Rationally Inattentive Behavior: Characterizing and Generalizing
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
An Analog of the Minimax Theorem for Vector Payoffs
Pacific Journal of Mathematics AN ANALOG OF THE MINIMAX THEOREM FOR VECTOR PAYOFFS DAVID BLACKWELL Vol. 6, No. 1 November 1956 AN ANALOG OF THE MINIMAX THEOREM FOR VECTOR PAYOFFS DAVID BLACKWELL 1. Introduction* The von Neumann minimax theorem [2] for finite games asserts that for every rxs matrix M=\\m(i, j)\\ with real elements there exist a number v and vectors P=(Pi, •••, Pr)f Q={QU •••> Qs)f Pi, Qj>β, such that i> 3) for all i, j. Thus in the (two-person, zero-sum) game with matrix Λf, player I has a strategy insuring an expected gain of at least v, and player II has a strategy insuring an expected loss of at most v. An alternative statement, which follows from the von Neumann theorem and an appropriate law of large numbers is that, for any ε>0, I can, in a long series of plays of the game with matrix M, guarantee, with probability approaching 1 as the number of plays becomes infinite, that his average actual gain per play exceeds v — ε and that II can similarly restrict his average actual loss to v-he. These facts are assertions about the extent to which each player can control the center of gravity of the actual payoffs in a long series of plays. In this paper we investigate the extent to which this center of gravity can be controlled by the players for the case of matrices M whose elements m(i9 j) are points of ΛΓ-space. Roughly, we seek to answer the following question. -
Blackwell, David; Diaconis, Persi a Non-Measurable Tail Set
Blackwell, David; Diaconis, Persi A non-measurable tail set. Statistics, probability and game theory, 1--5, IMS Lecture Notes Monogr. Ser., 30, Inst. Math. Statist., Hayward, CA, 1996. Blackwell, David Operator solution of infinite $G\sb \delta$ games of imperfect information. Probability, statistics, and mathematics, 83--87, Academic Press, Boston, MA, 1989. 60040 Blackwell, David; Mauldin, R. Daniel Ulam's redistribution of energy problem: collision transformations. Lett. Math. Phys. 10 (1985), no. 2-3, 149--153. Blackwell, David; Dubins, Lester E. An extension of Skorohod's almost sure representation theorem. Proc. Amer. Math. Soc. 89 (1983), no. 4, 691--692. 60B10 Blackwell, David; Maitra, Ashok Factorization of probability measures and absolutely measurable sets. Proc. Amer. Math. Soc. 92 (1984), no. 2, 251--254. Blackwell, David; Girshick, M. A. Theory of games and statistical decisions. Reprint of the 1954 edition. Dover Publications, Inc., New York, 1979. xi+355 pp. ISBN: 0-486-63831-6 90D35 (62Cxx) Blackwell, David On stationary policies. With discussion. J. Roy. Statist. Soc. Ser. 133 (1970), no. 1, 33--37. 90C40 Blackwell, David The stochastic processes of Borel gambling and dynamic programming. Ann. Statist. 4 (1976), no. 2, 370--374. Blackwell, David; Dubins, Lester E. On existence and non-existence of proper, regular, conditional distributions. Ann. Probability 3 (1975), no. 5, 741--752. Blackwell, David; MacQueen, James B. Ferguson distributions via Pólya urn schemes. Ann. Statist. 1 (1973), 353--355. Blackwell, David; Freedman, David On the amount of variance needed to escape from a strip. Ann. Probability 1 (1973), 772--787. Blackwell, David Discreteness of Ferguson selections. -
THE RISE of LIFESTYLE ACTIVISM from New Left to Occupy
THE RISE OF LIFESTYLE ACTIVISM From New Left to Occupy NIKOS SOTIRAKOPOULOS The Rise of Lifestyle Activism Nikos Sotirakopoulos The Rise of Lifestyle Activism From New Left to Occupy Nikos Sotirakopoulos Loughborough University United Kingdom ISBN 978-1-137-55102-3 ISBN 978-1-137-55103-0 (eBook) DOI 10.1057/978-1-137-55103-0 Library of Congress Control Number: 2016947743 © Th e Editor(s) (if applicable) and Th e Author(s) 2016 Th e author(s) has/have asserted their right(s) to be identifi ed as the author(s) of this work in accordance with the Copyright, Designs and Patents Act 1988. Th is work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifi cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfi lms or in any other physical way, and trans- mission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Th e use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specifi c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Th e publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. -
Rational Inattention with Sequential Information Sampling∗
