Arrow's theorem, countably many agents, and more visible invisible dictators Export

@article{mihara99jme, abstract = {For infinite societies, Fishburn [Fishburn, P.C., 1970. Arrow's impossibility theorem: Concise proof and infinite voters. Journal of Economic Theory, 2: 103-106], Kirman and Sondermann [Kirman, A.P., Sondermann, D., 1972. Arrow's theorem, many agents, and invisible dictators. Journal of Economic Theory, 5: 267-277], and Armstrong [Armstrong, T.E., 1980. Arrow's theorem with restricted coalition algebras. Journal of Mathematical Economics, 7: 55-75] gave a nonconstructive proof of the existence of a social welfare function satisfying Arrow's conditions (Unanimity, Independence, and Nondictatorship). This paper improves on their results by (i) giving a concrete example of such a function, and (ii) showing how to compute, from a description of a profile on a pair of alternatives, which alternative is socially preferred under the function. The introduction of a certain [`]oracle' resolves Mihara's impossibility result (1997) about computability of social welfare functions.}, author = {Mihara, H. R.}, citeulike-article-id = {2818141}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/S0304-4068(98)00061-5}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6VBY-3Y9TWFV-1/1/12e14f10c0226477b009eb5ae6291644}, doi = {10.1016/S0304-4068(98)00061-5}, journal = {Journal of Mathematical Economics}, keywords = {arrow-impossibility-theorem, computability, computer\_science, economics, free-ultrafilters, oracle-algorithms, political\_science, preference-aggregation, recursion-theory, social\_choice, vita}, month = {November}, number = {3}, pages = {267--287}, posted-at = {2008-05-21 05:07:29}, priority = {0}, title = {Arrow's theorem, countably many agents, and more visible invisible dictators}, url = {http://dx.doi.org/10.1016/S0304-4068(98)00061-5}, volume = {32}, year = {1999} }

TY - JOUR ID - mihara99jme L3 - citeulike-article-id:2818141 N2 - For infinite societies, Fishburn [Fishburn, P.C., 1970. Arrow's impossibility theorem: Concise proof and infinite voters. Journal of Economic Theory, 2: 103-106], Kirman and Sondermann [Kirman, A.P., Sondermann, D., 1972. Arrow's theorem, many agents, and invisible dictators. Journal of Economic Theory, 5: 267-277], and Armstrong [Armstrong, T.E., 1980. Arrow's theorem with restricted coalition algebras. Journal of Mathematical Economics, 7: 55-75] gave a nonconstructive proof of the existence of a social welfare function satisfying Arrow's conditions (Unanimity, Independence, and Nondictatorship). This paper improves on their results by (i) giving a concrete example of such a function, and (ii) showing how to compute, from a description of a profile on a pair of alternatives, which alternative is socially preferred under the function. The introduction of a certain [`]oracle' resolves Mihara's impossibility result (1997) about computability of social welfare functions. IS - 3 JF - Journal of Mathematical Economics EP - 287 TI - Arrow's theorem, countably many agents, and more visible invisible dictators VL - 32 SP - 267 KW - arrow-impossibility-theorem KW - computability KW - computer_science KW - economics KW - free-ultrafilters KW - oracle-algorithms KW - political_science KW - preference-aggregation KW - recursion-theory KW - social_choice KW - vita AU - Mihara, HR PY - 1999/11// UR - http://dx.doi.org/10.1016/S0304-4068(98)00061-5 ER -