I'll Have What She's Having: Reflective Desires and Consequentialism
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The Allais Paradox: What It Became, What It Really Was, What It Now Suggests to Us
Economics and Philosophy (2019), 35, 423–459 doi:10.1017/S0266267118000469 ARTICLE The Allais paradox: what it became, what it really was, what it now suggests to us Philippe Mongin GREGHEC, 1 rue de la Libération, F-78350 Jouy-en-Josas, France Email: [email protected] (Received 11 June 2018; revised 24 August 2018; accepted 27 August 2018; first published online 30 January 2019) Abstract Whereas many others have scrutinized the Allais paradox from a theoretical angle, we study the paradox from an historical perspective and link our findings to a suggestion as to how decision theory could make use of it today. We emphasize that Allais proposed the paradox as anormativeargument, concerned with ‘the rational man’ and not the ‘real man’,touse his words. Moreover, and more subtly, we argue that Allais had an unusual sense of the normative, being concerned not so much with the rationality of choices as with the rationality of the agent as a person. These two claims are buttressed by a detailed investigation – the first of its kind – of the 1952 Paris conference on risk, which set the context for the invention of the paradox, and a detailed reconstruction – also the first of its kind – of Allais’s specific normative argument from his numerous but allusive writings. The paper contrasts these interpretations of what the paradox historically represented, with how it generally came to function within decision theory from the late 1970s onwards: that is, as an empirical refutation of the expected utility hypothesis, and more specifically of the condition of von Neumann–Morgenstern independence that underlies that hypothesis. -
Review of Paradoxes Afflicting Various Voting Procedures Where One out of M Candidates (M ≥ 2) Must Be Elected
Dan S. Felsenthal Review of paradoxes afflicting various voting procedures where one out of m candidates (m ≥ 2) must be elected Workshop Paper Original citation: Felsenthal, Dan S. (2010) Review of paradoxes afflicting various voting procedures where one out of m candidates (m ≥ 2) must be elected. In: Assessing Alternative Voting Procedures, London School of Economics and Political Science, London, UK. This version available at: http://eprints.lse.ac.uk/27685/ Available in LSE Research Online: April 2010 © 2010 Dan S. Felsenthal LSE has developed LSE Research Online so that users may access research output of the School. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL (http://eprints.lse.ac.uk) of the LSE Research Online website. Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected* Dan S. Felsenthal University of Haifa and Centre for Philosophy of Natural and Social Science London School of Economics and Political Science Revised 3 May 2010 Prepared for presentation in a symposium and a workshop on Assessing Alternative Voting Procedures Sponsored by The Leverhulme Trust (Grant F/07-004/AJ) London School of Economics and Political Science, 27 May 2010 and Chateau du Baffy, Normandy, France, 30 July – 2 August, 2010 Please send by email all communications regarding this paper to the author at: [email protected] or at [email protected] * I wish to thank Rudolf Fara and Moshé Machover for helpful comments, and Hannu Nurmi for sending me several examples contained in this paper. -
Victory and Defeat in a Model of Behavior in Games and Toward Risk
Victory and Defeat in a Model of Behavior in Games and Toward Risk William S. Neilson Department of Economics Texas A&M University College Station, TX 77843-4228 [email protected] January 24, 2000 The standard expected utility model is augmented by allowing individuals to receive additional utility in states in which they consider themselves victorious and to lose a utility increment in which they consider themselves defeated. The resulting event-dependent expected utility model is used to explain behavior in games and toward risk. In games, players consider themselves defeated when their monetary payoffs are low compared to their opponents' payoffs, and they consider themselves victorious when their payoffs are high, but not too high, compared to their opponents' payoffs. Under these conditions the model can accommodate behavior that has been interpreted elsewhere as inequity aversion, as well as cooperation in the prisoner's dilemma and in public good provision games. In situations of risk, individuals consider themselves victorious (defeated) when they receive an unlikely, avoidable, high (low) outcome. Under these conditions the model can accommodate such behavior as the Allais paradox, boundary effects, and simultaneous gambling and insurance. Keywords: Event-dependent preferences, behavioral economics, inequity aversion, Allais paradox, boundary effects JEL codes: D81, C72 I am grateful to Robert Slonim and participants at the 1999 Lonestars Conference for helpful comments, and to the Private Enterprise Research Center for financial support. 1. Introduction People like winning and dislike losing, yet this feature has never been incorporated into the study of games. This paper remedies that situation. It is assumed that besides the utility he receives from his monetary payoff, a player gets a positive utility increment in situations in which he considers himself victorious, and suffers a negative utility increment in any situation that he considers a defeat. -
New Paradoxes in Intertemporal Choice
