Parliament Shapes and Sizes
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PARLIAMENT SHAPES AND SIZES RAPHAEL GODEFROY and NICOLAS KLEIN∗ This paper proposes a model of Parliamentary institutions in which a society makes three decisions behind the veil of ignorance: whether a Parliament should comprise one or two chambers, what the relative bargaining power of each chamber should be if the Parliament is bicameral, and how many legislators should sit in each chamber. We document empirical regularities across countries that are consistent with the predictions of our model. (JEL D71, D72) between the population and the number of repre- I. INTRODUCTION sentatives.2 In “Federalist No. 62,” he argues in Parliamentary institutions vary widely favor of an Upper Chamber as a safeguard against 3 across countries. For instance, the Indian the errors of a large Lower Chamber. Lower Chamber—Lok Sabha—has 543 to 545 However, little is known on the institutional seats, and the Indian Upper Chamber—Rajya regularities of Parliaments across countries. Sabha—has 250. The U.S. Congress has 535 Indeed, only two stylized facts have been docu- seats: 435 in the House of Representatives and mented: a linear relationship between the log of 100 in the Senate. The Luxembourg Parliament the size of the population and the log of the size has 60 legislators, in a single chamber.1 As of of Parliament (Stigler 1976) and an increasing 2012, there were 58 bicameral and 110 unicam- relationship between the population size and eral systems recorded in the Database of Political the probability to have a bicameral Parliament Institutions (DPI; Beck et al. 2001 [updated (Massicotte 2001). in 2012]). The purpose of this paper is twofold: to pro- The main questions that arise when design- pose a model of Parliament design and to doc- ing Parliamentary institutions are fundamentally ument empirical institutional regularities across quantitative: should there be one or two cham- countries, following the lead of the predictions of bers, what should be their respective bargaining the model. One of our contributions is that our power, what should be the size of Parliament, and simple model generates predictions concerning so on. James Madison, in the “Federalist No. 10,” variables that have an unambiguous equivalent in postulates a concave and increasing relationship the data we observe. 2. “In the first place, it is to be remarked that, however ∗ The authors gratefully acknowledge financial support small the republic may be, the representatives must be raised from the Fonds de Recherche du Québec—Société et Culture. to a certain number, in order to guard against the cabals of a The second author also gratefully acknowledges financial few; and that, however large it may be, they must be limited support from the Social Sciences and Humanities Research to a certain number, in order to guard against the confusion of Council of Canada. a multitude. Hence, the number of representatives in the two Godefroy: Assistant Professor, Department of Economics, cases [will be] proportionally greater in the small republic” Université de Montréal and CIREQ, Montréal, Quebec (Madison 1788a). H3T1N8, Canada. Phone 514-343-2397, Fax 514-343- 3. “The necessity of a senate is not less indicated by the 7221, E-mail [email protected] propensity of all single and numerous assemblies, to yield Klein: Assistant Professor, Department of Economics, to the impulse of sudden and violent passions, and to be Université de Montréal and CIREQ, Montréal, Que- seduced by factious leaders into intemperate and pernicious bec H3T1N8, Canada. Phone 514-343-7908, Fax resolutions” (Madison 1788d). 514-343-7221, E-mail [email protected] 1. Throughout the paper, we use the term “legislator” to refer to a member of Parliament. If a Parliament is unicameral, ABBREVIATIONS we refer to its chamber as the House or the Lower Chamber, DPI: Database of Political Institutions indifferently. If there is a second chamber, we refer to it as the Senate or Upper Chamber, indifferently. i.i.d.: Identically and Independently Distributed 1 Economic Inquiry doi:10.1111/ecin.12584 (ISSN 0095-2583) © 2018 Western Economic Association International 2 ECONOMIC INQUIRY There are two stages in the model: a Constitu- from a two-stage game. In the first stage, par- tional stage and a Legislative stage. At the Con- ties may form coalitions to maximize the share of stitutional stage, society, which is made up of a seats they obtain in a proportional single-district discrete population of individuals, designs a Con- election. In the second stage, each individual stitution by writing three decisions into the social casts one vote, either for a party or for a coalition contract: whether a Parliament should comprise of parties, to maximize his expected utility, which one or two chambers, what the relative bargain- is a function of the policy adopted, under per- ing power of each chamber should be if