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The interplay between intergenerational justice and mathematical utility theory. (English) Zbl 1452.91137
Bosi, Gianni (ed.) et al., Mathematical topics on representations of ordered structures and utility theory. Essays in honor of Professor Ghanshyam B. Mehta. Cham: Springer. Stud. Syst. Decis. Control 263, 325-351 (2020).
Summary: Intergenerational justice has produced nice arguments in relation to the existence and the non-existence of utility representations of social welfare orderings on infinite chains of social states. Rather surprisingly, nearly all results neglect the extensive literature on mathematical utility theory. This chapter is an attempt to draw a bridge between both fields. In fact, we show that techniques and results from the latter discipline may be quite enlightening in the analysis of the intergenerational aggregation of utilities. Conversely, conclusions about social welfare binary relations that are relevant in the intergenerational debate facilitate the investigation of their Richter-Peleg representability. The interplay between mathematical utility theory and intergenerational justice becomes apparent.
For the entire collection see [Zbl 1446.91009].
MSC:
91B16 Utility theory
91B08 Individual preferences
91B15 Welfare economics
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[1] Alcantud, J.C.R.: Weak utilities from acyclicity. Theory Decis. 47(2), 185-196 (1999) · Zbl 0939.91039
[2] Alcantud, J.C.R.: Inequality averse criteria for evaluating infinite utility streams: the impossibility of Weak Pareto. J. Econ. Theory 147, 353-363 (2012) · Zbl 1258.91054
[3] Alcantud, J.C.R.: The impossibility of social evaluations of infinite streams with strict inequality aversion. Econ. Theory Bull. 1, 123-130 (2013)
[4] Alcantud, J.C.R.: Liberal approaches to ranking infinite utility streams: when can we avoid interference? Soc. Choice Welf. 41, 381-396 (2013) · Zbl 1288.91079
[5] Alcantud, J.C.R., Bosi, G., Zuanon, M.: Richter-Peleg multi-utility representations of preorders. Theory Decis. 80, 443-450 (2016) · Zbl 1378.91082
[6] Alcantud, J.C.R., Dubey, R.S.: Ordering infinite utility streams: efficiency, continuity, and no impatience. Math. Soc. Sci. 72, 33-40 (2014) · Zbl 1308.91057
[7] Alcantud, J.C.R., García-Sanz, M.D.: Evaluations of infinite utility streams: Pareto-efficient and egalitarian axiomatics. Metroeconomica 64, 432-447 (2013) · Zbl 1283.91061
[8] Alcantud, J.C.R., Giarlotta, A.: Necessary and possible hesitant fuzzy sets: a novel model for group decision making. Inf. Fus. 46, 63-76 (2019)
[9] Alcantud, J.C.R., Giarlotta, A.: Sequential Social Rules. University of Catania, Mimeo (2019)
[10] Alcantud, J.C.R., Giarlotta, A.: Benchmarking Social Rules. University of Catania, Mimeo (2019)
[11] Alcantud, J.C.R., Rodríguez-Palmero, C.: Characterization of the existence of semicontinuous weak utilities. J. Math. Econ. 32, 503-509 (1999) · Zbl 0939.91040
[12] Asheim, G.B., Mitra, T., Tungodden, B.: A new equity condition for infinite utility streams and the possibility of being Paretian. In: Roemer, J., Suzumura, K. (eds.), Intergenerational Equity and Sustainability. Conference Proceedings of the IWEA Roundtable Meeting on Intergenerational Equity, Palgrave, pp. 69-84 (2007)
[13] Asheim, G.B., Mitra, T., Tungodden, B.: Sustainable recursive social welfare functions. Econ. Theory 49, 267-292 (2012) · Zbl 1277.91051
[14] Asheim, G.B., Tungodden, B.: Resolving distributional conflicts between generations. Econ. Theory 24, 221-230 (2004) · Zbl 1084.91052
[15] Asheim, G.B., and Tungodden, B.: Do Koopmans’ postulates lead to discounted utilitarianism? Discussion paper 32/04, Norwegian School of Economics and Business Administration