Judgment and Decision Making, Vol. 6, No. 2, February 2011, pp. 122–129 New paradoxes in intertemporal choice Li-Lin Rao∗ Shu Li† Abstract Similar to research on risky choice, the traditional analysis of intertemporal choice takes the view that an individual behaves so as to maximize the discounted sum of all future utilities. The well-known Allais paradox contradicts the fundamental postulates of maximizing the expected value or utility of a risky option. We describe a violation of the law of diminishing marginal utility as well as an intertemporal version of the Allais paradox. Keywords: intertemporal choice, risky choice, cancellation. 1 Introduction The most prominent idea to account for these anoma- lies is the hyperbolic discounting model (Ainslie, 1975). In the field of intertemporal choice, the discounted-utility This model suggests that the discount rate is not dy- (DU) theory proposed by Paul Samuelson in 1937 was namically consistent but that the rate is higher be- presented not only as a valid normative standard but also tween the present and near future and lower between as a descriptive theory of actual intertemporal choice be- the near and far distant future. Numerous theories have havior (Frederick, Loewenstein, & O’Donoghue, 2002; been developed by transforming the discount function Samuelson, 1937). In its general form, the DU theory to other forms, from one-parameter hyperbolic discount- proposes that the value of an option, (x; t), is the prod- ing (Mazur, 1984) to generalized hyperbolic discounting uct of its present utility, U(x), and an exponential tem- (Loewenstein & Prelec, 1992), to proportional discount- poral discounting function, F(t), where t is the time at ing (Harvey, 1994), and to quasi-hyperbolic discount- which x is acquired. -
Trump, Condorcet and Borda: Voting Paradoxes in the 2016 Republican Presidential Primaries
Munich Personal RePEc Archive Trump, Condorcet and Borda: Voting paradoxes in the 2016 Republican presidential primaries Kurrild-Klitgaard, Peter University of Copenhagen 15 December 2016 Online at https://mpra.ub.uni-muenchen.de/75598/ MPRA Paper No. 75598, posted 15 Dec 2016 16:00 UTC Trump, Condorcet and Borda: Voting paradoxes in the 2016 Republican presidential primaries1 PETER KURRILD-KLITGAARD Dept. of Political Science, University of Copenhagen Abstract. The organization of US presidential elections make them potentially vulnerable to so-called “voting paradoxes”, identified by social choice theorists but rarely documented empirically. The presence of a record high number of candidates in the 2016 Republican Party presidential primaries may have made this possibility particularly latent. Using polling data from the primaries we identify two possible cases: Early in the pre-primary (2015) a cyclical majority may have existed in Republican voters’ preferences between Bush, Cruz and Walker—thereby giving a rare example of the Condorcet Paradox. Furthermore, later polling data (March 2016) suggests that while Trump (who achieved less than 50% of the total Republican primary vote) was the Plurality Winner, he could have been beaten in pairwise contests by at least one other candidate—thereby exhibiting a case of the Borda Paradox. The cases confirm the empirical relevance of the theoretical voting paradoxes and the importance of voting procedures. Key words: Social choice; Condorcet Paradox; Borda Paradox; US presidential election 2016; Jeb Bush; Chris Christie; Ted Cruz; John Kasich; Marco Rubio; Donald Trump; Scot Walker; voting system. JEL-codes: D71; D72. 1. Introduction Since the 1950s social choice theory has questioned the possibility of aggregating individual preferences to straightforward, meaningful collective choices (Arrow [1951] 1963). -
Paradoxes Situations That Seems to Defy Intuition
Paradoxes Situations that seems to defy intuition PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Tue, 08 Jul 2014 07:26:17 UTC Contents Articles Introduction 1 Paradox 1 List of paradoxes 4 Paradoxical laughter 16 Decision theory 17 Abilene paradox 17 Chainstore paradox 19 Exchange paradox 22 Kavka's toxin puzzle 34 Necktie paradox 36 Economy 38 Allais paradox 38 Arrow's impossibility theorem 41 Bertrand paradox 52 Demographic-economic paradox 53 Dollar auction 56 Downs–Thomson paradox 57 Easterlin paradox 58 Ellsberg paradox 59 Green paradox 62 Icarus paradox 65 Jevons paradox 65 Leontief paradox 70 Lucas paradox 71 Metzler paradox 72 Paradox of thrift 73 Paradox of value 77 Productivity paradox 80 St. Petersburg paradox 85 Logic 92 All horses are the same color 92 Barbershop paradox 93 Carroll's paradox 96 Crocodile Dilemma 97 Drinker paradox 98 Infinite regress 101 Lottery paradox 102 Paradoxes of material implication 104 Raven paradox 107 Unexpected hanging paradox 119 What the Tortoise Said to Achilles 123 Mathematics 127 Accuracy paradox 127 Apportionment paradox 129 Banach–Tarski paradox 131 Berkson's paradox 139 Bertrand's box paradox 141 Bertrand paradox 146 Birthday problem 149 Borel–Kolmogorov paradox 163 Boy or Girl paradox 166 Burali-Forti paradox 172 Cantor's paradox 173 Coastline paradox 174 Cramer's paradox 178 Elevator paradox 179 False positive paradox 181 Gabriel's Horn 184 Galileo's paradox 187 Gambler's fallacy 188 Gödel's incompleteness theorems -
Learning in the Allais Paradox
