×

Functional voting operators: The non-monotonic case. (English) Zbl 0791.90006

We extend the non-binary framework of social choice introduced by M. A. Aizerman and F. T. Aleskerov [ibid. 11, 201-242 (1986; Zbl 0597.90006)], in which individual choice functions are aggregated into a social choice function, by considering non-monotonic operators. We characterize the class of ‘local’ operators and provide the explicit forms of local operators satisfying various combinations of normative and rationality conditions in the absence of monotonicity. Surprisingly, the restriction of monotonicity is not binding for operators satisfying the usual rationality conditions. We identify two rationality restrictions which do admit non-monotonic operators. One restriction admits every sovereign and neutral operator, and the other admits only dictatorship and anti-dictatorship operators. This last result is a direct non-binary counterpart to Wilson’s theorem [see R. Wilson, J. Econ. Theory 5, 478-486 (1972)].

MSC:

91B14 Social choice
91B12 Voting theory

Citations:

Zbl 0597.90006
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Aizerman, M. A.; Aleskerov, F. T., Voting operators in the space of choice functions, Math. Soc. Sci., 11, 201-242 (1986) · Zbl 0597.90006
[2] Aizerman, M. A.; Malishevski, A. V., General theory of best variants choice: some aspects, IEEE Trans. Automatic Control, AC-26, 1030-1041 (1981) · Zbl 0466.90003
[3] Aleskerov, F. T.; Vladmirov, A. V., Hierarchical voting, Info. Sci., 39, 41-86 (1986) · Zbl 0618.90006
[4] Arrow, K. J., Rational choice functions and orderings, Econometrica, 26, 121-127 (1959)
[5] Arrow, K. J., Social Choice and Individual Values (1963), Wiley: Wiley New York · Zbl 0984.91513
[6] Chernoff, H., Rational selection of decision functions, Econometrica, 22, 422-443 (1954) · Zbl 0059.12602
[7] Plott, C. R., Path independence, rationality, and social choice, Econometrica, 41, 1075-1091 (1973) · Zbl 0297.90017
[8] Sen, A. K., Collective Choice and Social Welfare (1970), Holden-Day: Holden-Day San Francisco · Zbl 0227.90011
[9] Wilson, R., Social choice theory without the Pareto principle, J. Econom. Theory, 5, 478-486 (1972)
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.