[16] Atsumi, H.: Neoclassical growth and the efficient program of capital accumulation. Rev. Econ. Stud. 32, 127-136 (1965)
[17] Banerjee, K.: On the equity-efficiency trade off in aggregating infinite utility streams. Econ. Lett. 93, 63-67 (2006) · Zbl 1254.91134
[18] Banerjee, K., Dubey, R.S.: On multi-utility representation of equitable intergenerational preferences. In: Basu, B., Chakravarty, S.R., Chakrabarti, B.K., Gangopadhyay, K. (eds.) Econophysics and Economics of Games, Social Choices and Quantitative Techniques, pp. 175-180. Springer (2010) · Zbl 1188.91065
[19] Basu, K., Mitra, T.: Aggregating infinite utility streams with intergenerational equity: the impossibility of being Paretian. Econometrica 71, 1557-1563 (2003) · Zbl 1153.91648
[20] Basu, K., and Mitra, T.: Possibility theorems for equitably aggregating infinite utility streams. In: Roemer, J., Suzumura, K. (eds.) Intergenerational Equity and Sustainability. Conference Proceedings of the IWEA Roundtable Meeting on Intergenerational Equity, Palgrave, pp. 69-84 (2007)
[21] Beardon, A.F., Candeal, J.C., Herden, G., Induráin, E., Mehta, G.B.: The non-existence of a utility function and the structure of non-representable preference relations. J. Math. Econ. 37, 17-38 (2002) · Zbl 1005.91033
[22] Beardon, A.F., Candeal, J.C., Herden, G., Induráin, E., Mehta, G.B.: Lexicographic decomposition of chains and the concept of a planar chain. J. Math. Econ. 37(2), 95-104 (2002) · Zbl 1027.91019
[23] Beardon, A.F., Mehta, G.B.: The utility theorems of Wold, Debreu, and Arrow-Hahn. Econometrica 62(1), 181-186 (1994) · Zbl 0797.90005
[24] Bewley, T.F.: Existence of equilibria in economies with infinitely many commodities. J. Econ. Theory 4, 514-540 (1972)
[25] Bosi, G., Herden, G.: Continuous multi-utility representations of preorders. J. Math. Econ. 48, 212-218 (2012) · Zbl 1250.91045
[26] Bosi, G., Herden, G.: On continuous multi-utility representations of semi-closed and closed preorders. Math. Soc. Sci. 79, 20-29 (2016) · Zbl 1347.91140
[27] Bridges, D.S., Mehta, G.B.: Representations of Preference Orderings. Springer, Berlin (1995) · Zbl 0836.90017
[28] Bossert, W., Sprumont, Y., Suzumura, K.: Ordering infinite utility streams. J. Econ. Theory 135, 579-589 (2007) · Zbl 1186.91086
[29] Campión, M.J., Candeal, J.C., Induráin, E.: The existence of utility functions for weakly continuous preferences on a Banach space. Math. Soc. Sci. 51, 227-237 (2006) · Zbl 1184.91076
[30] Campión, M.J., Candeal, J.C., Catalán, R.G., Giarlotta, A., Greco, S., Induráin, E., Montero, J.: An axiomatic approach to finite means. Inf. Sci. 457-458, 12-28 (2018) · Zbl 1444.03150
[31] Caserta, A., Giarlotta, A., Watson, S.: On resolutions of linearly ordered spaces. Appl. Gen. Topol. 7(2), 211-231 (2006) · Zbl 1120.54022
[32] Caserta, A., Giarlotta, A., Watson, S.: Debreu-like properties of utility representations. J. Math. Econ. 44, 1161-1179 (2008) · Zbl 1154.91016
[33] Cerreia-Vioglio, S., Giarlotta, A., Greco, S., Maccheroni, F., Marinacci, M.: Rational preference and rationalizable choice. Econ. Th. forthcoming (2018) · Zbl 1437.91163
[34] Chambers, C.P., Miller, A.D.: Benchmarking. Theor. Econ. 11, 485-504 (2018) · Zbl 1396.91106
[35] Chipman, J.S.: On the lexicographic representations of preference orderings. In: Chipman, J.S., Hurwicz, L., Richter, M., Sonnenschein, H.F. (eds.) Preference, pp. 276-288. Utility and Demand, Harcourt Brace and Jovanovich, New York (1971)
[36] Cohen, P.J.: The Independence of the Continuum Hypothesis. Proc. Natl. Acad. Sci. U.S.A. 50(6), 1143-1148 (1963) · Zbl 0192.04401
[37] Cohen, P.J.: The Independence of the Continuum Hypothesis II. Proc. Natl. Acad. Sci. U.S.A. 51(1), 105-110 (1963)
[38] Crespo, J., Núñez, C., Rincón-Zapatero, J.P.: On the impossibility of representing infinite utility streams. Econ. Theory 40, 47-56 (2009) · Zbl 1159.91010
