Gerrymander-proof representative democracies. (English) Zbl 1259.91028
Summary: This article is devoted to the analysis of electoral systems involving two step procedures. It appears that designers are able to manipulate the result of these type of elections by gerrymandering, except in a very few cases. When imposing an unanimity condition on every jurisdiction’s voting rule, it is shown that, for any finite number of candidates, a two step voting rule that is gerrymander-proof necessarily gives every voter the power of overruling the unanimity. A characterization of the set of gerrymander proof rules is provided in the case of two candidates.
MSC:
| 91A35 | Decision theory for games |
| 91B06 | Decision theory |
| 90B50 | Management decision making, including multiple objectives |
References:
| [1] | Balinski M, Young P (1982) Fair representation. Yale University Press, New Haven |
| [2] | Banzhaf J (1968) One man, 3.312 votes: a mathematical analysis of electoral college. Villanova Law Rev 13: 304–332 |
| [3] | Barberà S, Jackson MO (2006) On the weights of nations: assigning voting weights in a heterogeneous union. J Polit Econ 114: 317–339 · doi:10.1086/501172 |
| [4] | Beisbart C, Bovens L, Hartmann S (2005) An utilitarian assessment of alternative decision rules in the council of ministers. Eur Union Polit 6: 395–418 · doi:10.1177/1465116505057814 |
| [5] | Boumedienne-Thiery A, Duhamel O (2000) Le droit de vote des étrangers, une question européenne. Le Monde, 27 April 2000 |
| [6] | Chambers C (2008) Consistent representative democracy. Games Econ Behav 62: 348–363 · Zbl 1142.91023 · doi:10.1016/j.geb.2007.06.003 |
| [7] | Feix MR, Lepelley D, Merlin VR, Rouet JL (2004) The probability of conflicts in a U.S. presidential type election. Econ Theory 23: 227–257 · Zbl 1128.91316 · doi:10.1007/s00199-003-0375-2 |
| [8] | Felsenthal DS, Machover M (1999) Minimizing the mean majority deficit: the second square-root rule. Math Soc Sci 37: 25–37 · Zbl 0953.91005 · doi:10.1016/S0165-4896(98)00011-0 |
| [9] | Fine K (1972) Some necessary and sufficient conditions for representative decision on two alternatives. Econometrica 40: 1083–1090 · Zbl 0261.90003 · doi:10.2307/1913856 |
| [10] | Fishburn PC (1971) The theory of representative majority decision. Econometrica 39: 279–284 · Zbl 0227.90004 · doi:10.2307/1913345 |
| [11] | Fishburn PC (1973) The theory of social choice. Princeton University Press, Princeton · Zbl 0253.92006 |
| [12] | Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41: 587–601 · Zbl 0325.90081 · doi:10.2307/1914083 |
| [13] | Hartvigsen D (2006) Vote trading in public elections. Math Soc Sci 52: 31–48 · Zbl 1141.91372 · doi:10.1016/j.mathsocsci.2006.03.004 |
| [14] | Laffond G, Lainé J (1999) A general impossibility theorem on representative democracy. In: de Swart H (ed) Logic, game theory and social choice, proceedings of the international conference LGS99. Tilburg University Press, Tilburg, pp 504–521 |
| [15] | Laffond G, Lainé J (2000) Representation in majority tournaments. Math Soc Sci 39: 35–53 · Zbl 0937.91041 · doi:10.1016/S0165-4896(99)00007-4 |
| [16] | Maaser N, Napel S (2007) Equal representation in two-tier voting systems. Soc Choice Welf 28: 401–402 · Zbl 1211.91101 · doi:10.1007/s00355-006-0186-z |
| [17] | May K (1952) A set of independent, necessary and sufficient conditions for simple majority decision. Econometrica 20: 680–684 · Zbl 0047.38402 · doi:10.2307/1907651 |
| [18] | Moulin H (1988) Axioms of cooperative decision making, monograph of the econometric society. Cambridge University Press, Cambridge · Zbl 0699.90001 |
| [19] | Murakami Y (1966) Formal structure of majority decision. Econometrica 34: 709–718 · Zbl 0152.18704 · doi:10.2307/1909779 |
| [20] | Murakami Y (1968) Logic and social choice. Dover Publications Inc, New York |
| [21] | Nurmi H (1999) Voting oaradoxes, and how to deal with them?. Springer, Berlin · Zbl 0943.91030 |
| [22] | Penrose LS (1946) The elementary statistics of majority voting. J Roy Stat Soc 109: 53–57 · doi:10.2307/2981392 |
| [23] | Perote Peña J (2005) Gerrymendering proof social welfare functions. Universidad de Zaragoza, Mimeo |
| [24] | Satterthwaite M (1975) Strategy proofness and Arrow’s conditions. J Econ Theory 10: 187–217 · Zbl 0315.90088 · doi:10.1016/0022-0531(75)90050-2 |
| [25] | Young HP (1974) An axiomatization of Borda’s rule. J Econ Theory 9: 43–52 · doi:10.1016/0022-0531(74)90073-8 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
