In economics and social choice single-peakedness is one of the most important and commonly studied models for preferences. It is well known that single-peaked consistency for total orders is in P. However in practice a preference profile is not always comprised of total orders. Often voters have indifference between some of the candidates. In a weak preference order indifference must be transitive. We show that single-peaked consistency for weak orders is in P for three different variants of single-peakedness for weak orders. Specifically, we consider Black's original definition of single-peakedness for weak orders, Black's definition of single-plateaued preferences, and the existential model recently introduced by Lackner. We accomplish our results by transforming each of these single-peaked consistency problems to the problem of determining if a 0-1 matrix has the consecutive ones property.
{"title":"Single-Peaked Consistency for Weak Orders Is Easy","authors":"Zack Fitzsimmons","doi":"10.4204/EPTCS.215.10","DOIUrl":"https://doi.org/10.4204/EPTCS.215.10","url":null,"abstract":"In economics and social choice single-peakedness is one of the most important and commonly studied models for preferences. It is well known that single-peaked consistency for total orders is in P. However in practice a preference profile is not always comprised of total orders. Often voters have indifference between some of the candidates. In a weak preference order indifference must be transitive. We show that single-peaked consistency for weak orders is in P for three different variants of single-peakedness for weak orders. Specifically, we consider Black's original definition of single-peakedness for weak orders, Black's definition of single-plateaued preferences, and the existential model recently introduced by Lackner. We accomplish our results by transforming each of these single-peaked consistency problems to the problem of determining if a 0-1 matrix has the consecutive ones property.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130877682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Epistemic protocols are communication protocols aiming at transfer of knowledge in a controlled way. Typically, the preconditions or goals for protocol actions depend on the knowledge of agents, often in nested form. Informal epistemic protocol descriptions for muddy children, coordinated attack, dining cryptographers, Russian cards, secret key exchange are well known. The contribution of this paper is a formal study of a natural requirement on epistemic protocols, that the contents of the protocol can be assumed to be common knowledge. By formalizing this requirement we can prove that there can be no unbiased deterministic protocol for the Russian cards problem. For purposes of our formal analysis we introduce an epistemic protocol language, and we show that its model checking problem is decidable.
{"title":"Verifying epistemic protocols under common knowledge","authors":"Yanjing Wang, Lakshmanan Kuppusamy, J. Eijck","doi":"10.1145/1562814.1562848","DOIUrl":"https://doi.org/10.1145/1562814.1562848","url":null,"abstract":"Epistemic protocols are communication protocols aiming at transfer of knowledge in a controlled way. Typically, the preconditions or goals for protocol actions depend on the knowledge of agents, often in nested form. Informal epistemic protocol descriptions for muddy children, coordinated attack, dining cryptographers, Russian cards, secret key exchange are well known. The contribution of this paper is a formal study of a natural requirement on epistemic protocols, that the contents of the protocol can be assumed to be common knowledge. By formalizing this requirement we can prove that there can be no unbiased deterministic protocol for the Russian cards problem. For purposes of our formal analysis we introduce an epistemic protocol language, and we show that its model checking problem is decidable.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124169863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a logic designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We give a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We show the decidability of the logic and give a complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof.
{"title":"A logic of propositional control for truthful implementations","authors":"N. Troquard, W. Hoek, M. Wooldridge","doi":"10.1145/1562814.1562846","DOIUrl":"https://doi.org/10.1145/1562814.1562846","url":null,"abstract":"We introduce a logic designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We give a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We show the decidability of the logic and give a complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124276759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables, are defined in a natural way. The mystery presented by the algebraic equations satisfied by (non-commuting) observables that cannot be observed in the same states is elucidated.
