Results for 'impossibility theorem'

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  1. An Impossibility Theorem for Welfarist Axiologies.Gustaf Arrhenius - 2000 - Economics and Philosophy 16 (2):247-266.
    A search is under way for a theory that can accommodate our intuitions in population axiology. The object of this search has proved elusive. This is not surprising since, as we shall see, any welfarist axiology that satisfies three reasonable conditions implies at least one of three counter-intuitive conclusions. I shall start by pointing out the failures in three recent attempts to construct an acceptable population axiology. I shall then present an impossibility theorem and conclude with a short (...)
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  2. An Impossibility Theorem for Amalgamating Evidence.Jacob Stegenga - 2013 - Synthese 190 (12):2391-2411.
    Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the (...). (shrink)
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  3. An Impossibility Theorem for Verisimilitude.Sjoerd Zwart & Maarten Franssen - 2007 - Synthese 158 (1):75-92.
    In this paper, we show that Arrow’s well-known impossibility theorem is instrumental in bringing the ongoing discussion about verisimilitude to a more general level of abstraction. After some preparatory technical steps, we show that Arrow’s requirements for voting procedures in social choice are also natural desiderata for a general verisimilitude definition that places content and likeness considerations on the same footing. Our main result states that no qualitative unifying procedure of a functional form can simultaneously satisfy the requirements (...)
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  4.  50
    An Impossibility Theorem on Beliefs in Games.Adam Brandenburger & H. Jerome Keisler - 2006 - Studia Logica 84 (2):211-240.
    A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes that.
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  5. Zwart and Franssen’s Impossibility Theorem Holds for Possible-World-Accounts but Not for Consequence-Accounts to Verisimilitude.Gerhard Schurz & Paul Weingartner - 2010 - Synthese 172 (3):415 - 436.
    Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts , content-aspects and likeness-aspects of verisimilitude are not in conflict with each (...)
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  6.  19
    Zwart and Franssen’s Impossibility Theorem Holds for Possible-World-Accounts but Not for Consequence-Accounts to Verisimilitude.Gerhard Schurz & Paul Weingartner - 2010 - Synthese 172 (3):415-436.
    Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts, content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, (...)
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  7. An Impossibility Theorem in Population Axiology with Weak Ordering Assumptions.Gustaf Arrhenius - 1999 - In Ryszard Sliwinski (ed.), Philosophical crumbs. Essays dedicated to Ann-Mari Henschen-Dahlquist on the occasion of her seventy-fifth birthday. Uppsala: Uppsala philosophical studies. pp. 11-21.
  8.  73
    One More Axiological Impossibility Theorem.Gustaf Arrhenius - 2009 - In Lars-Göran Johansson, Jan Österberg & Ryszard Sliwinski (eds.), Logic, Ethics and All That Jazz. Essays in Honour of Jordan Howard Sobel. Uppsala: Uppsala Philosophical Studies. pp. 23-37.
    Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations “is better than” and “is as good as”. This field has been riddled with impossibility results which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies.1 All of these results have one thing in common, however. They all involve an adequacy condition that rules out Derek Parfit’s Repugnant (...)
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  9.  43
    Impossibility Theorems for Normal Form Games.David Squires - 1998 - Theory and Decision 44 (1):67-81.
    Two recent papers (Cubitt and Sugden, 1994; Samuelson, 1992) have established impossibility results which cast doubt on the coherence of the assumption of ’common knowledge of rationality'. It is shown that the Cubitt–Sugden result is the more powerful of the two impossibilities. Second, it is proved that the existence of a quasi-strict equilibrium is sufficient to construct sets which satisfy the Cubitt–Sugden axioms. This fact is used to establish that their impossibility result cannot arise in 2-player games. Finally, (...)
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  10.  36
    An Impossibility Theorem for Allocation Aggregation.Carl Wagner & Mark Shattuck - 2014 - Journal of Philosophical Logic 43 (6):1173-1186.
    Among the many sorts of problems encountered in decision theory, allocation problems occupy a central position. Such problems call for the assignment of a nonnegative real number to each member of a finite set of entities, in such a way that the values so assigned sum to some fixed positive real number s. Familiar cases include the problem of specifying a probability mass function on a countable set of possible states of the world, and the distribution of a certain sum (...)
