Combined Feed
https://feeds.library.caltech.edu/people/Border-K-C/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenMon, 27 Nov 2023 18:52:14 +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/ncg03-srq34An 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-wn678A 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-9ys23Positive Operators, Riesz Spaces, and Economics
https://resolver.caltech.edu/CaltechAUTHORS:20181011-142851140
Authors: Aliprantis, Charalambos D.; Border, Kim C.; Luxemburg, Wilhelmus A. J.
Year: 1991
DOI: 10.1007/978-3-642-58199-1
Over the last fifty years advanced mathematical tools have become an integral part in the development of modern economic theory. Economists continue to invoke sophisticated mathematical techniques and ideas in order to understand complex economic and social problems. In the last ten years the theory of Riesz spaces (vector lattices) has been successfully applied to economic theory. By now it is understood relatively well that the lattice structure of Riesz spaces can be employed to capture and interpret several economic notions. On April 16-20, 1990, a small conference on Riesz Spaces, Positive Opera tors, and their Applications to Economics took place at the California Institute of Technology. The purpose of the conference was to bring mathematicians special ized in Riesz Spaces and economists specialized in General Equilibrium together to exchange ideas and advance the interdisciplinary cooperation between math ematicians and economists. This volume is a collection of papers that represent the talks and discussions of the participants at the week-long conference. We take this opportunity to thank all the participants of the conference, especially those whose articles are contained in this volume. We also greatly ap preciate the financial support provided by the California Institute of Technology. In particular, we express our sincerest thanks to David Grether, John Ledyard, and David Wales for their support. Finally, we would like to thank Susan Davis, Victoria Mason, and Marge D'Elia who handled the delicate logistics for the smooth running of the conference.https://authors.library.caltech.edu/records/p6hyp-bgv06Positive Operators, Riesz Spaces, and Economics
https://resolver.caltech.edu/CaltechAUTHORS:20200515-130605911
Authors: Aliprantis, Charalambos D.; Border, Kim C.; Luxemburg, Wilhelmus A. J.
Year: 1991
DOI: 10.1007/978-3-642-58199-1
Over the last fifty years advanced mathematical tools have become an integral part in the development of modern economic theory. Economists continue to invoke sophisticated mathematical techniques and ideas in order to understand complex economic and social problems. In the last ten years the theory of Riesz spaces (vector lattices) has been successfully applied to economic theory. By now it is understood relatively well that the lattice structure of Riesz spaces can be employed to capture and interpret several economic notions. On April 16-20, 1990, a small conference on Riesz Spaces, Positive Opera tors, and their Applications to Economics took place at the California Institute of Technology. The purpose of the conference was to bring mathematicians special ized in Riesz Spaces and economists specialized in General Equilibrium together to exchange ideas and advance the interdisciplinary cooperation between math ematicians and economists. This volume is a collection of papers that represent the talks and discussions of the participants at the week-long conference. We take this opportunity to thank all the participants of the conference, especially those whose articles are contained in this volume. We also greatly ap preciate the financial support provided by the California Institute of Technology. In particular, we express our sincerest thanks to David Grether, John Ledyard, and David Wales for their support. Finally, we would like to thank Susan Davis, Victoria Mason, and Marge D'Elia who handled the delicate logistics for the smooth running of the confer ence.https://authors.library.caltech.edu/records/wcnfe-2bg85Functional analytic tools for expected utility theory
https://resolver.caltech.edu/CaltechAUTHORS:20201211-170108337
Authors: Border, K. C.
Year: 1991
DOI: 10.1007/978-3-642-58199-1_4
Depending on the school of thought, expected utility theory states that choices among lotteries either should be made or actually made by maximizing the expected value of a real valued function of the outcomes—a utility function. This article provides a look at some of the functional analytic results used in expected utility theory. I concentrate on applications to the theory of stochastic dominance relations and the revealed preference approach to expected utility. Few of these results are deep, given the underlying tools, but many of them are not widely known, and their combination is novel. In particular, the revealed preference results of Border [4] are extended to higher degree stochastic dominance relations.https://authors.library.caltech.edu/records/hdbb8-sv984Infinite Dimensional Analysis: A Hitchhiker's Guide
https://resolver.caltech.edu/CaltechAUTHORS:20200519-083921808
Authors: Aliprantis, Charalambos D.; Border, Kim C.
