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PDL As a Multi-Agent Strategy Logic
PDL as a Multi-Agent Strategy Logic ∗ Extended Abstract Jan van Eijck CWI and ILLC Science Park 123 1098 XG Amsterdam, The Netherlands [email protected] ABSTRACT The logic we propose follows a suggestion made in Van Propositional Dynamic Logic or PDL was invented as a logic Benthem [4] (in [11]) to apply the general perspective of ac- for reasoning about regular programming constructs. We tion logic to reasoning about strategies in games, and links propose a new perspective on PDL as a multi-agent strategic up to propositional dynamic logic (PDL), viewed as a gen- logic (MASL). This logic for strategic reasoning has group eral logic of action [29, 19]. Van Benthem takes individual strategies as first class citizens, and brings game logic closer strategies as basic actions and proposes to view group strate- to standard modal logic. We demonstrate that MASL can gies as intersections of individual strategies (compare also express key notions of game theory, social choice theory and [1] for this perspective). We will turn this around: we take voting theory in a natural way, we give a sound and complete the full group strategies (or: full strategy profiles) as basic, proof system for MASL, and we show that MASL encodes and construct individual strategies from these by means of coalition logic. Next, we extend the language to epistemic strategy union. multi-agent strategic logic (EMASL), we give examples of A fragment of the logic we analyze in this paper was pro- what it can express, we propose to use it for posing new posed in [10] as a logic for strategic reasoning in voting (the questions in epistemic social choice theory, and we give a cal- system in [10] does not have current strategies). -
The University of Texas at Brownsville and Texas Southmost College Fall 2005
The University of Texas at Brownsville and Texas Southmost College Fall 2005 Course Pro-Seminar on Sociological Theory (SOCI 6333) Time Tuesday, 7:15-10:00 p.m. Place North 228 Instructor David E. Pearson, Ph.D. Office South 295 Phone 882-7265 Email [email protected] Office Hours Monday-Thursday 12:05-1:30 (and by appointment) Description: During the Fall 2005 semester, SOCI 6333 examines the assumptions of neo-Darwinian theory and its relevance for sociology. The major neo-Darwinian concepts examined are three: sexual selection, kin selection, and reciprocal altruism. Format: Classes will include both lectures and discussions in which students assume primary responsibility for analyzing the week’s readings. Given this format, it is required that all readings be completed prior to the class session. Attendance: Regular class attendance is expected. More than one unexcused absence will result in a lowering of your final grade. Make-Up Policy: You are responsible for all readings and class materials missed due to absences. A grade of zero will be given when you are not present to take an examination, give a presentation, or when written work is handed in late. Make-ups and extensions will be given only in documented instances of emergency or extreme illness. Scholastic Dishonesty: Students who engage in scholastic dishonesty are subject to disciplinary penalties, including the possibility of failure in the course and expulsion. Scholastic dishonesty includes but is not limited to cheating, plagiarism, or any act designed to give unfair advantage to a student or the attempt to commit such acts. -
Norms, Repeated Games, and the Role of Law
Norms, Repeated Games, and the Role of Law Paul G. Mahoneyt & Chris William Sanchiricot TABLE OF CONTENTS Introduction ............................................................................................ 1283 I. Repeated Games, Norms, and the Third-Party Enforcement P rob lem ........................................................................................... 12 88 II. B eyond T it-for-Tat .......................................................................... 1291 A. Tit-for-Tat for More Than Two ................................................ 1291 B. The Trouble with Tit-for-Tat, However Defined ...................... 1292 1. Tw o-Player Tit-for-Tat ....................................................... 1293 2. M any-Player Tit-for-Tat ..................................................... 1294 III. An Improved Model of Third-Party Enforcement: "D ef-for-D ev". ................................................................................ 1295 A . D ef-for-D ev's Sim plicity .......................................................... 1297 B. Def-for-Dev's Credible Enforceability ..................................... 1297 C. Other Attractive Properties of Def-for-Dev .............................. 1298 IV. The Self-Contradictory Nature of Self-Enforcement ....................... 1299 A. The Counterfactual Problem ..................................................... 1300 B. Implications for the Self-Enforceability of Norms ................... 1301 C. Game-Theoretic Workarounds ................................................ -
Moral Implications of Darwinian Evolution for Human Reference
