Abstract
In this paper we address several issues related to collective dichotomous decision-making by means of quaternary voting rules, i.e., when voters may choose between four actions: voting yes, voting no, abstaining and not turning up-which are aggregated by a voting rule into a dichotomous decision: acceptance or rejection of a proposal. In particular we study the links between the actions and preferences of the actors. We show that quaternary rules (unlike binary rules, where only two actions -yes or no- are possible) leave room for “manipulability” (i.e., strategic behaviour). Thus a preference profile does not in general determine an action profile. We also deal with the notions of success and decisiveness and their ex ante assessment for quaternary voting rules, and discuss the role of information and coordination in this context.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Arrow K (1963) Social choice and individual values, 2nd edn. Wiley, New York
Braham M, Steffen F (2002) Voting power in games with abstentions. In: Holler MJ, Kliemt H, Schmidtchen D, Streit ME (eds) Jahrbuch für Neue Politische Ökonomie 20: Power and Fairness, Mohr Sieberg, Tübingen
Côrte-Real P, Pereira PT (2004) The voter who wasn’t there: referenda, representation and abstention. Soc Choice Welfare 22: 349–369
Dougherty KL, Edward J (2010) The properties of simple vs. absolute majority rule: cases where absences and abstentions are important. J Theor Politics 22(1): 85–122
Felsenthal DS, Machover M (1997) Ternary voting games. Int J Game Theory 26: 335–351
Freixas J, Zwicker W (2003) Weighted voting, abstention and multiple levels of approval. Soc Choice Welfare 21: 399–431
Freixas J, Zwicker W (2009) Anonymous yes–no voting with abstention and multiple levels of approval. Games Econ Behav 67: 428–444
Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41: 587–601
Herrera H, Mattozzi A (2010) Quorum and turnout in referenda. J Eur Econ Assoc (forthcoming)
Laruelle A, Valenciano F (2005) Assessing success and secisiveness in voting situations. Soc Choice Welfare 24: 171–197
Laruelle A, Martínez R, Valenciano F (2006) Success versus decisiveness: conceptual discussion and case study. J Theor Politics 18: 185–205
Laruelle A, Valenciano F (2008) Voting and collective decision-making: bargaining and power. Cambridge University Press, Cambridge
Laruelle A, Valenciano F (2010) Quaternary dichotomous voting rules. Soc Choice Welf (forthcoming)
Laruelle A, Valenciano F (2011) Majorities with a quorum. J Theor Politics (forthcoming)
Maniquet F, Morelli M (2010) Approval quorums dominate participation quorums. EUI Working Paper 2010/13, Department of Economics, European University Institute, Florence, Italy
Pauly M (2010) Non-manipulable referenda with quorums, Mimeo
Pongou R, Tchantcho B, Lambo LD (2010) Political influence in multi-choice institutions: cyclicity, anonymity and transitivity. Theory Decis (forthcoming)
Satterthwaite MA (1975) Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10: 187–217
Tchantcho B, Diffo Lambo L, Pongou R, Mbama Engoulou B (2010) Voters’ power in voting games with abstention: Influence relation and ordinal equivalence of power theories. Games Econ Behav 64: 335–350
Uleri PV (2002) On referendum voting in Italy: yes, no or non-vote? How Italian parties learned to control referenda. Eur J Politics Res 41: 863–883
Author information
Authors and Affiliations
Corresponding author
Additional information
This research is supported by the Spanish Ministerio de Ciencia e Innovación under project ECO2009-11213, co-funded by the ERDF, and by Basque Government funding to Grupo Consolidado GIC07/146-IT-377-07. The first author thanks the Basque Government for aid through the “Programas de Ayudas para la Formación y Perfeccionamiento del Personal Investigador del Departamento de Educación, Universidades e Investigación”.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Artabe, A., Laruelle, A. & Valenciano, F. Preferences, actions and voting rules. SERIEs 3, 15–28 (2012). https://doi.org/10.1007/s13209-011-0040-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13209-011-0040-0