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  11.  34
    The Gärdenfors Impossibility Theorem in Non-Monotonic Contexts.David Makinson - 1990 - Studia Logica 49 (1):1 - 6.
    Gärdenfors' impossibility theorem draws attention to certain formal difficulties in defining a conditional connective from a notion of theory revision, via the Ramsey test. We show that these difficulties are not avoided by taking the background inference operation to be non-monotonic.
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  12. Arrow’s Impossibility Theorem and the National Security State.S. M. Amadae - 2005 - Studies in History and Philosophy of Science Part A 36 (4):734-743.
    This paper critically engages Philip Mirowki's essay, "The scientific dimensions of social knowledge and their distant echoes in 20th-century American philosophy of science." It argues that although the cold war context of anti-democratic elitism best suited for making decisions about engaging in nuclear war may seem to be politically and ideologically motivated, in fact we need to carefully consider the arguments underlying the new rational choice based political philosophies of the post-WWII era typified by Arrow's impossibility theorem. A (...)
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  13.  36
    A Note on an Impossibility Theorem of Gardenfors.Krister Segerberg - 1989 - Noûs 23 (3):351-354.
  14.  88
    Coherence & Confirmation: The Epistemic Limitations of the Impossibility Theorems.Ted Poston - 2022 - Kriterion - Journal of Philosophy 36 (1):83-111.
    It is a widespread intuition that the coherence of independent reports provides a powerful reason to believe that the reports are true. Formal results by Huemer, M. 1997. “Probability and Coherence Justification.” Southern Journal of Philosophy 35: 463–72, Olsson, E. 2002. “What is the Problem of Coherence and Truth?” Journal of Philosophy XCIX : 246–72, Olsson, E. 2005. Against Coherence: Truth, Probability, and Justification. Oxford University Press., Bovens, L., and S. Hartmann. 2003. Bayesian Epistemology. Oxford University Press, prove that, under (...)
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  15. An Arrovian Impossibility Theorem for the Epistemology of Disagreement.Nicholaos Jones - 2012 - Logos and Episteme 3 (1):97-115.
    According to conciliatory views about the epistemology of disagreement, when epistemic peers have conflicting doxastic attitudes toward a proposition and fully disclose to one another the reasons for their attitudes toward that proposition (and neither has independent reason to believe the other to be mistaken), each peer should always change his attitude toward that proposition to one that is closer to the attitudes of those peers with which there is disagreement. According to pure higher-order evidence views, higher-order evidence for a (...)
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  16. The Relation Between Degrees of Belief and Binary Beliefs: A General Impossibility Theorem.Franz Dietrich & Christian List - 2021 - In Lotteries, Knowledge, and Rational Belief. Essays on the Lottery Paradox. Cambridge University Press. pp. 223-54.
    Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem (...)
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  17.  35
    Why Arrow's Impossibility Theorem is Invalid.Sidney Gendin - 1994 - Journal of Social Philosophy 25 (1):144-159.
    In 1951, Kenneth Arrow published his now celebrated book Social Choice and Individual Values. Although not the first book to be written on social choice, Arrow's work ushered in a voluminous literature mostly produced by economists but by philosophers and political scientists as well. Arrow's chief result was a proof of the impossibility of a social welfare function . He showed that there could be no decision procedure for aggregating individual preference orderings into a grand, overall social preference ordering. (...)
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  18.  8
    Arrow’s Impossibility Theorem as a Special Case of Nash Equilibrium: A Cognitive Approach to the Theory of Collective Decision-Making.Andrea Oliva & Edgardo Bucciarelli - 2020 - Mind and Society 19 (1):15-41.
    Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, it is (...)
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  19.  29
    Kenneth Arrow’s Impossibility Theorem Stretching to Other Fields.Wulf Gaertner - 2018 - Public Choice.
    Arrow’s impossibility result not only had a profound influence on welfare economics, but was, as this paper shows, also widely discussed in philosophy of science and in the engineering design literature.
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  20.  46
    A Note On Impossibility Theorems and Seniority Rules.Matthias Hild - 2004 - Theory and Decision 57 (1):69-78.