Rational Inattention with Sequential Information Sampling∗ Benjamin Hébert y Michael Woodford z Stanford University Columbia University July 1, 2016 Preliminary and Incomplete. WARNING: Some results in this draft are not corrected as stated. Please contact the authors before citing. Comments welcome. Abstract We generalize the rationalize inattention framework proposed by Sims [2010] to allow for cost functions other than Shannon’s mutual information. We study a prob- lem in which a large number of successive samples of information about the decision situation, each only minimally informative by itself, can be taken before a decision must be made. We assume that the cost required for each individual increment of in- formation satisfies standard assumptions about continuity, differentiability, convexity, and monotonicity with respect to the Blackwell ordering of experiments, but need not correspond to mutual information. We show that any information cost function sat- isfying these axioms exhibits an invariance property which allows us to approximate it by a particular form of Taylor expansion, which is accurate whenever the signals acquired by an agent are not very informative. We give particular attention to the case in which the cost function for an individual increment to information satisfies the ad- ditional condition of “prior invariance,” so that it depends only on the way in which the probabilities of different observations depend on the state of the world, and not on the prior probabilities of different states. This case leads to a cost function for the overall quantity of information gathered that is not prior-invariant, but “sequentially prior-invariant.” We offer a complete characterization of the family of sequentially prior-invariant cost functions in the continuous-time limit of our dynamic model of in- formation sampling, and show how the resulting theory of rationally inattentive choice differs from both static and dynamic versions of a theory based on mutual information. -
An Annotated Bibliography on the Foundations of Statistical Inference
• AN ANNOTATED BIBLIOGRAPHY ON THE FOUNDATIONS OF STATISTICAL INFERENCE • by Stephen L. George A cooperative effort between the Department of Experimental • Statistics and the Southeastern Forest Experiment Station Forest Service U.S.D.A. Institute of Statistics Mimeograph Series No. 572 March 1968 The Foundations of Statistical Inference--A Bibliography During the past two hundred years there have been many differences of opinion on the validity of certain statistical methods and no evidence that ,. there will be any general agreement in the near future. Also, despite attempts at classification of particular approaches, there appears to be a spectrum of ideas rather than the existence of any clear-cut "schools of thought. " The following bibliography is concerned with the continuing discussion in the statistical literature on what may be loosely termed ''the foundations of statistical inference." A major emphasis is placed on the more recent works in this area and in particular on recent developments in Bayesian analysis. Invariably, a discussion on the foundations of statistical inference leads one to the more general area of scientific inference and eventually to the much more general question of inductive inference. Since this bibliography is intended mainly for those statisticians interested in the philosophical foundations of their chosen field, and not for practicing philosophers, the more general discussion of inductive inference was deliberately de-emphasized with the exception of several distinctive works of particular relevance to the statistical problem. Throughout, the temptation to gather papers in the sense of a collector was resisted and most of the papers listed are of immediate relevance to the problem at hand. -
Diversion Tactics
Diversion Tactics U N D E R S T A N D I N G M A L A D A P T I V E B E H A V I O R S I N R E L A T I O N S H I P S Toxic people often engage in maladaptive behaviors in relationships that ultimately exploit, demean and hurt their intimate partners, family members and friends. They use a plethora of diversionary tactics that distort the reality of their victims and deflect responsibility. Abusive people may employ these tactics to an excessive extent in an effort to escape accountability for their actions. Here are 20 diversionary tactics toxic people use to silence and degrade you. 1 Diversion Tactics G A S L I G H T I N G Gaslighting is a manipulative tactic that can be described in different variations three words: “That didn’t happen,” “You imagined it,” and “Are you crazy?” Gaslighting is perhaps one of the most insidious manipulative tactics out there because it works to distort and erode your sense of reality; it eats away at your ability to trust yourself and inevitably disables you from feeling justified in calling out abuse and mistreatment. When someone gaslights you, you may be prone to gaslighting yourself as a way to reconcile the cognitive dissonance that might arise. Two conflicting beliefs battle it out: is this person right or can I trust what I experienced? A manipulative person will convince you that the former is an inevitable truth while the latter is a sign of dysfunction on your end. -
The Sound of Silence By Maury Brown
