As examples such as the Monty Hall puzzle show, applying conditioning to update a probability dis... more As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a ``naive space'', which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR (``coarsening at random'') in the statistical literature characterizes when ``naive'' conditioning in a naive space works. We show that the CAR condition holds rather infrequently, and we provide a procedural characterization of it, by giving a randomized algorithm that generates all and only distributions for which CAR holds. This substantially extends previous characterizations of CAR. We also consider more generalized notions of update such as Jeffrey conditioning and minimizing relative entropy (MRE). We give a generalization of the CAR condition that characterizes when Jeffrey conditioning leads to appropriate answers, and show that there exist some very simple settings in which MRE essen...
As a highly consequential biological trait, a memory “bottleneck” cannot escape selection pressur... more As a highly consequential biological trait, a memory “bottleneck” cannot escape selection pressures. It must therefore co-evolve with other cognitive mechanisms rather than act as an independent constraint. Recent theory and an implemented model of language acquisition suggest that a limit on working memory may evolve to help learning. Furthermore, it need not hamper the use of language for communication.
How do people assign responsibility for the outcome of an election? In previous work, we have sho... more How do people assign responsibility for the outcome of an election? In previous work, we have shown that responsibility judgments in achievement contexts are affected by the probability that a person’s contribution is necessary, and by how close it was to being pivotal (Lagnado, Gerstenberg, & Zultan, 2013). Here we focus on responsibility judgments in voting scenarios. We varied the number of people in different voting committees, their political affiliations, the number of votes required for a policy to pass, which party supports the policy, and the pattern of votes (creating 170 different situations). As expected, we found that participants’ responsibility judgments increased the closer the voter was to being pivotal. Further, judgments increased the more unexpected a vote was. Voters were assigned more responsibility when they voted against the majority in the committee, and when they voted against their party affiliation.
We consider how an agent should update her beliefs when her beliefs are represented by a set P of... more We consider how an agent should update her beliefs when her beliefs are represented by a set P of probability distributions, given that the agent makes decisions using the minimax criterion, perhaps the best-studied and most commonly-used criterion in the literature. We adopt a game-theoretic framework, where the agent plays against a bookie, who chooses some distribution from P. We consider two reasonable games that differ in what the bookie knows when he makes his choice. Anomalies that have been observed before, like time inconsistency, can be understood as arising because different games are being played, against bookies with different information. We characterize the important special cases in which the optimal decision rules according to the minimax criterion amount to either conditioning or simply ignoring the information. Finally, we consider the relationship between updating and calibration when uncertainty is described by sets of probabilities. Our results emphasize the ke...
How are hierarchically structured sequences of objects, events or actions learned from experience... more How are hierarchically structured sequences of objects, events or actions learned from experience and represented in the brain? When several streams of regularities present themselves, which will be learned and which ignored? Can statistical regularities take effect on their own, or are additional factors such as behavioral outcomes expected to influence statistical learning? Answers to these questions are starting to emerge through a convergence of findings from naturalistic observations, behavioral experiments, neurobiological studies, and computational analyses and simulations. We propose that a small set of principles are at work in every situation that involves learning of structure from patterns of experience and outline a general framework that accounts for such learning.
TARK 2003 is the 9th conference on theoretical aspects of rationality and knowledge. In its early... more TARK 2003 is the 9th conference on theoretical aspects of rationality and knowledge. In its early days TARK explored formal models of knowledge and belief as they arise in disciplines such as computer science, economics, philosophy, and psychology. The recent years however have been very fruitful in establishing further connections between these disciplines. This includes work on resource-bounded reasoning, the design and analysis of protocols and algorithms for non-cooperative environments, computational approaches to game-theoretic problems, nonprobabilistic representations of uncertainty, and causality, among many other areas.The program of TARK 2003 shows the breadth and depth of these connections. In these proceedings the reader will find papers that deal with rationality and knowledge, bridging and combining perspectives taken from computer science, economics, philosophy, linguistics, psychology, and biology. The reader will also find novel approaches to dealing with basic problems in the design and analysis of social and computational mechanisms.In order to develop such a diverse program, the papers were selected after very Careful evaluation by a multi-disciplinaxy program committee consisting of Geir Asheim (Economics, Oslo), Maya Bar Hillel (Psydhology, Hebrew University), Cristina Bicchieri (Decision Sciences and Philosophy, CMU), Craig Boutilier (AI, Toronto), Yossi Feinberg (Economics, Stanford), Daniel Lehmann (Computer Science, ttebrew University), Stephen Morris (Economics, Yale), Motty Perry (Economics, Hebrew Universiity), Avi Pfeffer (AI, Harvard), Ilya Segal (Economics, Stanford), Jeremy Seligman (Philosophy, Auckland ), Brian Skyrms (Philosophy and Economics, Irvine), Moshe Tennenholtz (PC Chair, AI, Technion), Moshe Vardi (Computer Science, Rice), and Frank Veltman (Philosophy, Amsterdam).Important ingredients in the TARK conferences have been the opportunity for informal interactions, and the invited talks and tutorials. In TARK 2003 we are fortunate to have four outstanding invited speakers-- Steven Brams (NYU), Michael Kearns, (University of Pennsylvania), Dov Monderer (Technion), and Wolfgang Spohn (University of Konstanz). This year TARK is being coordinated with NASSLLI (the North American Summer School in Logic, Language and Information), and shares with NASSLLI two tutorials: Algorithmic verification for epistemic logic, by Ron von der Meyden, and Games in informational form, by Dov Monderer.