Year: 1994
DOI: 10.1007/978-3-662-03004-2
This text was born out of an advanced mathematical economics seminar at Caltech in 1989-90. We realized that the typical graduate student in mathematical economics has to be familiar with a vast amount of material that spans several traditional fields in mathematics. Much of the mate¬rial appears only in esoteric research monographs that are designed for specialists, not for the sort of generalist that our students need be. We hope that in a small way this text will make the material here accessible to a much broader audience. While our motivation is to present and orga¬nize the analytical foundations underlying modern economics and finance, this is a book of mathematics, not of economics. We mention applications to economics but present very few of them. They are there to convince economists that the material has so me relevance and to let mathematicians know that there are areas of application for these results. We feel that this text could be used for a course in analysis that would benefit mathematicians, engineers, and scientists. Most of the material we present is available elsewhere, but is scattered throughout a variety of sources and occasionally buried in obscurity. Some of our results are original (or more likely, independent rediscoveries). We have included some material that we cannot honestly say is neces¬sary to understand modern economic theory, but may yet prove useful in future research.https://authors.library.caltech.edu/records/wxtvp-gpj71Dynamic 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-pf106Infinite Dimensional Analysis: A Hitchhiker's Guide
https://resolver.caltech.edu/CaltechAUTHORS:20200519-082837523
Authors: Aliprantis, Charalambos D.; Border, Kim C.
Year: 1999
DOI: 10.1007/978-3-662-03961-8
In the nearly five years since the publication of what we refer to as The Hitchhiker's Guide, we have been the recipients of much advice and many complaints. That, combined with the economics of the publishing industry, convinced us that the world would be a better place if we published a second edition of our book, and made it available in paperback at a more modest price. The most obvious difference between the second and the original edition is the reorganization of material that resulted in three new chapters. Chapter 4 collects many of the purely set-theoretical results about measurable structures such as semirings and a-algebras. The material in this chapter is quite independent from notions of measure and integration, and is easily accessible, so we thought it should come sooner. We also divided the chapter on correspondences into two separate chapters, one dealing with continuity, the other with measurability. The material on measurable correspondences is more detailed and, we hope, better written. We also put many of the representation theorems into their own Chapter 13. This arrangement has the side effect of forcing the renumbering of almost every result in the text, thus rendering the original version obsolete. We feel bad about that, but like Humpty Dumpty, we doubt we could put it back the way it was. The second most noticeable change is the addition of approximately seventy pages of new material.https://authors.library.caltech.edu/records/x9d1v-gnb48Infinite Dimensional Analysis: A Hitchhiker's Guide
https://resolver.caltech.edu/CaltechAUTHORS:20200519-082246408
Authors: Aliprantis, Charalambos D.; Border, Kim C.
Year: 2006
DOI: 10.1007/3-540-29587-9
This new edition of The Hitchhiker's Guide has benefitted from the comments of many individuals, which have resulted in the addition of some new material, and the reorganization of some of the rest. The most obvious change is the creation of a separate Chapter 7 on convex analysis. Parts of this chapter appeared in elsewhere in the second edition, but much of it is new to the third edition. In particular, there is an expanded discussion of support points of convex sets, and a new section on subgradients of convex functions. There is much more material on the special properties of convex sets and functions in finite dimensional spaces. There are improvements and additions in almost every chapter. There is more new material than might seem at first glance, thanks to a change in font that reduced the page count about five percent. We owe a huge debt to Valentina Galvani, Daniela Puzzello, and Francesco Rusticci, who were participants in a graduate seminar at Purdue University and whose suggestions led to many improvements, especially in chapters five through eight. We particularly thank Daniela Puzzello for catching uncountably many errors throughout the second edition, and simplifying the statements of several theorems and proofs. In another graduate seminar at Caltech, many improvements and corrections were suggested by Joel Grus, PJ Healy, Kevin Roust, Maggie Penn, and Bryan Rogers.https://authors.library.caltech.edu/records/jj552-gpj20Reduced 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-hbr03Reduced Form Auctions Revisited
https://resolver.caltech.edu/CaltechAUTHORS:20170731-164441362
Authors: Border, Kim C.
