Asking Infinite Voters ‘Who is a J?’: Group Identification Problems in $\mathbb {N}$
Tóm tắt
We analyze the problem of classifying individuals in a group N taking into account their opinions about which of them should belong to a specific subgroup N′⊆ N, in the case that |N| > ∞. We show that this problem is relevant in cases in which the group changes in time and/or is subject to uncertainty. The approach followed here to find the ensuing classification is by means of a Collective Identity Function (CIF) that maps the set of opinions into a subset of N. Kasher and Rubinstein (Logique & Analyse, 160, 385–395 1997) characterized different CIFs axiomatically when |N| < ∞, in particular, the Liberal and Oligarchic aggregators. We show that in the infinite setting, the liberal result is still valid but the result no longer holds for the oligarchic case and give a characterization of all the aggregators satisfying the same axioms as the Oligarchic CIF. In our motivating examples, the solution obtained according to the alternative CIF is most cogent.
Tài liệu tham khảo
Barthelemy, J.R., Leclerc, B., Monjardet, B. (1986). On the use of ordered sets in problems of comparison and consensus of classifications. Journal of Classification, 3, 187–224.
Biais, B., Bisiére, C., Bouvard, M., Casamatta, C. (2018). The blockchain folk theorem. Toulousse School of Economics Working Paper [17-817].
Cho, W.J., & Ju, B.-G. (2017). Multinary group identification. Theoretical Economics, 12, 513–531.
Cho, W.J., & Saporiti, A. (2015). Incentives, fairness, and efficiency in group identification, The School of Economics Discussion Paper Series 1117 Economics, The University of Manchester.
Fishburn, P.C. (1970). Arrow’s impossibility theorem: concise proof and infinite voters. Journal of Economic Theory, 2, 103–106.
Fishburn, P.C., & Rubinstein, A. (1986). Aggregation of equivalence relations. Journal of Classfication, 3, 61–65.
Kasher, A. (1993). Jewish collective identity. In Goldberg, D.T., & Kraus, M. (Eds.) Jewish Identity. Philadelphia: Temple University Press.
Kasher, A., & Rubinstein, A. (1997). On the question “Who is a J?”: a social choice approach. Logique & Analyse, 160, 385–395.
McMorris, F.R., & Powers, R.C. (2008). A characterization of majority rule for hierarchies. Journal of Classification, 25, 153–158.
Mirkin, B. (1975). On the problem of reconciling partitions. In Blalock, H.M., Aganbegian, A., Borodkin, F.M., Boudon, R., Capecchi, V. (Eds.) Quantitative sociology, international perspectives on mathematical and statistical modelling (pp. 441–449). Academic Press: New York.
Saporiti, A. (2012). A proof for ‘Who is a J’ impossibility theorem. Economics Bulletin, 32, 494–501.
Shorish, J. (2018). Blockchain state machine representation, open science framework. (https://osf.io/hbmje/).
Sung, S.C., & Dimitrov, D. (2005). On the axiomatic characterization of ‘Who is a J?’. Logique & Analyse, 48, 101–112.
Suppes, P. (1972). Axiomatic set theory. Toronto: Dover Publications.