As examples such as the Monty Hall puzzle show, applying conditioning to update a probability dis... more As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a ``naive space'', which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR (``coarsening at random'') in the statistical literature characterizes when ``naive'' conditioning in a naive space works. We show that the CAR condition holds rather infrequently, and we provide a procedural characterization of it, by giving a randomized algorithm that generates all and only distributions for which CAR holds. This substantially extends previous characterizations of CAR. We also consider more generalized notions of update such as Jeffrey conditioning and minimizing relative entropy (MRE). We give a generalization of the CAR condition that characterizes when Jeffrey conditioning leads to appropriate answers, and show that there exist some very simple settings in which MRE essen...
As a highly consequential biological trait, a memory “bottleneck” cannot escape selection pressur... more As a highly consequential biological trait, a memory “bottleneck” cannot escape selection pressures. It must therefore co-evolve with other cognitive mechanisms rather than act as an independent constraint. Recent theory and an implemented model of language acquisition suggest that a limit on working memory may evolve to help learning. Furthermore, it need not hamper the use of language for communication.
How do people assign responsibility for the outcome of an election? In previous work, we have sho... more How do people assign responsibility for the outcome of an election? In previous work, we have shown that responsibility judgments in achievement contexts are affected by the probability that a person’s contribution is necessary, and by how close it was to being pivotal (Lagnado, Gerstenberg, & Zultan, 2013). Here we focus on responsibility judgments in voting scenarios. We varied the number of people in different voting committees, their political affiliations, the number of votes required for a policy to pass, which party supports the policy, and the pattern of votes (creating 170 different situations). As expected, we found that participants’ responsibility judgments increased the closer the voter was to being pivotal. Further, judgments increased the more unexpected a vote was. Voters were assigned more responsibility when they voted against the majority in the committee, and when they voted against their party affiliation.
We consider how an agent should update her beliefs when her beliefs are represented by a set P of... more We consider how an agent should update her beliefs when her beliefs are represented by a set P of probability distributions, given that the agent makes decisions using the minimax criterion, perhaps the best-studied and most commonly-used criterion in the literature. We adopt a game-theoretic framework, where the agent plays against a bookie, who chooses some distribution from P. We consider two reasonable games that differ in what the bookie knows when he makes his choice. Anomalies that have been observed before, like time inconsistency, can be understood as arising because different games are being played, against bookies with different information. We characterize the important special cases in which the optimal decision rules according to the minimax criterion amount to either conditioning or simply ignoring the information. Finally, we consider the relationship between updating and calibration when uncertainty is described by sets of probabilities. Our results emphasize the ke...
How are hierarchically structured sequences of objects, events or actions learned from experience... more How are hierarchically structured sequences of objects, events or actions learned from experience and represented in the brain? When several streams of regularities present themselves, which will be learned and which ignored? Can statistical regularities take effect on their own, or are additional factors such as behavioral outcomes expected to influence statistical learning? Answers to these questions are starting to emerge through a convergence of findings from naturalistic observations, behavioral experiments, neurobiological studies, and computational analyses and simulations. We propose that a small set of principles are at work in every situation that involves learning of structure from patterns of experience and outline a general framework that accounts for such learning.
TARK 2003 is the 9th conference on theoretical aspects of rationality and knowledge. In its early... more TARK 2003 is the 9th conference on theoretical aspects of rationality and knowledge. In its early days TARK explored formal models of knowledge and belief as they arise in disciplines such as computer science, economics, philosophy, and psychology. The recent years however have been very fruitful in establishing further connections between these disciplines. This includes work on resource-bounded reasoning, the design and analysis of protocols and algorithms for non-cooperative environments, computational approaches to game-theoretic problems, nonprobabilistic representations of uncertainty, and causality, among many other areas.The program of TARK 2003 shows the breadth and depth of these connections. In these proceedings the reader will find papers that deal with rationality and knowledge, bridging and combining perspectives taken from computer science, economics, philosophy, linguistics, psychology, and biology. The reader will also find novel approaches to dealing with basic problems in the design and analysis of social and computational mechanisms.In order to develop such a diverse program, the papers were selected after very Careful evaluation by a multi-disciplinaxy program committee consisting of Geir Asheim (Economics, Oslo), Maya Bar Hillel (Psydhology, Hebrew University), Cristina Bicchieri (Decision Sciences and Philosophy, CMU), Craig Boutilier (AI, Toronto), Yossi Feinberg (Economics, Stanford), Daniel Lehmann (Computer Science, ttebrew University), Stephen Morris (Economics, Yale), Motty Perry (Economics, Hebrew Universiity), Avi Pfeffer (AI, Harvard), Ilya Segal (Economics, Stanford), Jeremy Seligman (Philosophy, Auckland ), Brian Skyrms (Philosophy and Economics, Irvine), Moshe Tennenholtz (PC Chair, AI, Technion), Moshe Vardi (Computer Science, Rice), and Frank Veltman (Philosophy, Amsterdam).Important ingredients in the TARK conferences have been the opportunity for informal interactions, and the invited talks and tutorials. In TARK 2003 we are fortunate to have four outstanding invited speakers-- Steven Brams (NYU), Michael Kearns, (University of Pennsylvania), Dov Monderer (Technion), and Wolfgang Spohn (University of Konstanz). This year TARK is being coordinated with NASSLLI (the North American Summer School in Logic, Language and Information), and shares with NASSLLI two tutorials: Algorithmic verification for epistemic logic, by Ron von der Meyden, and Games in informational form, by Dov Monderer.
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