Article records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 17:49:35 +0000Straightforward Elections, Unanimity and Phantom Voters
https://resolver.caltech.edu/CaltechAUTHORS:20171116-170213213
Authors: Border, Kim C.; Jordan, J. S.
Year: 1983
DOI: 10.2307/2296962
Non-manipulable direct revelation social choice functions are characterized for societies where the space of alternatives is a euclidean space and all voters have separable star-shaped preferences with a global optimum. If a non-manipulable choice function satisfies a weak unanmity-respecting condition (which is equivalent to having an unrestricted range) then it will depend only on voters' ideal points. Further, such a choice function will decompose into a product of one-dimensional mechanisms in the sense that each coordinate of the chosen point depends only on the respective coordinate of the voters' ideal points. Each coordinate function will also be non-manipulable and respect unanimity. Such one-dimensional mechanisms are uncompromising in the sense that voters cannot take an extreme position to influence the choice to their advantage. Two characterizations of uncompromising choice functions are presented. One is in terms of a continuity condition, the other in terms of "phantom voters" i.e. those points which are chosen which are not any voter's ideal point. There are many such mechanisms which are not dictatorial. However, if differentiability is required of the choice function, this forces it to be either constant or dictatorial. In the multidimensional case, non-separability of preferences leads to dictatorship, even if preferences are restricted to be quadratic.https://authors.library.caltech.edu/records/m0p73-gf968Social welfare functions for economic environments with and without the pareto principle
https://resolver.caltech.edu/CaltechAUTHORS:20171016-101933174
Authors: Border, Kim C.
Year: 1983
DOI: 10.1016/0022-0531(83)90045-5
It is shown for the case of private goods economies that every social welfare function satisfying a weak nonimposition condition and the independence of irrelevant alternatives axiom is of one of the following forms. It is either null, or the class of decisive coalitions is an ultrafilter, or the class of anti-decisive coalitions is an ultrafilter. In the case of a private goods economy with finitely many traders, the latter conditions imply the existence of either a dictator or anti-dictator. By requiring the Pareto principle as well, it is easily seen that the social welfare function must be dictatorial.https://authors.library.caltech.edu/records/e8kfv-j6m40An impossibility theorem for spatial models
https://resolver.caltech.edu/CaltechAUTHORS:20171004-145251315
Authors: Border, Kim C.
Year: 1984
DOI: 10.1007/BF00118938
This paper examines the implications for social welfare functions of restricting the domain of individual preferences to type-one preferences. Type-one preferences assume that each person has a most preferred alternative in a euclidean space and that alternatives are ranked according to their euclidean distance from this point. The result is that if we impose Arrow's conditions of collective rationality, IIA, and the Pareto principle on the social welfare function, then it must be dictatorial. This result may not seem surprising, but it stands in marked contrast to the problem considered by Gibbard and Satterthwaite of finding a social-choice function. With unrestricted domain, under the Gibbard-Satterthwaite hypotheses, choices must be dictatorial. With type-one preferences this result has been previously shown not to be true. This finding identifies a significant difference between the Arrow and Gibbard-Satterthwaite problems.https://authors.library.caltech.edu/records/5ws86-wn678An impossibility theorem for spatial models
https://resolver.caltech.edu/CaltechAUTHORS:20171004-145251315
Authors: Border, Kim C.
Year: 1984
DOI: 10.1007/BF00118938
This paper examines the implications for social welfare functions of restricting the domain of individual preferences to type-one preferences. Type-one preferences assume that each person has a most preferred alternative in a euclidean space and that alternatives are ranked according to their euclidean distance from this point. The result is that if we impose Arrow's conditions of collective rationality, IIA, and the Pareto principle on the social welfare function, then it must be dictatorial. This result may not seem surprising, but it stands in marked contrast to the problem considered by Gibbard and Satterthwaite of finding a social-choice function. With unrestricted domain, under the Gibbard-Satterthwaite hypotheses, choices must be dictatorial. With type-one preferences this result has been previously shown not to be true. This finding identifies a significant difference between the Arrow and Gibbard-Satterthwaite problems.https://authors.library.caltech.edu/records/ncg03-srq34A Core Existence Theorem for Games Without Ordered Preferences
https://resolver.caltech.edu/CaltechAUTHORS:20171004-171808719
Authors: Border, Kim C.
