Abstract
We characterize voting procedures according to the social choice correspondence they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In a larger class of rules, Approval Voting is characterized by a single axiom that implies both U and MEW but is weaker than Condorcet-consistency (CON)—it is the only direct mechanism scoring rule that is majoritarian after eliminating a Pareto-dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected); among all finite scoring rules that satisfy MEPD, Approval Voting is the most decisive. However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). There exists no direct mechanism scoring rule that satisfies both MEPD and MON and no finite scoring rule satisfying CON.
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References
Baharad, E., Nitzan, S.: Approval voting reconsidered. Econ. Theor. 26(3), 619–628 (2005)
Baharad, E., Nitzan, S.: Scoring rules: An alternative parameterization. Econ. Theor. 30(1), 187–190 (2007)
Barberà, S., Dutta, B., Sen, A.: Strategy-proof social choice correspondences. J. Econom. Theory 101(2), 374–394 (2001)
Barbie, M., Puppe, C., Tasnádi, A.: Non-manipulable domains for the Borda count. Econ. Theor. 27(2), 411–430 (2006)
Brams, S.J., Fishburn, P.C.: Approval voting. Am. Polit. Sci. Rev. 72(03), 831–847 (1978)
Buenrostro, L., Dhillon, A., Vida, P.: Scoring rule voting games and dominance solvability. Soc. Choice Welfare 40(2), 329–352 (2013)
Campbell, D.E., Kelly, J.S.: Gains from manipulating social choice rules. Econ. Theor. 40(3), 349–371 (2009)
Ching, S., Zhou, L.: Multi-valued strategy-proof social choice rules. Soc. Choice Welfare 19(3), 569–580 (2002)
Condorcet, M.d.: Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. L’imprimerie royale, Paris (1785)
Courtin, S., Núñez, M.: Dominance solvable approval voting games. J. Public Econom. Theory 19(6), 1055–1076 (2017)
Dhillon, A., Lockwood, B.: When are plurality rule voting games dominance-solvable? Games Econom. Behavior 46(1), 55–75 (2004)
Dietrich, F.: Scoring rules for judgment aggregation. Soc. Choice Welfare 42(4), 873–911 (2014)
Farquharson, R.: Theory of Voting. Blackwell, Oxford (1969)
Gärdenfors, P.: Manipulation of social choice functions. J. Econom. Theory 13(2), 217–228 (1976)
Gärdenfors, P.: On definitions of manipulation of social choice functions. In: Laffont, J.J. (ed.) Aggregation and Revelation of Preferences, pp. 29–36. North-Holland, Amsterdam (1979)
Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica 41(4), 587–602 (1973)
Goertz, J.M., Maniquet, F.: On the informational efficiency of simple scoring rules. J. Econom. Theory 146(4), 1464–1480 (2011)
Kelly, J.S.: Almost all social choice rules are highly manipulable, but a few aren’t. Soc. Choice Welfare 10(2), 161–175 (1993)
Lepelley, D., Merlin, V.: Scoring run-off paradoxes for variable electorates. Econ. Theor. 17(1), 53–80 (2001)
Marx, L.M., Swinkels, J.M.: Order independence for iterated weak dominance. Games Econom. Behavior 18(2), 219–245 (1997)
May, K.O.: A set of independent necessary and sufficient conditions for simple majority decision. Econometrica 20(4), 680–684 (1952)
Moulin, H.: Dominance solvable voting schemes. Econometrica 47(6), 1337–1351 (1979)
Moulin, H.: Choosing from a tournament. Soc. Choice Welfare 3(4), 271–291 (1986)
Moulin, H.: Axioms of Cooperative Decision Making. Econometric Society Monographs. Cambridge University Press, Cambridge (1991)
Myerson, R.B.: Axiomatic derivation of scoring rules without the ordering assumption. Soc. Choice Welfare 12(1), 59–74 (1995)
Myerson, R.B.: Comparison of scoring rules in poisson voting games. J. Econom. Theory 1(103), 219–251 (2002)
Núñez, M., Laslier, J.F.: Preference intensity representation: strategic overstating in large elections. Soc. Choice Welfare 42(2), 313–340 (2014)
Sanver, M.R.: Strategy-proofness of the plurality rule over restricted domains. Econ. Theor. 39(3), 461–471 (2009)
Sanver, M.R., Zwicker, W.S.: Monotonicity properties and their adaptation to irresolute social choice rules. Soc. Choice Welfare 39(2–3), 371–398 (2012)
Satterthwaite, M.A.: Strategy-proofness and arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions. J. Econom. Theory 10(2), 187–217 (1975)
Young, P.: Optimal voting rules. J. Econom. Perspect. 9(1), 51–64 (1995)
Acknowledgements
I thank Tilman Börgers, Micael Castanheira, Sébastien Courtin, Frank Heinemann and Matías Núñez as well as participants at the 9th Conference on Economic Design in Istanbul and the 26th International Conference on Game Theory in Stony Brook for their helpful comments and suggestions.
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Open Access funding enabled and organized by Projekt DEAL. Support by German Science Foundation through CRC TRR 190 and Fonds de la Recherche Scientifique-FNRS, fellowship-grant n\(^{\circ }\)1.B.222.17F, is gratefully acknowledged.
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Basteck, C. Characterising scoring rules by their solution in iteratively undominated strategies. Econ Theory 74, 161–208 (2022). https://doi.org/10.1007/s00199-021-01353-w
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DOI: https://doi.org/10.1007/s00199-021-01353-w