 1]. This implies that Mψ ≥ Mφ . To prove this claim, note that, from the definition of dominance, (y) ≤ (y) for all y. Thus, F(Mφ ) (Mφ ) ≤ F(Mφ )(Mφ ) = 12 . But this implies Mψ ≥ Mφ . The intuition for the result is quite simple: First-order dominance implies that the distribution puts more weight on higher income voters than . A sufficient condition is that the difference in participation rates for any income level, φ(y) − ψ(y), is nondecreasing in income. For instance, if participation is increasing in income, and with larger population the same number of voters abstains at each income level, the new distribution of voters dominates the previous one.
5. The size of government Does centralization increase the size of government? Following Oates (1985), there has been a debate on this topic, based largely on contradictory empirical evidence. Oates’ study followed a suggestion by Brennan and Buchanan (1980) that competition would tame Leviathan governments, and, therefore, limit the size of government. This approach assumes that competition forces revenue maximizing governments to lower tax rates or increase public service levels in order to attract citizens. In a model based on voting without mobility,
258 Persson and Tabellini (1994) found that the effect of centralization on the size of government depends on the shape of the income distribution function, and the nature of government activity. Suppose government redistributes income along the lines of Meltzer and Richard (1981). In particular, a linear income tax is used to finance lump-sum transfers. The size of the transfer is decided by the median income earner; transfers are positive if and only if median income is below mean income. Then the size of government increases if median income falls relative to mean income. If there are two regions with different income distributions, under reasonable assumptions, Persson and Tabellini (1994) find that centralization decreases the size of government. The reason is that in the richer region, centralization implies that some voters (namely, the formerly ‘poor’ who are now relatively rich) will want less redistribution, while conversely, some voters in the poor region (the formerly ‘rich’ who are now relatively poor) will want more redistribution under centralization. Since distribution functions are assumed to be skewed to the right, there are more of the former than of the latter, so the decisive voter under centralization favors less redistribution. Our model has implications which differ from those of Persson and Tabellini (1994). Indeed, centralization would affect the size of government even if the income distribution in all local jurisdictions were identical.9 Suppose for simplicity this were the case. Then centralization would lead to a richer decisive voter. For social programs that redistribute from rich to poor, this would clearly reduce the size of government, contrary to the prediction of the Leviathan model. Of course, this assumes that the distribution of income is the same in all jurisdictions, which is clearly not reasonable. For public goods, the effect would depend on the shape of the demand function. Suppose that demand for a public good x is of the form x = yβ pγ , where p is a voter’s tax price, and β and γ denote the income and price elasticity of demand, respectively. With the assumption that the tax price is of the form τ = yδ , we would find that demand increases with income if and only β + γ δ > 0. Suppose publicly provided goods were purely private. Taking some typical examples, say, β = 0.75, and γ = –0.4, we would find that x increases with y iff δ < 1.875. For public goods, then, if the tax system is not too progressive, one would reasonably suspect demand to increase with income. Suppose further that the median voter’s income were some function of population, yM = Nθ . We would then find the size of government increases with population if θ(β + γ δ) > 0.
259 Hence, if the decisive voter’s income increases with population size (θ > 0), the parameters above would imply that centralization increases the size of government for publicly provided goods and decreases the size of social spending. 6. Measuring publicness In this section, we briefly outline the implications of the argument for the measurement of the publicness of publicly provided goods (see Reiter and Weichenrieder, 1997, for a survey). Suppose, again, that demand for publicly provided goods is q = yβ pγ , where q is the amount of the good consumed by each voter, and p the voter’s tax price per unit of q. The literature usually assumes that q is related to the total amount provided, X by q = XN−α , where α is a measure of publicness. For α = 0, each individual consumes the total amount provided, so the good is purely public. For α = 1, provision is proportional to population, i.e., the good is purely private. The lower α, the higher the degree of publicness. Suppose that the decisive voter’s tax price per unit of q is X/q = tNα , where t is the voter’s share of total costs of X. Then, total expenditures (assuming constant marginal costs of one and t = 1/N) can be written as X = yβ N(α−1)(1+γ ).