    We characterize seniority rules, also known as lexical dictatorships, under weak consistency constraints on the group’s choice function. These constraints are base triple-acyclicity in the case of binary choices and rationalizability (although not rationality) in the case of choices between an arbitrary number of alternatives. Existing results on these weakened constraints remain silent on the treatment of the group’s most junior individuals and therefore do not yield a complete characterization of seniority rules. We also impose a universal domain, binary strict (...)
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  21.  66
    Bayesian Decision Theory, Rule Utilitarianism, and Arrow's Impossibility Theorem.John C. Harsanyi - 1979 - Theory and Decision 11 (3):289-317.
  22.  85
    First-Order Logic Formalisation of Impossibility Theorems in Preference Aggregation.Umberto Grandi & Ulle Endriss - 2013 - Journal of Philosophical Logic 42 (4):595-618.
    In preference aggregation a set of individuals express preferences over a set of alternatives, and these preferences have to be aggregated into a collective preference. When preferences are represented as orders, aggregation procedures are called social welfare functions. Classical results in social choice theory state that it is impossible to aggregate the preferences of a set of individuals under different natural sets of axiomatic conditions. We define a first-order language for social welfare functions and we give a complete axiomatisation for (...)
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  23.  58
    Combinatorial Versus Decision-Theoretic Components of Impossibility Theorems.David Makinson - 1996 - Theory and Decision 40 (2):181-189.
    Separates the purely combinatorial component of Arrow's impossibility theorem in the theory of collective preference from its decision-theoretic part, and likewise for the closely related Blair/Bordes/Kelly/Suzumura theorem. Such a separation provides a particularly elegant proof of Arrow's result, via a new 'splitting theorem'.
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  24.  27
    Invoking a Cartesian Product Structure on Social States: New Resolutions of Sen’s and Gibbard’s Impossibility Theorems.Herrade Igersheim - 2013 - Theory and Decision 74 (4):463-477.
    The purpose of this article is to introduce a Cartesian product structure into the social choice theoretical framework and to examine if new possibility results to Gibbard’s and Sen’s paradoxes can be developed thanks to it. We believe that a Cartesian product structure is a pertinent way to describe individual rights in the social choice theory since it discriminates the personal features comprised in each social state. First we define some conceptual and formal tools related to the Cartesian product structure. (...)
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  25.  27
    A Simplified Proof of an Impossibility Theorem.Alfred F. Mackay - 1973 - Philosophy of Science 40 (2):175-177.
    In this paper I prove a theorem which is similar to Arrow's famous impossibility theorem. I show that no social welfare function can be both minimally majoritarian and also independent of irrelevant alternatives. My condition of minimal majoritarianism is substantially weaker than simple majority rule.
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  26.  1
    Computer-Aided Proofs of Arrow's and Other Impossibility Theorems.Pingzhong Tang & Fangzhen Lin - 2009 - Artificial Intelligence 173 (11):1041-1053.
  27.  18
    Repairing Proofs of Arrow's General Impossibility Theorem and Enlarging the Scope of the Theorem.R. Routley - 1979 - Notre Dame Journal of Formal Logic 20 (4):879-890.
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  28.  7
    A Critique of Cultural Theory's Impossibility Theorem.Mark Nowacki - unknown
    Various proponents of Cultural Theory have claimed that CT's Impossibility Theorem, namely that there are precisely five viable ways of life, has been formally proved. In this paper, I show that the Impossibility Theorem has not been formally proved and present a refutation of the Impossibility Theorem. With regard to, the problem areas identified include a failure to take into account the analogical nature of their theory and also a failure to carefully consider the (...)
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  29.  84
    The Real Foundations of the Alleged Errors in Allais' Impossibility Theorem: Unceasingly Repeated Errors or Contradictions of Mark Machina.Maurice Allais - 1995 - Theory and Decision 38 (3):251-299.
  30.  38
    Two Errors in The?Allais Impossibility Theorem?Mark J. Machina - 1995 - Theory and Decision 38 (3):231-250.
  31.  20
    Welfarist-Consequentialism, Similarity of Attitudes, and Arrow's General Impossibility Theorem.Kotaro Suzumura - manuscript
  32.  17
    The Two Tasks of Epistemology—an Impossibility Theorem.Bengt Hansson - unknown
  33.  14
    On the Philosophical Life: A Refutation of Cultural Theory's Impossibility Theorem.Mark Nowacki - unknown
    Cultural Theory is breathtaking in its comprehensiveness and in its simplicity. With regard to CT’s comprehensiveness, it is entirely characteristic that when the three authors of Cultural Theory get around to asking themselves “What does cultural theory leave out?”, their answer turns out to be a hearty “Not much!” In a single work, Michael Thompson manages to credit CT with shedding light on everything from environmental policies and Kondratiev waves, to Everest expeditions, the literary preferences of Benjamin Disraeli, and Aristotle’s (...)