[39] Debreu, G.: Representation of a Preference Ordering by a Numerical Function. In: Thrall, R.M., Coombs, C.H., Davis, R.L. (eds.) Decision Processes, pp. 159-166. Chapter XI. Wiley, N.Y. (1954) · Zbl 0058.13803
[40] Diamond, P.A.: The evaluation of infinite utility streams. Econometrica 33(1), 170-177 (1965) · Zbl 0127.36602
[41] Dubey, R.S.: A note on social welfare orders satisfying Pigou-Dalton transfer principle. Hitotsubashi J. Econ. 57, 243-262 (2016)
[42] Dubey, R.S., Mitra, T.: On equitable social welfare functions satisfying the weak Pareto axiom: a complete characterization. Int. J. Econ. Theory 7, 231-250 (2011)
[43] Estevan, A.: Generalized Debreu’s open gap lemma and continuous representability of biorders. Order 33(2), 213-229 (2016) · Zbl 1355.06002
[44] Estévez, M., Hervés, C.: On the existence of continuous preference orderings without utility representations. J. Math. Econ. 24, 305-309 (1995) · Zbl 0826.90006
[45] Evren, O., Ok, E.A.: On the multi-utility representation of preference relations. J. Math. Econ. 47, 554-563 (2011) · Zbl 1236.91054
[46] Fishburn, P.C.: Lexicographic orders, utilities and decision rules. Manag. Sci. 20, 1442-1471 (1974) · Zbl 0311.90007
[47] Giarlotta, A.: New trends in preference, utility, and choice: From a mono-approach to a multi-approach. In: Doumpos, M., Figueira, J.R., Greco, S., Zopounidis, C. (eds.) New Perspectives in Multiple Criteria Decision Making. Multiple Criteria Decision Making Series, pp. 3-80. Springer International Publishing, Cham (2019)
[48] Giarlotta, A.: The representability number of a chain. Topol. Appl. 150, 157-177 (2005) · Zbl 1077.06001
[49] Giarlotta, A.: A genesis of interval orders and semiorders: transitive NaP-preferences. Order 31, 239-258 (2014) · Zbl 1301.06018
[50] Giarlotta, A.: Normalized and strict NaP-preferences. J. Math. Psychol. 66, 34-40 (2015) · Zbl 1354.91048
[51] Giarlotta, A., Greco, S.: Necessary and possible preference structures. J. Math. Econ. 42(1), 163-172 (2013) · Zbl 1271.91045
[52] Giarlotta, A., Watson, S.: Pointwise Debreu lexicographic powers. Order 26(4), 377-409 (2009) · Zbl 1191.06001
[53] Giarlotta, A., Watson, S.: A hierarchy of chains embeddable into the lexicographic power \({\mathbb{R}}^\omega_{\rm lex} \). Order 30, 463-485 (2013) · Zbl 1283.06001
[54] Giarlotta, A., Watson, S.: Lexicographic preferences representable by real-branching trees with countable height: a dichotomy result. Ind. Math. 25, 78-92 (2014) · Zbl 1316.06002
[55] Giarlotta, A., Watson, S.: Well-graded families of NaP-preferences. J. Math. Psychol. 77, 21-28 (2017) · Zbl 1396.91113
[56] Giarlotta, A., Watson, S.: Necessary and possible indifferences. J. Math. Psychol. 81, 98-109 (2017) · Zbl 1397.91160
[57] Giarlotta, A., Watson, S.: The interplay between two rationality tenets: extending Schmeidler’s theorem to bi-preferences. University of Catania, Mimeo (2019)
[58] Giarlotta, A., Watson, S.: Benchmarking: revisited, extended, and generalized. University of Catania, Mimeo (2019)
[59] Hara, C., Shinotsuka, T., Suzumura, K., Xu, Y.: Continuity and egalitarianism in the evaluation of infinite utility streams. Soc. Choice Welf. 31, 179-191 (2008) · Zbl 1163.91347
[60] Herden, G., Mehta, G.B.: Open gaps, metrization and utility. Econ. Theory 7, 541-546 (1996) · Zbl 0859.90017
[61] Herden, G., Mehta, G.B.: The Debreu Gap Lemma and some generalizations. J. Math. Econ. 40, 747-769 (2004) · Zbl 1099.91045
[62] Hicks, J.: A Revision of Demand Theory. Clarendon Press, Oxford (1956)
[63] Jaffray, J.-Y.: Existence of a continuous utility function: an elementary proof. Econometrica 43, 981-983 (1975) · Zbl 0321.90006
[64] Knoblauch, V.: Lexicographic orders and preference representation. J. Math. Econ. 34, 255-267 (200) · Zbl 0966.91025