Year: 1984
[Introduction] To a large extent the cooperative theory of games has an altogether different
appearance from the noncooperative theory. The noncooperative theory generally deals
with games in either extensive form or normal form, while the cooperative theory is usually
described in characteristic function form. One of the central concepts in the cooperative
theory is that of the core, which is the set of utility allocations which no coalition can
improve upon. This notion of the core and of the characteristic function form of a game
depends heavily on the existence of a utility representation for players' preferences. Recently
Gale and Mas-Colell [3] and Shafer and Sonnenschein [6] have proven theorems on the
existence of a Nash equilibrium for noncooperative games in normal form in which the
players' preferences over strategy vectors are not necessarily complete or transitive and
so may fail to have a utility representation. Thus it might appear that the noncooperative
theory is applicable in environments where the cooperative theory is not. In order to
formulate theorems in the cooperative theory of games which can be applied to environments
in which players may have nonordered preferences, the characteristic function must
be reformulated in terms of physical outcomes as opposed to utility outcomes. The players'
preferences can then be expressed in terms of the physical outcomes without the use of
a utility function.https://authors.library.caltech.edu/records/kkcr6-kth70More on Harsanyi's utilitarian cardinal welfare theorem
https://resolver.caltech.edu/CaltechAUTHORS:20170919-101333544
Authors: Border, K. C.
Year: 1985
DOI: 10.1007/BF00649263
If individuals and society both obey the expected utility hypothesis and social alternatives are uncertain, then the social utility must be a linear combination of the individual utilities, provided the society is indifferent when all its members are. This result was first proven by Harsanyi [4] who made implicit assumptions in the proof not actually needed for the result (see [5]). This note presents a straightforward proof of Harsanyi's theorem based on a separating hyperplane argument.https://authors.library.caltech.edu/records/6mcys-9ys23Dynamic Consistency Implies Approximately Expected Utility Preferences
https://resolver.caltech.edu/CaltechAUTHORS:20170829-155548155
Authors: Border, Kim C.; Segal, Uzi
Year: 1994
DOI: 10.1006/jeth.1994.1038
Machina has proposed a definition of dynamic consistency which admits non-expected utility functionals. We show that even under this new definition a dynamically consistent preference relation that is differentiable becomes arbitrarily close to an expected utility preference after the realization of a low probability event.https://authors.library.caltech.edu/records/af8gj-aks36Market economies with many commodities
https://resolver.caltech.edu/CaltechAUTHORS:20200519-155409664
Authors: Aliprantis, Charalambos D.; Border, Kim C.; Burkinshaw, Owen
Year: 1996
DOI: 10.1007/bf02441265
In this survey problems from the consideration of infinite dimensional commodity spaces in the Arrow-Debreu-McKenzie model are discussed. It has become clear in the last couple of decades that in order to address real policy questions, economic models that are both stochastic and dynamic have to be employed. These models lead naturally to infinite dimensional commodity spaces.https://authors.library.caltech.edu/records/venx5-c4v75Preferences Over Solutions to the Bargaining Problem
https://resolver.caltech.edu/CaltechAUTHORS:20170830-160727267
Authors: Border, Kim C.; Segal, Uzi
Year: 1997
DOI: 10.2307/2171811
There are several solutions to the Nash bargaining problem in the literature. Since various authors have expressed preferences for one solution over another, we find it useful to study preferences over solutions in their own right. We identify a set of appealing axioms on such preferences that lead to unanimity in the choice of solution, which turns out to be the solution of Nash.https://authors.library.caltech.edu/records/j7cra-wcv36Economies with Many Commodities
https://resolver.caltech.edu/CaltechAUTHORS:20170830-110545023
Authors: Aliprantis, Charalambos D.; Border, Kim C.; Burkinshaw, Owen
Year: 1997
DOI: 10.1006/jeth.1996.2240
We discuss the two fundamental theorems of welfare economics in the context of the Arrow–Debreu–McKenzie model with an infinite dimensional commodity space.https://authors.library.caltech.edu/records/xqkhn-4th17Economies with Many Commodities
https://resolver.caltech.edu/CaltechAUTHORS:20170830-110545023
Authors: Aliprantis, Charalambos D.; Border, Kim C.; Burkinshaw, Owen
Year: 1997
DOI: 10.1006/jeth.1996.2240
We discuss the two fundamental theorems of welfare economics in the context of the Arrow–Debreu–McKenzie model with an infinite dimensional commodity space.https://authors.library.caltech.edu/records/8zzvc-pf106Reduced form auctions revisited
https://resolver.caltech.edu/CaltechAUTHORS:20171103-155759339
Authors: Border, Kim C.
Year: 2007
DOI: 10.1007/s00199-006-0080-z
This note uses the Theorem of the Alternative to prove newresults on the
implementability of general, asymmetric auctions, and to provide simpler proofs
of known results for symmetric auctions. The tradeoff is that type spaces are taken
to be finite.https://authors.library.caltech.edu/records/tytmx-vfq61Unanimous subjective probabilities
https://resolver.caltech.edu/CaltechAUTHORS:20090506-113153983
Authors: Border, Kim C.; Ghirardato, Paolo; Segal, Uzi
Year: 2008
DOI: 10.1007/s00199-006-0174-7
This note shows that if the space of events is sufficiently rich and the subjective probability function of each individual is non-atomic, then there is a σ-algebra of events over which everyone will have the same probability function, and moreover, the range of this common probability is the entire unit interval.https://authors.library.caltech.edu/records/r9441-hbr03