the Par- fect information about legislators’ partisan affili- liament is bicameral, and how many legislators ations, but imperfect information about the exact should sit in each chamber. These decisions are value of their bliss points.5,6 made behind a veil of ignorance, that is, before The problem at the Constitutional stage the members of society know their own prefer- involves two trade-offs. On one hand, there is a ences. As everyone is identical behind the veil of trade-off between the unit cost of a member of ignorance, they will unanimously agree that the Parliament and the marginal benefit of having a goal should be to maximize the expected utility larger Parliament to lower the risk that the policy of the representative agent. They know that each will be decided by legislators whose preferences individual’s utility is the opposite of the quadratic are far from those of the population at large. difference between the policy adopted by the Par- One could see this trade-off in terms of external liament and the individual’s bliss point, which costs and internal or decision-making costs. are both real numbers, minus the costs associated (External costs are the costs that individuals have with the functioning of Parliament. to bear as a result of others’ decisions whenever We assume that the population is partitioned an action is chosen collectively. Internal costs into parties and that two types of issues may arise: stem from an individual’s participation in an partisan and nonpartisan. For nonpartisan issues, organized activity, such as legislative bargaining, individuals’ bliss points are identically and inde- see Buchanan and Tullock 1962, Chapter 15.) pendently distributed (i.i.d.), whereas for partisan The former decrease in expectation as the size issues, all members of a party share the same of Parliament increases; indeed, the larger the bliss point, the party’s bliss point. Parties’ bliss Parliament the more precisely it will estimate the points are i.i.d. across parties. Individuals do not average bliss point of the population. The latter know their partisan affiliations at the Constitu- costs, by contrast, will increase as Parliament tional stage. Nor do they know which type of becomes larger; indeed, the more numerous the issue may arise, the distribution of shares of par- assembly, the costlier it will be to ensure its ties’ members in the population, or the realized proper functioning. In our model, we assume that distribution of bliss points in the population or the marginal internal cost of parliamentarians is among legislators. constant. On the other hand, there is a trade-off At the Legislative stage, the Parliament between the unit cost of a chamber and the decides on a policy. To formalize society’s infor- benefit of instituting a Senate to mitigate the mation about Parliament’s decision process, we negative impact of the error term in the adopted assume that only one issue arises, and that the policy. That error term formalizes in the simplest policy adopted for that issue is the weighted aver- way possible the common point in defenses age of the policies that maximize the aggregate of bicameralism, such as Madison’s, which is utility of each chamber, subject to some error.4 that members of the Lower Chamber might not We consider two allocation systems of Parlia- mentary seats: a proportional representation and 5. Any game using a nonproportional voting system a nonproportional representation system. In the requires many more assumptions than the game in which vot- ing is at-large and proportional. For the latter, we would need proportional representation system, the distribu- to specify the number of districts, the size of each district tion of seat shares across parties is equal to the (which may not be uniform in practice), the distribution of distribution of shares of partisans in the popula- partisans in each district, the possibility for parties to form coalitions within and across districts, and so on. We do not tion. In the nonproportional system, these distri- propose such a model; instead, we make an assumption on the butions may differ. In an extension (Appendix C), system of allocation of seats that is consistent with an empir- we show that the distribution of legislators in the ical analysis of nonproportional voting systems. proportional representation system is obtained 6. The conclusions of the model would be the same if we considered an electorate whose votes are determined by partisan loyalty, which is the main determinant of voting 4. In a unicameral system, the policy adopted is the policy behavior according to Achen and Bartels (2016), rather than proposed by the unique chamber. policy preferences. GODEFROY & KLEIN: PARLIAMENT SHAPES AND SIZES 3 adopt the best policy according to some measure in nonproportional representation systems. First, of welfare. we estimate that, on average across observations The model provides several predictions.