The Sound of Silence by Maury Brown Number of players: Minimum: 2, Maximum: 12 2 players: storyteller and silencer are opposite each other. 3 players: storyteller is the point of a triangle and silencers are at 10 and 2 o’clock facing each other. 4-6 players (optimal): storyteller at center, silencers circle around them; storyteller turns to face each as they speak. 7+ players: two storytellers, in groups of 2-6 configured as above. Background: This is a game about communication and trying to be heard. Players will play the roles of people trying to tell their stories, and of people responding in various ways that oppress or silence the storyteller, sometimes in well-meaning ways. It’s an exploration of privilege, agonistic rhetoric, and the Enlightenment separation of emotion from reason. It codifies emotional abuse into a set of mechanics that are used strategically against the storyteller. Many of you will play the roles of authority figures and abusers who use manipulative and domineering tactics to control conversations and silence dissent. They do so for the purpose of maintaining the status quo, a position they vigorously defend as best for society (if not themselves). The result is to keep those who are oppressed or marginalized in their place. This may feel very uncomfortable and difficult. We will debrief following the game to discuss how it felt to be both silenced and the silencer. Setup: the game is played in rounds, where the role of the storyteller(s) switches until each player has been both a storyteller and a silencer. -
David Blackwell Instance for Activities That Could Run Sometime Between Now and the End of June 2012
Volume 39 • Issue 8 IMS1935–2010 Bulletin October 2010 IMS Short Courses Proposal New IMS President Peter Hall outlines a proposed IMS program of short courses and Contents short meetings: 1 IMS Short Courses The IMS is considering developing a program of short courses and short meetings, reflecting all of the research areas encompassed by our journals. The motivation is at 2–3 Members’ News: Marta Sanz- Solé; David Brillinger; PK Sen; Elizaveta least two-fold. Firstly, we are not very widely involved in specialist meetings, and from Levina; Jerry Friedman; Samuel Kou; this point of view our scientific leadership can probably be enhanced. Secondly, in the Emily Berg; Wayne Fuller; Xuming He; area of short courses, there is an opportunity for both the IMS and its members to earn Jun Liu; Yajun Mei, Nicoleta Serban, a little extra income, by sharing the profits earned by delivering those courses. Roshan Joseph Vengazihiyil, Ming Yuan The best way in which to operate our short courses and short meetings will prob- ably be learned over time, but a few principles can be predicted in advance. In particu- 4 IMS 2010 Gothenburg meeting report & photos lar, the short courses and meetings should be held in places not in direct competition with relevant, major existing conferences, for example the Joint Statistical Meetings. Of 6 Peking University’s Center course, there are many opportunities for avoiding clashes such as these. The concept of for Statistical Science “IMS Winter Workshops” in North America, perhaps held in early January in southern 7 Conference in memory of US, is only one suggestion. -
David Blackwell, 1919–2010: an Explorer In
RETROSPECTIVE David Blackwell, 1919–2010: An explorer in mathematics and statistics RETROSPECTIVE Peter J. Bickela,1 David Blackwell, a pioneering explorer who made foundational contributions to several branches of mathematics and statistics, passed away on July 8, 2010. He was born in Centralia, Illinois, on April 24, 1919, and, as his mathematical talents were recog- nized early, he entered the University of Illinois at Urbana–Champaign at age 16. Although racial dis- crimination affected his life and career in painful ways, his accomplishments were eventually rewarded with the honors they deserved, including election to the National Academy of Sciences in 1965 as the first Black member and the American Academy of Arts and Sciences in 1968. Nevertheless, his love of math- ematics, science, people, and his sunny personality prevailed. Blackwell left contributions that bear his name and other major ideas in five quite different areas of mathematics, statistics, and operations research. With limited opportunities available to him, Black- well initially thought of becoming an elementary school teacher. However, his professors at the Univer- sity of Illinois soon recognized his talent for mathe- matics and encouraged him to pursue graduate studies in the Illinois Mathematics program instead. During his graduate studies, Blackwell worked with Joseph Doob, one of the founding figures of modern David Blackwell. Image credit: The Blackwell family. probability theory, a National Academy of Sciences member, and National Medal of Science winner. In sequential analysis, game theory, and decision the- 1941, at age 22, he completed a doctoral thesis in the ory. They included: what is now known as the Rao- theory of Markov chains, a set of ideas to which he Blackwell theorem, a fundamental improvement frequently returned in his later work. -
SCHOOL BOARD BUSINESS MEETING Sept. 14, 2020 at 6:30 P.M