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  34. The impossibility of a satisfactory population prospect axiology (independently of Finite Fine-Grainedness).Elliott Thornley - 2021 - Philosophical Studies 178 (11):3671-3695.
    Arrhenius’s impossibility theorems purport to demonstrate that no population axiology can satisfy each of a small number of intuitively compelling adequacy conditions. However, it has recently been pointed out that each theorem depends on a dubious assumption: Finite Fine-Grainedness. This assumption states that there exists a finite sequence of slight welfare differences between any two welfare levels. Denying Finite Fine-Grainedness makes room for a lexical population axiology which satisfies all of the compelling adequacy conditions in each theorem. (...)
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  35.  13
    The Impossible Causality: The No Hidden Variables Theorem of John von Neumann.Roberto Giuntini & Federico Laudisa - 2001 - Vienna Circle Institute Yearbook 8:173-188.
    The debate over the question whether quantum mechanics should be considered as a complete account of microphenomena has a long and deeply involved history, a turning point in which has been certainly the Einstein-Bohr debate, with the ensuing charge of incompleteness raised by the Einstein-Podolsky-Rosen argument. In quantum mechanics, physical systems can be prepared in pure states that nevertheless have in general positive dispersion for most physical quantities; hence in the EPR argument, the attention is focused on the question whether (...)
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  36. Arrow's Theorem in Judgment Aggregation.Franz Dietrich & Christian List - 2007 - Social Choice and Welfare 29 (1):19-33.
    In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although (...)
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  37. The Impossibility of Unbiased Judgment Aggregation.Franz Dietrich & Christian List - 2010 - Theory and Decision 68 (3):281-299.
    Standard impossibility theorems on judgment aggregation over logically connected propositions either use a controversial systematicity condition or apply only to agendas of propositions with rich logical connections. Are there any serious impossibilities without these restrictions? We prove an impossibility theorem without requiring systematicity that applies to most standard agendas: Every judgment aggregation function (with rational inputs and outputs) satisfying a condition called unbiasedness is dictatorial (or effectively dictatorial if we remove one of the agenda conditions). Our agenda (...)
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  38. Factoring Out the Impossibility of Logical Aggregation.Philippe Mongin - 2008 - Journal of Economic Theory 141:p. 100-113.
    According to a theorem recently proved in the theory of logical aggregation, any nonconstant social judgment function that satisfies independence of irrelevant alternatives (IIA) is dictatorial. We show that the strong and not very plausible IIA condition can be replaced with a minimal independence assumption plus a Pareto-like condition. This new version of the impossibility theorem likens it to Arrow’s and arguably enhances its paradoxical value.
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  39.  47
    Impossibility: The Limits of Science and the Science of Limits.John D. Barrow - 1998 - Oxford University Press.
    John Barrow is increasingly recognized as one of our most elegant and accomplished science writers, a brilliant commentator on cosmology, mathematics, and modern physics. Barrow now tackles the heady topic of impossibility, in perhaps his strongest book yet. Writing with grace and insight, Barrow argues convincingly that there are limits to human discovery, that there are things that are ultimately unknowable, undoable, or unreachable. He first examines the limits on scientific inquiry imposed by the deficiencies of the human mind: (...)
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  40. Judgment Aggregation: (Im)Possibility Theorems.Franz Dietrich - 2006 - Journal of Economic Theory 1 (126):286-298.
    The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment aggregation. (...)
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  41.  15
    Escaping Arrow's Theorem: The Advantage-Standard Model.Wesley Holliday & Mikayla Kelley - manuscript
    There is an extensive literature in social choice theory studying the consequences of weakening the assumptions of Arrow's Impossibility Theorem. Much of this literature suggests that there is no escape from Arrow-style impossibility theorems unless one drastically violates the Independence of Irrelevant Alternatives (IIA). In this paper, we present a more positive outlook. We propose a model of comparing candidates in elections, which we call the Advantage-Standard (AS) model. The requirement that a collective choice rule (CCR) be (...)