[65] Koopmans, T.C.: Stationary ordinal utility and impatience. Econometrica 28, 287-309 (1960) · Zbl 0149.38401
[66] Koopmans, T.C.: Representation of preference orderings over time. In: McGuire, C.B., Radner, R. (eds.) Decision and Organization. North-Holland, Amsterdam, 79-100 (1972). Econometrica 28, 287-309 (1960)
[67] Kunen, K.: Set Theory. An Introduction to Independence Proofs. North-Holland, Amsterdam (1980) · Zbl 0443.03021
[68] Lauwers, L.: Rawlsian equity and generalised utilitarianism with an infinite population. Econ. Theory 9, 143-150 (1997) · Zbl 0872.90007
[69] Lauwers, L.: Continuity and equity with infinite horizons. Soc. Choice Welf. 14, 345-356 (1997) · Zbl 0886.90024
[70] Lauwers, L.: Infinite utility: Insisting on strong monotonicity. Australas. J. Philos. 75, 222-233 (1997)
[71] Lauwers, L.: Ordering infinite utility streams comes at the cost of a non-Ramsey set. J. Math. Econ. 46, 32-37 (2010) · Zbl 1197.91085
[72] Levin, V.L.: The Monge-Kantorovich problems and stochastic preference relation. Adv. Math. Econ. 3, 97-124 (2001) · Zbl 1019.91018
[73] Lombardi, M., Miyagishima, K., Veneziani, R.: Liberal egalitarianism and the Harm Principle. Econ. J. 126, 2173-2196 (2016)
[74] Mariotti, M., Veneziani, R.: ‘Non-interference’ implies equality. Soc. Choice Welf. 32, 123-128 (2009) · Zbl 1184.91087
[75] Mariotti, M., Veneziani, R.: The liberal ethics of non-interference. Br. J. Pol. Sci. 1-18 (2017)
[76] Mehta, G.B.: Preference and utility. In: Barberà, S., Hammond, P., Seidl, C. (eds.) Handbook of Utility Theory, pp. 1-47. Kluwer Academic Publisher, Dordrecht (1998)
[77] Minguzzi, E.: Normally preordered spaces and utilities. Order 30, 137-150 (2013) · Zbl 1262.54008
[78] Mitra, T., Ozbek, M.K.: On representation of monotone preference orders in a sequence space. Soc. Choice Welf. 41(3), 473-487 (2013) · Zbl 1288.91051
[79] Monteiro, P.K.: Some results on the existence of utility functions on path connected spaces. J. Math. Econ. 16, 147-156 (1987) · Zbl 0642.90018
[80] Peleg, B.: Utility functions for partially ordered topological spaces. Econometrica 38(1), 93-96 (1970) · Zbl 0195.31501
[81] Pivato, M.: Multiutility representations for incomplete difference preorders. Math. Soc. Sci. 66, 196-220 (2013) · Zbl 1296.91094
[82] Sakai, T.: Equitable intergenerational preferences on restricted domains. Soc. Choice Welf. 27, 41-54 (2006) · Zbl 1180.91085
[83] Sakai, T.: Limit representations of intergenerational equity. Soc. Choice Welf. 47(2), 481-500 (2016) · Zbl 1392.91086
[84] Sakamoto, N.: Impossibilities of Paretian social welfare functions for infinite utility streams with distributive equity. Hitotsubashi J. Econ. 53, 121-130 (2012)
[85] Sierpiński, W.: Cardinal and Ordinal Numbers. Polish Scientific, Warsaw (1965) · Zbl 0131.24801
[86] Smith, A.: The Wealth of Nations: A Translation into Modern English. Industrial Systems Research (2015)
[87] Svensson, L.-G.: Equity among generations. Econometrica 48, 1251-1256 (1980) · Zbl 0436.90029
[88] Vallentyne, P.: Utilitarianism and infinite utility. Australas. J. Philos. 71, 212-215 (1993)
[89] Wakker, P.P.: Continuity of preference relations for separable topologies. Int. Econ. Rev. 29, 105-110 (1988) · Zbl 0638.90005
[90] Watson, S.: The Construction of Topological Spaces: Planks and Resolutions. In: Hus̄ek, M., van Mill, J. (eds.) Recent Progress in General Topology, pp. 673-757 North-Holland, Amsterdam (1992) · Zbl 0803.54001
[91] von Weizsäcker, C.C.: Existence of optimal program of accumulation for an infinite time horizon. Rev. Econ. Stud. 32, 85-104 (1965)
[92] Wold, H.: A synthesis of pure demand analysis Part II. Skandinavisk Aktuaritidskrift 26, 220-263 (1943) · Zbl 0063.08307
[93] Zame, W.R.: Can intergenerational equity be operationalized? Theor. Econ. 2, 187-
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