Abstract
This paper studies aspects of sequential choice (and elimination) through the ‘routewise’ application of choice. (A choice is a mapping of the subsets of a set X into their respective subsets.) This approach sheds some further light on the ‘path-independence’ of choice, as well as on the logical structure of several rationality criteria for choice, as expressed through the properties of the comparison (or preference relation) revealed by a choice. The results bear particular relevance to the theory of collective choice.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arrow, K.J. (1963). Social Choice and Individual Values. New Haven and London: Yale University Press.
Blair, D.H. (1975). ‘Path-Independent Social Choice Functions: A Further Result.’ Econometrica, 43: 173–174.
Blair, D.H., Bordes, G., Kelly, J.S., and Suzumura, K. (1976). ‘Impossibility Theorems without Collective Rationality.’ Journal of Economic Theory, 13: 361–379.
Condorcet, Marquis de. (1785). ‘Essai sur l'application de l'analy se a la probabilite des decisions rendues a la pluralite des voix.’ Paris.
Dugundji, J. (1970). Topology. Boston: Allen & Bacon.
Fishburn, P.C. (1970). ‘The Irrationality of Transitivity in Social Choice.’ Behavioural Science, 15: 119–123.
Fishburn, P.C. (1971). ‘Should Social Choice be Based on Binary Comparisons? Journal of Mathenatical Sociology, 1: 133–142.
Fishburn, P.C. (1973). The Theory of Social Choice. Princeton: Princeton University Press.
Parks, R.P. (1976). ‘Further Results on Path Independence, Quasi-Transitivity, and Social Choice.’ Public Choice, 26: 75–88.
Plott, C.R. (1971). ‘Recent Results in the Theory of Voting.’ In M.D. Intriligator (Ed.), Frontiers of Quantitative Economics. Amsterdam: North Holland. 109–127.
Plott, C.R. (1973). ‘Path Independence, Rationality and Social Choice.’ Econometrica, 41: 1075–1091.
Richelson, J. (1977). ‘Conditions on Social Choice Functions.’ Public Choice, 31: 79–110.
Richter, M.K. (1966). ‘Revealed Preference Theory.’ Econometrica, 34: 635–645.
Richter, M.K. (1971). ‘Rational Choice.’ In J.S. Chipman et al. (Eds.), Preferences, Utility, and Demand. New York: Harcourt Brace Ivanovich. 29–58.
Sen, A.K. (1970). Collective Choice and Social Welfare. San Francisco: Holden Day.
Sen, A.K. (1971). ‘Choice Functions and Revealed Preference.’ Rev. Econ. Stud., 38: 307–317.
Sen, A.K. (1977). ‘Social Choice Theory: A Reexamination.’ Econometrica, 45: 53–89.
Sertel, M.R. (1976). ‘Aggregating Choice.’ Preprint of the International Institute of Management, Berlin.
Sertel, M.R. (1978). ‘Choice by Binary Comparison is Semi-Independent of Path.’ Bogazici University Journal, forthcoming.
Sertel, M.R., and Van der Bellen, A. (1976). ‘The Algebraic Structure of Sequential Choice.’ Preprint of the International Institute of Management I/76–3, Berlin.
Sertel, M.R., and Van der Bellen, A. (1979a). ‘Computations in Choice Groupoids.’ Aequations Mathematicae, forthcoming.
Sertel, M.R., and Van der Bellen, A. (1979b). ‘Synopses in the Theory of Choice.’ Econometrica, 47: 1367–1389.
Sertel, M.R., and Van der Bellen, A. (1980). ‘Comparison and Choice.’ Theory and Decision, forthcoming.
Van der Bellen, A. (1976). Mathematische Auswahlfunktionen und gesellschaftliche Entscheidungen. Basel & Stuttgart: Birkhauser Verlag.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sertel, M.R., Van der Bellen, A. Routes and paths of comparison and choice. Public Choice 35, 205–218 (1980). https://doi.org/10.1007/BF00140844
Issue Date:
DOI: https://doi.org/10.1007/BF00140844