Welfarist evaluations of decision rules for boards of representatives. (English) Zbl 1180.91088
Summary: We consider a decision board with representatives who vote on proposals on behalf of their constituencies. We look for decision rules that realize utilitarian and (welfarist) egalitarian ideals. We set up a simple model and obtain roughly the following results. If the interests of people from the same constituency are uncorrelated, then a weighted rule with square root weights does best in terms of both ideals. If there are perfect correlations, then the utilitarian ideal requires proportional weights, whereas the egalitarian ideal requires equal weights. We investigate correlations that are in between these extremes and provide analytic arguments to connect our results to S. Barberà and M. Jackson [J. Polit. Econ. 114, No. 2, 317 – 339, (2006; doi:10.1086/501172)] and to Banzhaf voting power.
MSC:
| 91B12 | Voting theory |
References:
| [1] | Banzhaf JF (1965) Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Rev 19:317–334 |
| [2] | Barberà S, Jackson M (2006) On the weights of nations: assigning voting power to heterogeneous voters. J Polit Econ 114(2):317–339 · doi:10.1086/501172 |
| [3] | Bentham J (1980) Correspondence. In: Dinwiddy JR (ed) vol IV. Athlone, London |
| [4] | Beisbart C, Bovens L, Hartmann S (2005) A utilitarian assessment of alternative decision rules in the council of ministers. European Union of Politics 6:395–418 with appendix at http://www.uni- konstanz.de/eup/Data/6-4/Beisbart2_app.doc |
| [5] | Bovens L, Hartmann S (2007) Welfare, voting and the constitution of a federal assembly. In: Galavotti MC, Scazzieri R, Suppes P (eds) Reasoning, rationality and probability, (forthcoming) CSLI Publications, Stanford |
| [6] | Bovens L, Beisbart C (2007) Factions in Rousseau’s ’Du Contrat Social’ and Federal Representation. Analysis 67:12–20 |
| [7] | Brams SJ, Davis MD (1974) The 3/2’s Rule in presidential campaigning. Am Polit Sci Rev 68:113–134 · doi:10.2307/1959746 |
| [8] | Coelho D (2005) Maximin choice of voting rules for committees. Econ Gov 6:159–175 · doi:10.1007/s10101-004-0085-7 |
| [9] | Dubey P, Shapley LS (1979) Mathematical properties of the Banzhaf power index. Math Oper Res 4:99–131 · Zbl 0409.90008 · doi:10.1287/moor.4.2.99 |
| [10] | Feller W (1968) An introduction to probability theory and its applications, vol 1, 3rd edn. Wiley, New York · Zbl 0155.23101 |
| [11] | Felsenthal DS, Machover M (1998) The measurement of voting power: theory and practice, problems and paradoxes. Edward Elgar, Cheltenham · Zbl 0954.91019 |
| [12] | Felsenthal DS, Machover M (2002) Enlargement of the EU and weighted voting in its councils, revised version 2002. online at http://eprints.lse.ac.uk/archive/00000407/01/euenbook.pdf (checked April 2007) |
| [13] | Grofman B, Feld SL (2005) Thinking about the political impacts of the electoral college. Public Choice 123:1–18 · doi:10.1007/s11127-005-3210-4 |
| [14] | Harrison R (1993) Democracy. Routledge, London |
| [15] | Lindner I, Machover M (2004) L. S. Penrose’s limit theorem: proof of some special cases. Math Social Sci 47:37–49 · Zbl 1069.91025 · doi:10.1016/S0165-4896(03)00069-6 |
| [16] | Penrose LS (1952) On the objective study of crowd behaviour. H. K. Lewis & Co, London |
| [17] | Rae DW (1969) Decision rules and individual values in constitutional choice. Am Polit Sci Rev 63:40–53 · doi:10.2307/1954283 |
| [18] | Rawls J (1971) A theory of justice. Harvard University Press, Cambridge |
| [19] | Rousseau JJ (1993 [1762]) The social contract and discourses. Translated by GDH Cole. Everyman, London |
| [20] | Schweizer U (1990) Calculus of consent: A game-theoretic perspective. J Inst Theor Econ 146:28–54 |
| [21] | Shapley LS (1953) A value for n-Person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games, vol II. Princeton University Press, Princeton, pp 307–317 |
| [22] | Shapley LS, Shubik M (1954) A method for evaluating the distribution of power in a committee system. Am Polit Sci Rev 48:787–792 · doi:10.2307/1951053 |
| [23] | Straffin Jr PD, David MD, Brams SJ (1982) Power and satisfaction in an ideologically divided voting body. In: Holler M (ed) Voting, power, and voting power. Physica-Verlag, Würzburg, pp 239–255 |
| [24] | Widgrén M (1994) Voting power in the EC decision making and the consequences of two different enlargements. Eur Econ Rev 38:1153–1170 · doi:10.1016/0014-2921(94)90042-6 |
| [25] | Žyczkowski K, Słomczyński W (2004) Voting in the European Union: The square root system of Penrose and a critical point, Mimeo. http://arxiv.org/ftp/cond-mat/papers/0405/0405396.pdf (checked April 2007) |
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