(3)
A typical procedure is to estimate a (logarithmic) regression of X on median income, population, and other variables. The coefficient on population is then taken to be δ = (α −1)(1+γ ), and, given estimates of the price elasticity, one δ +1. Many studies have can recover the estimated crowding elasticity, α = 1+γ used this procedure to estimate parameter values of α close to one, which has caused some to infer that the public sector is providing goods which could be supplied in competitive markets.10 Apart from the problems already attached to this method, there are two additional issues concerning turnout and the identity of the decisive voter. One is the (mis)measurement of the decisive voter’s income and the ensuing estimation of the income elasticity. The other is the estimation of crowding.11 Suppose, again, that the median voter is related to population size by y = Nθ . Now, the “true” equation for X is
260 X = Nβθ+(α−1)(1+γ ).
(4)
+ 1. For β, θ > 0, it is apThe “true” crowding parameter is α = parent that disregarding the participation effect overestimates the crowding parameter: Part of the effect of population on spending comes from its effect on the composition of voters, not from crowding in publicly provided goods. δ−βθ 1+γ
7. Conclusion In a series of recent papers, Inman and Rubinfeld (1997a; 1997b) have argued that an optimal federalism should balance the benefits and costs stemming from economic efficiency and political participation. Small communities are likely to lead to economic inefficiency (since externalities might not be internalized and economies of scale not be exhausted), but at the same time increase political participation.12 If political participation is a valuable good, this should be weighed against the potential efficiency loss from decentralized decision making. But the definition of the benefits or costs of political participation should be broader than that of Inman and Rubinfeld. Namely, we have argued that political participation matters because it changes the identities of voters versus nonvoters. In particular, the larger the potential voting population, the less people will vote, and the richer will be those who do vote. In judging the desirability of this outcome, two additional effects should be considered. One is the redistribution of power. Decentralization may be judged beneficial not only because the higher political participation is valued, but also because the implied redistribution towards poorer voters is viewed as desirable (conversely, those who think that too much power for the poor is undesirable may dislike the idea). Second, the effect of participation on the allocative efficiency of voting outcomes is important. We started from the premise that political participation decreases with the size of the voting population, and increases with income. Both facts seem to be supported by the evidence. From these facts then follows the hypothesis that increasing population will increase the income of the decisive voter, if the reduction of participation falls on the poor at least as much as the rich. We then showed that increasing population may have positive or negative welfare consequences. For instance with very skewed income distribution, voting may put “too much” weight on poor voters and centralization may help correct this – up to some limit. Conversely, if the distribution is symmetric, increasing population will raise the income of the decisive voter further above the mean and hence worsen the allocative inefficiency of voting. This may provide an additional economic argument for small jurisdictions. The smaller the jurisdiction, the larger political participation, and, more
261 importantly, the more equally will participation be spread throughout the population. This increases efficiency if the tax system is not too progressive. If political participation is positively valued, as argued by Inman and Rubinfeld (1997b), the argument for small jurisdictions is even stronger.
Notes 1. In many countries, turnout seems to be much lower in local than in national elections. However, this is probably due to the fact that the stakes are much higher in national elections. 2. In fact, participation is a function of the population eligible to vote and not the entire population. Adding a functional relationship between population and those eligible to participate would not add substantive insight, however, as long as there is a positive relation between the two. 3. Assume that in this and the following problems, the relevant second-order conditions are fulfilled. 4. Another aspect which would have to be taken into account is that the identity of the median voter may change even if participation were constant, for instance, when two jurisdictions with differing distributions merge. See, e.g., Bolton and Roland (1997) or Borck (1998) for models along this line. 5. Larcinese (1999) argues that richer individuals are likely to be more informed, since the benefit of information on political issues increases with income. 6. Downs (1957) argued that the D term reflects individuals’ sense of responsibility for the working of democracy. Brennan and Lomasky (1993) argue that individuals vote largely because of the “expressive returns” from doing so. That is, voting is rather like cheering at a football match, where one person’s cheering has no effect on the outcome of the game. 7. A full blown survey of this huge literature is beyond the scope of this paper. 8. We assume that 0 < φ(y) < 1 for all y. 9. In “traditional” voting models, this could happen only due to economies or diseconomies of scale. 10. Even if the statistical finding were taken at face value, however, this inference is not necessarily correct, since private markets might fail for other reasons, e.g., externalities. 11. In fact, these problems are related, since if the true median voter were known, there would be no problem in measuring congestion. 12. Another argument for small jurisdictions is that they are more likely to provide public good levels tailored to differing preferences; see Oates’ (1972) “decentralization theorem”.
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