{"title":"Foundations of non-commutative probability theory","authors":"D. Lehmann","doi":"10.1145/1562814.1562841","DOIUrl":"https://doi.org/10.1145/1562814.1562841","url":null,"abstract":"Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables, are defined in a natural way. The mystery presented by the algebraic equations satisfied by (non-commuting) observables that cannot be observed in the same states is elucidated.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124813809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 1935, Oskar Morgenstern wrote: [T]here is exhibited an endless chain of reciprocally conjectural reactions and counter-reactions. The remedy would lie in analogous employment of the so-called Russell theory of types in logistics. This would mean that on the basis of the assumed knowledge by the economic subjects of theoretical tenets of Type I, there can be formulated higher propositions of the theory; thus, at least, of Type II. On the basis of information about tenets of Type II, propositions of Type III, at least, may be set up, etc. We will attempt to trace, from this promising start, the steps forward and backward on the path to the development of epistemic game theory. This will take us through von Neumann and Morgenstern, Nash, and Harsanyi, to an emerging field of epistemics as of the mid-1980s. We will continue with some comments on the variety of epistemic frameworks in use today.
{"title":"Origins of epistemics","authors":"Adam Brandenburger","doi":"10.1145/1562814.1562817","DOIUrl":"https://doi.org/10.1145/1562814.1562817","url":null,"abstract":"In 1935, Oskar Morgenstern wrote: [T]here is exhibited an endless chain of reciprocally conjectural reactions and counter-reactions. The remedy would lie in analogous employment of the so-called Russell theory of types in logistics. This would mean that on the basis of the assumed knowledge by the economic subjects of theoretical tenets of Type I, there can be formulated higher propositions of the theory; thus, at least, of Type II. On the basis of information about tenets of Type II, propositions of Type III, at least, may be set up, etc. We will attempt to trace, from this promising start, the steps forward and backward on the path to the development of epistemic game theory. This will take us through von Neumann and Morgenstern, Nash, and Harsanyi, to an emerging field of epistemics as of the mid-1980s. We will continue with some comments on the variety of epistemic frameworks in use today.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132469845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a logic combining Dynamic Epistemic Logic, a framework for reasoning about multi-agent communication, with a new multi-agent version of Justification Logic, a framework for reasoning about evidence and justification. This novel combination incorporates a new kind of multi-agent evidence elimination that cleanly meshes with the multi-agent communications from Dynamic Epistemic Logic, resulting in a system for reasoning about multi-agent communication and evidence elimination for groups of interacting rational agents.
{"title":"Evidence elimination in multi-agent justification logic","authors":"B. Renne","doi":"10.1145/1562814.1562845","DOIUrl":"https://doi.org/10.1145/1562814.1562845","url":null,"abstract":"This paper presents a logic combining Dynamic Epistemic Logic, a framework for reasoning about multi-agent communication, with a new multi-agent version of Justification Logic, a framework for reasoning about evidence and justification. This novel combination incorporates a new kind of multi-agent evidence elimination that cleanly meshes with the multi-agent communications from Dynamic Epistemic Logic, resulting in a system for reasoning about multi-agent communication and evidence elimination for groups of interacting rational agents.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114672373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
What happens if in the Muddy Children story [22] we drop the assumption that the public announcements (made by the father and by the children) are commonly known to be always true, and instead we simply assume that they are true and commonly believed to be true? More generally, what happens in the long term with a group's beliefs, knowledge and "epistemic states" (fully describable in fact by conditional beliefs), when receiving (or exchanging) a sequence of public announcements of truthful but uncertain information? Do the agents' beliefs (or knowledge, or conditional beliefs, or other doxastic attitudes such as "strong beliefs") reach a fixed point? Or do they exhibit instead a cyclic behavior, oscillating forever?