Andrews University Digital Commons @ Andrews University Dissertations Graduate Research 2006 Moral Implications of Darwinian Evolution for Human Reference Based in Christian Ethics: a Critical Analysis and Response to the "Moral Individualism" of James Rachels Stephen Bauer Andrews University Follow this and additional works at: https://digitalcommons.andrews.edu/dissertations Part of the Christianity Commons, Ethics in Religion Commons, Evolution Commons, and the Religious Thought, Theology and Philosophy of Religion Commons Recommended Citation Bauer, Stephen, "Moral Implications of Darwinian Evolution for Human Reference Based in Christian Ethics: a Critical Analysis and Response to the "Moral Individualism" of James Rachels" (2006). Dissertations. 16. https://digitalcommons.andrews.edu/dissertations/16 This Dissertation is brought to you for free and open access by the Graduate Research at Digital Commons @ Andrews University. It has been accepted for inclusion in Dissertations by an authorized administrator of Digital Commons @ Andrews University. For more information, please contact [email protected]. Thank you for your interest in the Andrews University Digital Library of Dissertations and Theses. Please honor the copyright of this document by not duplicating or distributing additional copies in any form without the author’s express written permission. Thanks for your cooperation. Andrews University Seventh-day Adventist Theological Seminary MORAL IMPLICATIONS OF DARWINIAN EVOLUTION FOR HUMAN PREFERENCE BASED IN CHRISTIAN ETHICS: A CRITICAL ANALYSIS AND RESPONSE TO THE “MORAL INDIVIDUALISM” OF JAMES RACHELS A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy by Stephen Bauer November 2006 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3248152 Copyright 2006 by Bauer, Stephen All rights reserved. -
Lecture Notes
Chapter 12 Repeated Games In real life, most games are played within a larger context, and actions in a given situation affect not only the present situation but also the future situations that may arise. When a player acts in a given situation, he takes into account not only the implications of his actions for the current situation but also their implications for the future. If the players arepatient andthe current actionshavesignificant implications for the future, then the considerations about the future may take over. This may lead to a rich set of behavior that may seem to be irrational when one considers the current situation alone. Such ideas are captured in the repeated games, in which a "stage game" is played repeatedly. The stage game is repeated regardless of what has been played in the previous games. This chapter explores the basic ideas in the theory of repeated games and applies them in a variety of economic problems. As it turns out, it is important whether the game is repeated finitely or infinitely many times. 12.1 Finitely-repeated games Let = 0 1 be the set of all possible dates. Consider a game in which at each { } players play a "stage game" , knowing what each player has played in the past. ∈ Assume that the payoff of each player in this larger game is the sum of the payoffsthat he obtains in the stage games. Denote the larger game by . Note that a player simply cares about the sum of his payoffs at the stage games. Most importantly, at the beginning of each repetition each player recalls what each player has 199 200 CHAPTER 12. -
Prisoner's Dilemma: Pavlov Versus Generous Tit-For-Tat
Proc. Natl. Acad. Sci. USA Vol. 93, pp. 2686-2689, April 1996 Evolution Human cooperation in the simultaneous and the alternating Prisoner's Dilemma: Pavlov versus Generous Tit-for-Tat CLAUS WEDEKIND AND MANFRED MILINSKI Abteilung Verhaltensokologie, Zoologisches Institut, Universitat Bern, CH-3032 Hinterkappelen, Switzerland Communicated by Robert M. May, University of Oxford, Oxford, United Kingdom, November 9, 1995 (received for review August 7, 1995) ABSTRACT The iterated Prisoner's Dilemma has become Opponent the paradigm for the evolution of cooperation among egoists. Since Axelrod's classic computer tournaments and Nowak and C D Sigmund's extensive simulations of evolution, we know that natural selection can favor cooperative strategies in the C 3 0 Prisoner's Dilemma. According to recent developments of Player theory the last champion strategy of "win-stay, lose-shift" D 4 1 ("Pavlov") is the winner only ifthe players act simultaneously. In the more natural situation of the roles players alternating FIG. 1. Payoff matrix of the game showing the payoffs to the player. of donor and recipient a strategy of "Generous Tit-for-Tat" Each player can either cooperate (C) or defect (D). In the simulta- wins computer simulations of short-term memory strategies. neous game this payoff matrix could be used directly; in the alternating We show here by experiments with humans that cooperation game it had to be translated: if a player plays C, she gets 4 and the dominated in both the simultaneous and the alternating opponent 3 points. If she plays D, she gets 5 points and the opponent Prisoner's Dilemma. -