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  42.  53
    On the Impossibility of Amalgamating Evidence.Aki Lehtinen - 2013 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):101-110.
    It is argued in this paper that amalgamating confirmation from various sources is relevantly different from social-choice contexts, and that proving an impossibility theorem for aggregating confirmation measures directs attention to irrelevant issues.
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  43. Why Arrow's Theorem Matters for Political Theory Even If Preference Cycles Never Occur.Sean Ingham - forthcoming - Public Choice.
    Riker (1982) famously argued that Arrow’s impossibility theorem undermined the logical foundations of “populism”, the view that in a democracy, laws and policies ought to express “the will of the people”. In response, his critics have questioned the use of Arrow’s theorem on the grounds that not all configurations of preferences are likely to occur in practice; the critics allege, in particular, that majority preference cycles, whose possibility the theorem exploits, rarely happen. In this essay, I (...)
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  44. Aggregating Sets of Judgments: An Impossibility Result.Christian List & Philip Pettit - 2002 - Economics and Philosophy 18 (1):89-110.
    Suppose that the members of a group each hold a rational set of judgments on some interconnected questions, and imagine that the group itself has to form a collective, rational set of judgments on those questions. How should it go about dealing with this task? We argue that the question raised is subject to a difficulty that has recently been noticed in discussion of the doctrinal paradox in jurisprudence. And we show that there is a general impossibility theorem (...)
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  45. The Impossibility of a Satisfactory Population Ethics.Gustaf Arrhenius - 2011 - In Hans Colonius & Ehtibar N. Dzhafarov (eds.), Descriptive and Normative Approaches to Human Behavior, Advanced Series on Mathematical Psychology. Singapore:
    Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations \is better than" and \is as good as". This eld has been riddled with para- doxes and impossibility results which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. All of these results have one thing in common, however. They all involve an adequacy condition that rules out (...)
     
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  46.  22
    von Neumann’s Theorem Revisited.Pablo Acuña - 2021 - Foundations of Physics 51 (3):1-29.
    According to a popular narrative, in 1932 von Neumann introduced a theorem that intended to be a proof of the impossibility of hidden variables in quantum mechanics. However, the narrative goes, Bell later spotted a flaw that allegedly shows its irrelevance. Bell’s widely accepted criticism has been challenged by Bub and Dieks: they claim that the proof shows that viable hidden variables theories cannot be theories in Hilbert space. Bub’s and Dieks’ reassessment has been in turn challenged by (...)
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  47.  58
    Epsilon Theorems in Intermediate Logics.Matthias Baaz & Richard Zach - forthcoming - Journal of Symbolic Logic:1-40.
    Any intermediate propositional logic (i.e., a logic including intuitionistic logic and contained in classical logic) can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s ε-calculus. The first and second ε-theorems for classical logic establish conservativity of the ε-calculus over its classical base logic. It is well known that the second ε-theorem fails for the intuitionistic ε-calculus, as prenexation is impossible. The paper investigates the effect of adding critical ε- (...)
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  48. The Impossibility of a Satisfactory Population Ethics.Gustaf Arrhenius - 2011 - In Ehtibar N. Dzhafarov & Lacey Perry (eds.), Descriptive and Normative Approaches to Human Behavior. World Scientific Publishing Company. pp. 1–26.
    Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations “is better than ” and “is as good as”. This field has been riddled with paradoxes and impossibility results which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. All of these results have one thing in common, however. They all involve an adequacy condition that rules out (...)
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  49.  70
    Arrow's Theorem.Michael Morreau - 2014 - Stanford Encyclopedia of Philosophy: N/A.
    Kenneth Arrow’s “impossibilitytheorem—or “general possibility” theorem, as he called it—answers a very basic question in the theory of collective decision-making. Say there are some alternatives to choose among. They could be policies, public projects, candidates in an election, distributions of income and labour requirements among the members of a society, or just about anything else. There are some people whose preferences will inform this choice, and the question is: which procedures are there for deriving, from what (...)
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  50.  61
    A Representation Theorem for Voting with Logical Consequences.Peter Gärdenfors - 2006 - Economics and Philosophy 22 (2):181-190.
    This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set (...)
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