×
Saaty, Thomas L.; Vargas, Luis G.

The possibility of group choice: pairwise comparisons and merging functions. (English) Zbl 1239.91040

Soc. Choice Welfare 38, No. 3, 481-496 (2012).
Summary: Preferences in Arrow’s conditions are ordinal. Here we show that when intensity of preference represented by reciprocal pairwise comparisons is considered, it is always possible to construct an Arrowian social welfare function using a two-stage social choice process. In stage 1, the individual pairwise relations are mapped into a social pairwise relation. In stage 2, the social pairwise relation is used to generate a cardinal ranking and this ranking is then used to select a particular member of the choice set.

Cited in 7 Documents

MSC:

91B10 Group preferences
PDF BibTeX XML Cite
\textit{T. L. Saaty} and \textit{L. G. Vargas}, Soc. Choice Welfare 38, No. 3, 481--496 (2012; Zbl 1239.91040)
Full Text: DOI

References:

[1] Aczel J, Alsina C (1986) On synthesis of judgments. Socio Econ Plan Sci 20: 333–339
[2] Aczel J, Saaty TL (1983) Procedures for synthesizing ratio judgments. J Math Psychol 27: 93–102 · Zbl 0522.92028
[3] Barrett CR, Pattanaik PK, Salles M (1992) Rationality and aggregation of preferences in an ordinally fuzzy framework. Fuzzy Sets Syst 49: 9–13 · Zbl 0772.90002
[4] Campbell DE (1973) Social choice and intensity of preference. J Political Econ 81(1): 211–218
[5] DeMeyer F, Plott CR (1971) A welfare function using ”relative intensity” of preference. Quart J Econ 85(1): 179–186 · Zbl 0217.26704
[6] Goodman LA, Markowitz H (1952) Social welfare functions based on individual rankings. Am J Sociol 58(3): 257–262
[7] Hylland A (1980) Aggregation procedure for cardinal preferences: a comment. Econometrica 48(2): 539–542 · Zbl 0437.90016
[8] Juola P (2008) Summary: FY09 Defense Appropriations Bill, US House of Representatives, Committee on Appropriations
[9] Kalai E, Schmeidler D (1977) Aggregation procedure for cardinal preferences: a formulation and proof of Samuelson’s impossibility conjecture. Econometrica 45(6): 1431–1438 · Zbl 0367.90008
[10] Kaneko M, Nakamura K (1979) The Nash social welfare function. Econometrica 47(2): 423–436 · Zbl 0431.90091
[11] Keeney RL (1976) A group preference axiomatization with cardinal utility. Manag Sci 23(2): 140–145 · Zbl 0351.90004
[12] Krantz DH, Luce RD, Suppes P, Tversky A (1971) Foundations of measurement, vol I. Academic Press, New York · Zbl 0232.02040
[13] Nash J (1950) The bargaining problem. Econometrica 18: 155–162 · Zbl 1202.91122
[14] Roberts FS (1979) Measurement theory with applications to decision making, utility and the social sciences. In: Rota GC (ed) Encyclopedia of mathematics and its applications. Addison-Wesley Publishing Company, Reading, MA
[15] Roberts KWS (1980) Interpersonal comparability and social choice theory. Rev Econ Stud 27(2): 421–439 · Zbl 0432.90009
[16] Saaty TL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15: 234–281 · Zbl 0372.62084
[17] Saaty TL (1980) The nalytic hierarchy process. McGraw Hill, New York
[18] Saaty TL (2000) Fundamentals of decision making with the analytic hierarchy process. RWS Publications, Pittsburgh
[19] Saaty TL (2001) The analytic network process. RWS Publications, Pittsburgh
[20] Saaty TL, Vargas LG (2006) Decision making with the analytic network process. International Series in Operations Research and Management Science, F. E. Hillier, Springer
[21] Samuelson P (1967) Arrow’s mathematical politics. In: Hook S (ed) Human values and economic policy. New York University Press, New York, pp 41–51
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.