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Self-selective social choice functions. (English) Zbl 1142.91438
Summary: It is not uncommon that a society facing a choice problem has also to choose the choice rule itself. In such situations, when information about voters’ preferences is complete, the voters’ preferences on alternatives induce voters’ preferences over the set of available voting rules. Such a setting immediately gives rise to a natural question concerning consistency between these two levels of choice. If a choice rule employed to resolve the society’s original choice problem does not choose itself, when it is also used for choosing the choice rule, then this phenomenon can be regarded as inconsistency of this choice rule as it rejects itself according to its own rationale. S. Koray [Econometrica 68, No. 4, 981–995 (2000; Zbl 1026.91509)] proved that the only neutral, unanimous universally self-selective social choice functions are the dictatorial ones. Here we introduce to our society a constitution, which rules out inefficient social choice rules. When inefficient social choice rules become unavailable for comparison, the property of self-selectivity becomes more interesting and we show that some non-trivial self-selective social choice functions do exist. Under certain assumptions on the constitution we describe all of them.

MSC:
91B14 Social choice
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[1] Arrow KJ (1951, 1963). Social choice and individual values. Wiley, New York · Zbl 0984.91513
[2] Arrow KJ (1959). Rational choice functions and orderings. Economica 26: 121–127 · doi:10.2307/2550390
[3] Barberà S and Beviá C (2002). Self-selection consistent functions. J Econ Theory 105: 263–277 · Zbl 1009.91005 · doi:10.1006/jeth.2001.2860
[4] Barberà S and Jackson M (2004). Choosing how to choose: self-stable majority rules. Quart J Econ 119: 1011–1048 · Zbl 1074.91515 · doi:10.1162/0033553041502207
[5] Houy N (2003) Dynamics of stable sets of constitutions. Mimeo, Université Paris 1
[6] Houy N (2006) On the (Im)possibility of a set of constitutions stable at different levels (to appear)
[7] Jackson M (2001). A crash course in implementation theory. Soc Choice Welfare 18: 655–708 · Zbl 1069.91557 · doi:10.1007/s003550100152
[8] Koray S (1998). Consistency in electoral system design. Bilkent University, Mimeo
[9] Koray S (2000). Self-selective social choice functions verify Arrow and Gibbard–Satterthwaite theorems. Econometrica 68: 981–995 · Zbl 1026.91509 · doi:10.1111/1468-0262.00143
[10] Koray S, Slinko A (2001) On \(\pi\)-consistent social choice functions, Report Series N. 461. Department of Mathematics. The University of Auckland · Zbl 1142.91438
[11] Koray S, Slinko A (2006) Self-selective social choice functions, The Centre for Interuniversity Research in Qualitative Economics (CIREQ), Cahier 18-2006, University of Montreal
[12] Koray S and Unel B (2003). Characterization of self-selective social choice functions on the tops-only domain. Soc Choice Welfare 20: 495–507 · Zbl 1073.91561 · doi:10.1007/s003550200195
[13] Laslier J-F (1997). Tournament solutions and majority voting. Springer, Heidelberg · Zbl 0948.91504
[14] Laffond G, Laine J and Laslier J-F (1996). Composition consistent tournament solutions and social choice functions. Soc Choice Welfare 13: 75–93 · Zbl 0843.90007 · doi:10.1007/BF00179100
[15] McCabe-Dansted J and Slinko A (2006). Exploratory analysis of Similarities between common social choice rules. Decis Negotiation 15(1): 77–107 · doi:10.1007/s10726-005-9007-5
[16] Moulin H (1998). Axioms of cooperative decision making. Cambridge University Press, Cambridge · Zbl 0699.90001
[17] Tideman TN (1987). Independence of clones as a criterion for voting rules. Social Choice Welfare 4: 185–206 · Zbl 0624.90005 · doi:10.1007/BF00433944
[18] Unel B (1999). Exploration of self-selective social choice functions. Master Thesis. Bilkent University, Ankara
[19] Zavist TM and Tideman TN (1989). Complete independence of clones in the ranked pairs rule. Social Choice Welfare 6: 167–173 · Zbl 0673.90009 · doi:10.1007/BF00303170
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