Sex, Survival, & Evolutionary Social Psychology
Sex, Survival, & Evolutionary Social Psychology Winter 2017 Tues/Thurs 10:00 – 11:30am 1360 East Hall Professor GSI Dr. Joshua Ackerman Iris Wang 3227 East Hall 3232 East Hall [email protected] [email protected] Professor Office Hours GSI Office Hours By appointment Thursdays 11:30-1:30 Course description Evolutionary Social Psychology represents a big-picture approach to understanding human behavior that has gained increasing attention—and notoriety—in recent years. An evolutionary approach posits that our brains and bodies act as specialized tools to address problems that affected our ancestors’ abilities to survive and reproduce, and continue to affect us today (though in the modern world, these tools sometimes create challenges in addition to solving them). From this perspective, principles of natural selection and sexual selection are applied to (1) “problems” such as aggression, friendship, attraction, and parenting as well as to (2) functional “solutions” to these problems, such as memory, reasoning, emotion, and self-control. In this class, we will re- examine traditional topics in social psychology through the lens of evolutionary theory in order to take a fresh look at the adaptive nature of who we are. We will also consider more unique topics that are particularly relevant to this scientific intersection of biology, economics and psychology, including animal behavior, disease, genes, and many of the common misunderstandings and critiques about evolutionary approaches. In doing so, we will continually ask “why” people think -
The Happiness Hypothesis
The Happiness Hypothesis Ch.4 - 1 This file contains a version of chapter 4 from the book The Happiness Hypothesis: Finding modern truth in ancient wisdom,1 by Jonathan Haidt. This version has been edited slightly to be used as a stand-alone reading as part of the OpenMind Library. If you want to skim the chapter, you can just read the highlighted sections Chapter 1 of the book develops the metaphor that the mind is divided like a small rider (conscious reasoning, or “System 2”) on the back of a large elephant (all the automatic intuitive processes that occur rapidly and often outside of conscious awareness, also known as “System 1”). The rider-and-elephant metaphor is helpful for understanding why it’s almost impossible to win a political argument: each person’s “rider” composes arguments aimed at the other person’s rider, but the elephant is really in charge. Unless you can change the elephant, you can’t persuade the other person. Chapter 4: The Faults of Others Why do you see the speck in your neighbor’s eye, but do not notice the log in your own eye? ....You hypocrite, first take the log out of your own eye, and then you will see clearly to take the speck out of your neighbor’s eye. (Matthew 7:3-5) It is easy to see the faults of others, but difficult to see one’s own faults. One shows the faults of others like chaff winnowed in the wind, but one conceals one’s own faults as a cunning gambler conceals his dice. -
Introduction to Game Theory: a Discovery Approach
Linfield University DigitalCommons@Linfield Linfield Authors Book Gallery Faculty Scholarship & Creative Works 2020 Introduction to Game Theory: A Discovery Approach Jennifer Firkins Nordstrom Linfield College Follow this and additional works at: https://digitalcommons.linfield.edu/linfauth Part of the Logic and Foundations Commons, Set Theory Commons, and the Statistics and Probability Commons Recommended Citation Nordstrom, Jennifer Firkins, "Introduction to Game Theory: A Discovery Approach" (2020). Linfield Authors Book Gallery. 83. https://digitalcommons.linfield.edu/linfauth/83 This Book is protected by copyright and/or related rights. It is brought to you for free via open access, courtesy of DigitalCommons@Linfield, with permission from the rights-holder(s). Your use of this Book must comply with the Terms of Use for material posted in DigitalCommons@Linfield, or with other stated terms (such as a Creative Commons license) indicated in the record and/or on the work itself. For more information, or if you have questions about permitted uses, please contact [email protected]. Introduction to Game Theory a Discovery Approach Jennifer Firkins Nordstrom Linfield College McMinnville, OR January 4, 2020 Version 4, January 2020 ©2020 Jennifer Firkins Nordstrom This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Preface Many colleges and universities are offering courses in quantitative reasoning for all students. One model for a quantitative reasoning course is to provide students with a single cohesive topic. Ideally, such a topic can pique the curios- ity of students with wide ranging academic interests and limited mathematical background. This text is intended for use in such a course. -
The Moral Animal