DRAFT SCHOOL BOARD BUSINESS MEETING Sept. 14, 2020 at 6:30 p.m. PUBLIC MEETING ROOM PRESENT: Ann C. Coker, Bermuda District; Ryan M. Harter, Matoaca District; Kathryn S. Haines, Midlothian District; Dorothy L. Heffron, Vice Chair, Clover Hill District; Debbie G. Bailey, Chair, Dale District; Mervin B. Daugherty, Ed.D., Superintendent; Dr. Thomas Taylor, Deputy Superintendent; Dr. Sharon Pope, Chief Academic Officer; Dr. Lisa High, Chief of Schools; Bob Meister, Chief Financial Officer; Josh Davis, Chief Operations Officer; Wendell Roberts, School Board Attorney; Stephanie Frick, Assistant School Board Attorney; Tim Bullis, Executive Director of Communications and Community Engagement; Dr. Kimberly Hough, Executive Director of Human Resources and Talent Management; Dr. Joseph Tylus, Executive Director of Constituent Services; Brian Jones, Executive Director of Technology; Shawn Smith, Director of Government, Policy, and Media Relations; Dr. Morgan Debusk-Lane, Coordinator of Research and Evaluation; Nick Oyler, Coordinator of Student Health Services; and, Robert McDaniel, School Board Clerk. A. MEETING OPENING Mrs. Bailey called the meeting to order at 6:34 p.m. Mr. Harter provided the invocation. Mrs. Haines led the pledge of allegiance. B. CONSENT AGENDA ● Agenda Adoption ● Approval of the Minutes ○ Aug. 11, 2020 Board Retreat ○ Aug. 11, 2020 Business Meeting ○ Aug. 25, 2020 Work Session ● Memo #101-20: Revisions to School Board Governance Handbook ● Memo #102-20: FY2021 - Acceptance of New Grants ● Memo #103-20: FY2021 Grant - Claude Moore Scholars ● Memo #104-20: Recommended Personnel Actions ● Memo #105-20: Appointment of Members to Advisory Committees ● Memo #106-20: Approval of Revisions to the Audit and Finance Committee Bylaws ● Memo #107-20: Approval of Revisions to the Citizens Budget Advisory Committee Bylaws ● Memo #108-20: Approval of Additional Budget Appropriation for Human Resources in FY2021 Mr. -
The First One Hundred Years
The Maryland‐District of Columbia‐Virginia Section of the Mathematical Association of America: The First One Hundred Years Caren Diefenderfer Betty Mayfield Jon Scott November 2016 v. 1.3 The Beginnings Jon Scott, Montgomery College The Maryland‐District of Columbia‐Virginia Section of the Mathematical Association of America (MAA) was established, just one year after the MAA itself, on December 29, 1916 at the Second Annual Meeting of the Association held at Columbia University in New York City. In the minutes of the Council Meeting, we find the following: A section of the Association was established for Maryland and the District of Columbia, with the possible inclusion of Virginia. Professor Abraham Cohen, of Johns Hopkins University, is the secretary. We also find, in “Notes on the Annual Meeting of the Association” published in the February, 1917 Monthly, The Maryland Section has just been organized and was admitted by the council at the New York meeting. Hearty cooperation and much enthusiasm were reported in connection with this section. The phrase “with the possible inclusion of Virginia” is curious, as members from all three jurisdictions were present at the New York meeting: seven from Maryland, one from DC, and three from Virginia. However, the report, “Organization of the Maryland‐Virginia‐District of Columbia Section of the Association” (note the order!) begins As a result of preliminary correspondence, a group of Maryland mathematicians held a meeting in New York at the time of the December meeting of the Association and presented a petition to the Council for authority to organize a section of the Association in Maryland, Virginia, and the District of Columbia. -
Avoiding Unconscious Bias
Avoiding unconscious bias Avoiding unconscious bias A guide for surgeons 2 Avoiding unconscious bias 3 The Royal College of Surgeons of England Contents Introduction 2 Equality and diversity 2 Bias 3 Addressing individual bias 3 Addressing bias in organisations 3 Advice for those recruiting to committees or posts, to improve diversity 4 Advice for those organising, chairing or administrating meetings 4 Bullying 5 Who is most at risk of being accused of bullying? 5 Advice on avoiding bullying behaviour 5 What can be changed to reduce bullying? 6 What to do if you are accused of bullying or if a unit needs more help 6 Behaviour 7 What is acceptable behaviour? 7 Unacceptable behaviours 8 Behaviour in surgical environments 9 Advice for mentors, line managers, supervisors, appraisers 9 Definitions 11 Inequalities at work 12 Literature on diversity 12 References 13 Appendix 1 15 Avoiding unconscious bias Introduction The College aims to support all surgeons throughout their careers in achieving the highest standards of surgery and in all their professional interactions. Surgeons continuously aim to improve our clinical practice and professional behaviours. Organisations that are more diverse are better able to withstand change and we will support our members and fellows in embracing diversity. All surgeons are role models for students and trainees and are ambassadors for the profession. Their behaviour must therefore be welcoming, supportive and inclusive. Everyone has biases – some of which we are aware of, others we are not. Doctors, probably more than most, are conditioned to make assumptions or spot diagnoses and are uniquely exposed to a full spectrum of individuals at their most vulnerable.