Year: 2017
This note uses Farkas's Lemma to prove new results 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/4f7kp-cze06Objective Subjective Probabilities
https://resolver.caltech.edu/CaltechAUTHORS:20170808-151011915
Authors: Border, Kim C.; Ghirardato, Paolo; Segal, Uzi
Year: 2017
This note shows that if the space of events is sufficiently rich and the subjective probability measure of each individual is non-atomic, then there is a σ-algebra of events on which everyone will have the same probability, and moreover, the range of these probabilities is the entire segment [0, 1].https://authors.library.caltech.edu/records/vtw3e-k9969Preferences Over Solution to the Bargaining Problem
https://resolver.caltech.edu/CaltechAUTHORS:20170818-141404867
Authors: Border, Kim C.; Segal, Uzi
Year: 2017
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 two sets of appealing axioms on such preferences that lead to unanimity in the choice of solution. Thus bargainers may be able to reach agreement on which solution to employ. Under the first set of axioms, the Nash solution is preferred to any other solution, while under the second set, a new solution, which we call the weighted linear solution, is best.https://authors.library.caltech.edu/records/6xdyr-40f88Economies With Many Commodities
https://resolver.caltech.edu/CaltechAUTHORS:20170817-150419178
Authors: Aliprantis, Charalambos D.; Border, Kim C.; Burkinshaw, Owen
Year: 2017
We discuss the two fundamental theorems of welfare economics in the context of the Arrow-Debreu-McKenzie model with an infinite dimensional commodity space. As an application, we prove the existence of competitive equilibrium in the standard single agent growth model.https://authors.library.caltech.edu/records/jjhxf-hrj08Dynamic Consistency Implies Approximately Expected Utility Preferences
https://resolver.caltech.edu/CaltechAUTHORS:20170828-143106635
Authors: Border, Kim C.; Segal, Uzi
Year: 2017
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/yxwaw-esd54Dutch Book Arguments and Subjective Probability
https://resolver.caltech.edu/CaltechAUTHORS:20170831-151749064
Authors: Border, Kim C.; Segal, Uzi
Year: 2017
[No abstract]https://authors.library.caltech.edu/records/0z0pw-6pj51A Theory of Auditing and Plunder
https://resolver.caltech.edu/CaltechAUTHORS:20170915-144256949
Authors: Border, Kim C.; Sobel, Joel
Year: 2017
Taxpayers know their income but the IRS does not. The IRS can audit taxpayers to discover their true income, but auditing is costly. We characterize optimal policies for the IRS when it is free to choose tax levies, audit probabilities and penalties. The main results are that optimal policies involve taxes which are monotonically increasing in reported incomes and audit probabilities are monotonically decreasing in reported income. In general optimal schemes involve stochastic auditing of reports and rebates for telling the truth. A theory of optimal plundering is described.https://authors.library.caltech.edu/records/hq4vr-2ev86More on Harsanyi's Utilitarian Cardinal Welfare Theorem
https://resolver.caltech.edu/CaltechAUTHORS:20170918-163836570
Authors: Border, Kim C.
Year: 2017
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/q0pxs-qmw64The Core of a Coalitional Production Economy Without Ordered Preferences
https://resolver.caltech.edu/CaltechAUTHORS:20170926-134414751
Authors: Border, Kim C.
Year: 2017
It is shown that the core of a coalitional production economy with a balanced technology (Bohm [1974]) is nonempty, even if the consumers have preferences which are intransitive, provided the preferences are convex and continuous. Since such preferences cannot be represented by utility functions, this result does not follow from the nonemptiness of the core of a characteristic function game. Rather, the approach is closer to that of Ichiishi's [1981] social coalitional equilibrium.https://authors.library.caltech.edu/records/t18hp-r5w51On Equilibria of Excess Demand Correspondences
https://resolver.caltech.edu/CaltechAUTHORS:20170926-135446678
Authors: Border, Kim C.
Year: 2017
A new lemma on the existence of maximal elements of binary relations is proved and applied to a revealed preference relation on price vectors. The resulting maximal elements are equilibrium prices. This technique allows one to generalize results of Aliprantis and Brown [1982], Neuefeind [1980], and Geistdoerfer-Florenzano [1982].https://authors.library.caltech.edu/records/e31jk-6s897An Impossibility Theorem for Spatial Models
https://resolver.caltech.edu/CaltechAUTHORS:20171002-150117835
Authors: Border, Kim C.
Year: 2017
This paper examines the implications for social welfare functions of restricting the domain of individual preferences lo 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 Saiterthwaite 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 the Gibbard-Satterwaite hypothesis.https://authors.library.caltech.edu/records/e3phc-jcr89Noncooperative Games, Abstract Economies, and Walrasian Equilibria
https://resolver.caltech.edu/CaltechAUTHORS:20171004-164203686
Authors: Border, Kim C.
Year: 2017
The introduction of an additional player to serve as coordinator in an N-person abstract economy leads in a natural way to an N+1-person noncooperative game. Sufficient conditions on the abstract economy are considered which lead to the existence of equilibrium in the resulting game and hence for the abstract economy.https://authors.library.caltech.edu/records/z8ajz-55h10Straightforward Elections, Unanimity, and Phantom Voters
https://resolver.caltech.edu/CaltechAUTHORS:20171005-161613179
Authors: Border, Kim C.; Jordan, J. S.
Year: 2017
Nonmanipulable direct revelation social choice functions are characterized for societies where the space of alternatives is a euclidean space and all voters have separable preferences with a global optimum. If a nonmanipulable choice function satisfies a weak unanimity-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 voter's ideal points. Each coordinate function will also be nonmanipulable 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, nonseparability of preferences leads to dictatorship, even if preferences are restricted to be quadratic.https://authors.library.caltech.edu/records/wckbb-nkp96Social Welfare Functions for Economic Environments with and without the Pareto Principle
https://resolver.caltech.edu/CaltechAUTHORS:20171012-170534239
Authors: Border, Kim C.
Year: 2017
Social welfare functions for private goods economies with classical preferences are considered. It is shown 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.https://authors.library.caltech.edu/records/2nh7t-93726