The Moral Animal By JONATHAN SACKS Published: December 23, 2012 NY Times IT is the religious time of the year. Step into any city in America or Britain and you will see the night sky lit by religious symbols, Christmas decorations certainly and probably also a giant menorah. Religion in the West seems alive and well. But is it really? Or have these symbols been emptied of content, no more than a glittering backdrop to the West’s newest faith, consumerism, and its secular cathedrals, shopping malls? At first glance, religion is in decline. In Britain, the results of the 2011 national census have just been published. They show that a quarter of the population claims to have no religion, almost double the figure 10 years ago. And though the United States remains the most religious country in the West, 20 percent declare themselves without religious affiliation — double the number a generation ago. Looked at another way, though, the figures tell a different story. Since the 18th century, many Western intellectuals have predicted religion’s imminent demise. Yet after a series of withering attacks, most recently by the new atheists, including Sam Harris, Richard Dawkins and the late Christopher Hitchens, still in Britain three in four people, and in America four in five, declare allegiance to a religious faith. That, in an age of science, is what is truly surprising. The irony is that many of the new atheists are followers of Charles Darwin. We are what we are, they say, because it has allowed us to survive and pass on our genes to the next generation. -
From Incan Gold to Dominion: Unraveling Optimal Strategies in Unsolved Games
From Incan Gold to Dominion: Unraveling Optimal Strategies in Unsolved Games A Senior Comprehensive Paper presented to the Faculty of Carleton College Department of Mathematics Tommy Occhipinti, Advisor by Grace Jaffe Tyler Mahony Lucinda Robinson March 5, 2014 Acknowledgments We would like to thank our advisor, Tommy Occhipinti, for constant technical help, brainstorming, and moral support. We would also like to thank Tristan Occhipinti for providing the software that allowed us to run our simulations, Miles Ott for helping us with statistics, Mike Tie for continual technical support, Andrew Gainer-Dewar for providing the LaTeX templates, and Harold Jaffe for proofreading. Finally, we would like to express our gratitude to the entire math department for everything they have done for us over the past four years. iii Abstract While some games have inherent optimal strategies, strategies that will win no matter how the opponent plays, perhaps more interesting are those that do not possess an objective best strategy. In this paper, we examine three such games: the iterated prisoner’s dilemma, Incan Gold, and Dominion. Through computer simulations, we attempted to develop strategies for each game that could win most of the time, though not necessarily all of the time. We strived to create strategies that had a large breadth of success; that is, facing most common strategies of each game, ours would emerge on top. We begin with an analysis of the iterated prisoner’s dilemma, running an Axelrod-style tournament to determine the balance of characteristics of winning strategies. Next, we turn our attention to Incan Gold, where we examine the ramifications of different styles of decision making, hoping to enhance an already powerful strategy. -
Bittorrent Is an Auction: Analyzing and Improving Bittorrent’S Incentives
BitTorrent is an Auction: Analyzing and Improving BitTorrent’s Incentives Dave Levin Katrina LaCurts Neil Spring Bobby Bhattacharjee University of Maryland University of Maryland University of Maryland University of Maryland [email protected] [email protected] [email protected] [email protected] ABSTRACT 1. INTRODUCTION Incentives play a crucial role in BitTorrent, motivating users to up- BitTorrent [2] is a remarkably successful decentralized system load to others to achieve fast download times for all peers. Though that allows many users to download a file from an otherwise under- long believed to be robust to strategic manipulation, recent work provisioned server. To ensure quick download times and scalabil- has empirically shown that BitTorrent does not provide its users ity, BitTorrent relies upon those downloading a file to cooperatively incentive to follow the protocol. We propose an auction-based trade portions, or pieces, of the file with one another [5]. Incentives model to study and improve upon BitTorrent’s incentives. The play an inherently crucial role in such a system; users generally insight behind our model is that BitTorrent uses, not tit-for-tat as wish to download their files as quickly as possible, and since Bit- widely believed, but an auction to decide which peers to serve. Our Torrent is decentralized, there is no global “BitTorrent police” to model not only captures known, performance-improving strategies, govern their actions. Users are therefore free to attempt to strate- it shapes our thinking toward new, effective strategies. For exam- gically manipulate others into helping them download faster. The ple, our analysis demonstrates, counter-intuitively, that BitTorrent role of incentives in BitTorrent is to motivate users to contribute peers have incentive to intelligently under-report what pieces of their resources to others so as to achieve desirable global system the file they have to their neighbors.