{"title":"Group belief dynamics under iterated revision: fixed points and cycles of joint upgrades","authors":"A. Baltag, S. Smets","doi":"10.1145/1562814.1562824","DOIUrl":"https://doi.org/10.1145/1562814.1562824","url":null,"abstract":"What happens if in the Muddy Children story [22] we drop the assumption that the public announcements (made by the father and by the children) are commonly known to be always true, and instead we simply assume that they are true and commonly believed to be true? More generally, what happens in the long term with a group's beliefs, knowledge and \"epistemic states\" (fully describable in fact by conditional beliefs), when receiving (or exchanging) a sequence of public announcements of truthful but uncertain information? Do the agents' beliefs (or knowledge, or conditional beliefs, or other doxastic attitudes such as \"strong beliefs\") reach a fixed point? Or do they exhibit instead a cyclic behavior, oscillating forever?","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133666977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The logical omniscience feature assumes that an epistemic agent knows all logical consequences of her assumptions. This paper offers a general theoretical framework that views logical omniscience as a computational complexity problem. We suggest the following approach: we assume that the knowledge of an agent is represented by an epistemic logical system E; we call such an agent not logically omniscient if for any valid knowledge assertion A of type F is known, a proof of F in E can be found in polynomial time in the size of A. We show that agents represented by major modal logics of knowledge and belief are logically omniscient, whereas agents represented by justification logic systems are not logically omniscient with respect to t is a justification for F.
{"title":"Logical omniscience as a computational complexity problem","authors":"Sergei N. Artëmov, R. Kuznets","doi":"10.1145/1562814.1562821","DOIUrl":"https://doi.org/10.1145/1562814.1562821","url":null,"abstract":"The logical omniscience feature assumes that an epistemic agent knows all logical consequences of her assumptions. This paper offers a general theoretical framework that views logical omniscience as a computational complexity problem. We suggest the following approach: we assume that the knowledge of an agent is represented by an epistemic logical system E; we call such an agent not logically omniscient if for any valid knowledge assertion A of type F is known, a proof of F in E can be found in polynomial time in the size of A. We show that agents represented by major modal logics of knowledge and belief are logically omniscient, whereas agents represented by justification logic systems are not logically omniscient with respect to t is a justification for F.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114072195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Motivated by classical decision-theoretic paradoxes (Allais 1953, Ellsberg 1961), we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the paradoxes, while retaining significant simplicity and tractability. In particular, every finite game within this larger class of preferences still has an equilibrium.
{"title":"Projective expected utility: a subjective formulation","authors":"Pierfrancesco La Mura","doi":"10.1145/1562814.1562840","DOIUrl":"https://doi.org/10.1145/1562814.1562840","url":null,"abstract":"Motivated by classical decision-theoretic paradoxes (Allais 1953, Ellsberg 1961), we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the paradoxes, while retaining significant simplicity and tractability. In particular, every finite game within this larger class of preferences still has an equilibrium.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115029243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A function is subsidized non-cooperative computable [SNCC] if honest agents can compute it by reporting truthfully their private inputs, while unilateral deviations by the players are not beneficial: if a deviation from truth revelation can mislead other agents, this deviation will decrease the deviator's chances of correct computation, or, it will not affect these chances but the expected payment to the deviator will decrease; in addition, deviations can not increase the expected monetary payments to a deviator without decreasing his chances of correct computation. This paper extends the study of SNCC functions to the context of group deviations. A function is K-SNCC if deviations by a group of at most K agents are not beneficial. We provide a full characterization of the K-SNCC functions, both for the independent values and the correlated values settings.
{"title":"K-SNCC: group deviations in subsidized non-cooperative computing","authors":"Andrey Klinger, Moshe Tennenholtz","doi":"10.1145/1562814.1562839","DOIUrl":"https://doi.org/10.1145/1562814.1562839","url":null,"abstract":"A function is subsidized non-cooperative computable [SNCC] if honest agents can compute it by reporting truthfully their private inputs, while unilateral deviations by the players are not beneficial: if a deviation from truth revelation can mislead other agents, this deviation will decrease the deviator's chances of correct computation, or, it will not affect these chances but the expected payment to the deviator will decrease; in addition, deviations can not increase the expected monetary payments to a deviator without decreasing his chances of correct computation. This paper extends the study of SNCC functions to the context of group deviations. A function is K-SNCC if deviations by a group of at most K agents are not beneficial. We provide a full characterization of the K-SNCC functions, both for the independent values and the correlated values settings.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121261495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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