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Erasmus University Digital Repository J Risk Uncertainty (2006) 33:155–164 DOI 10.1007/s11166-006-0390-3 Learning in the Allais paradox Gijs van de Kuilen · Peter P. Wakker∗ C Springer Science + Business Media, LLC 2006 Abstract Whereas both the Allais paradox, the first empirical challenge of the classical ra- tionality assumptions, and learning have been the focus of many experimental investigations, no experimental study exists today into learning in the pure context of the Allais paradox. This paper presents such a study. We find that choices converge to expected utility maxi- mization if subjects are given the opportunity to learn by both thought and experience, but less so when they learn by thought only. To the extent that genuine preferences should be measured with proper learning and incentives, our study gives the first pure demonstration that irrationalities such as in the Allais paradox are less pronounced than often thought. Keywords Learning . Rational choice . Allais paradox . Nonexpected utility JEL Classification D81 . D83 The first empirical challenge of the classical rationality assumption in economics was made by Allais (1953), through his famous choice paradox for decision under risk. It showed that the majority of people systematically violate expected utility, the model commonly accepted as the hallmark of rationality for choice under risk in those days. Allais’ paradox initiated a flurry of empirical demonstrations that more and more basic rationality assumptions are violated empirically (Camerer, 1995). To model these findings, theories were developed that explicitly depart from rational choice and only pretend to be descriptive, such as prospect theory (Kahneman and Tversky, 1979). -
Political Knowledge and the Paradox of Voting
Political Knowledge and the Paradox of Voting Edited by Sofia Magdalena Olofsson We have long known that Americans pay local elections less attention than they do elections for the Presidency and Congress. A recent Portland State University study showed that voter turnout in ten of America’s 30 largest cities sits on average at less than 15% of eligible voters. Just pause and think about this. The 55% of voting age citizens who cast a ballot in last year’s presidential election – already a two-decade low and a significant drop from the longer-term average of 65-80% – still eclipses by far the voter turnout at recent mayoral elections in Dallas (6%), Fort Worth (6%), and Las Vegas (9%). What is more, data tells us that local voter turnout is only getting worse. Look at America’s largest city: New York. Since the 1953 New York election, when 93% of residents voted, the city’s mayoral contests saw a steady decline, with a mere 14% of the city’s residents voting in the last election. Though few might want to admit it, these trends suggest that an unspoken hierarchy exists when it comes to elections. Atop this electoral hierarchy are national elections, elections that are widely considered the most politically, economically, and culturally significant. Extensively covered by the media, they are viewed as high-stakes moral contests that naturally attract the greatest public interest. Next, come state elections: though still important compared to national elections, their political prominence, media coverage, and voter turnout is already waning. At the bottom of this electoral hierarchy are local elections that, as data tells us, a vast majority of Americans now choose not to vote in. -
Economic Growth, Capitalism and Unknown Economic Paradoxes
Sustainability 2012, 4, 2818-2837; doi:10.3390/su4112818 OPEN ACCESS sustainability ISSN 2071-1050 www.mdpi.com/journal/sustainability Article Economic Growth, Capitalism and Unknown Economic Paradoxes Stasys Girdzijauskas *, Dalia Streimikiene and Andzela Mialik Vilnius University, Kaunas Faculty of Humanities, Muitines g. 8, LT-44280, Kaunas, Lithuania; E-Mails: [email protected] (D.S.); [email protected] (A.M.) * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +370-37-422-566; Fax: +370-37-423-222. Received: 28 August 2012; in revised form: 9 October 2012 / Accepted: 16 October 2012 / Published: 24 October 2012 Abstract: The paper deals with failures of capitalism or free market and presents the results of economic analysis by applying a logistic capital growth model. The application of a logistic growth model for analysis of economic bubbles reveals the fundamental causes of bubble formation—economic paradoxes related with phenomena of saturated markets: the paradox of growing returnability and the paradoxes of debt and leverage trap. These paradoxes occur exclusively in the saturated markets and cause the majority of economic problems of recent days including overproduction, economic bubbles and cyclic economic development. Unfortunately, these paradoxes have not been taken into account when dealing with the current failures of capitalism. The aim of the paper is to apply logistic capital growth models for the analysis of economic paradoxes having direct impact on the capitalism failures such as economic bubbles, economic crisis and unstable economic growth. The analysis of economic paradoxes and their implication son failures of capitalism provided in the paper presents the new approach in developing policies aimed at increasing economic growth stability and overcoming failures of capitalism. -
How Economists Came to Accept Expected Utility Theory: the Case of Samuelson and Savage
Journal of Economic Perspectives—Volume 30, Number 2—Spring 2016—Pages 219–236 Retrospectives How Economists Came to Accept Expected Utility Theory: The Case of Samuelson and Savage Ivan Moscati This feature addresses the history of economic terms and ideas. The hope is to deepen the workaday dialogue of economists, while perhaps also casting new light on ongoing questions. If you have suggestions for future topics or authors, please contact Joseph Persky, Professor of Economics, University of Illinois, Chicago, at [email protected]. Introduction In the expected utility approach to decision-making under risk, the utility of a risky prospect is given by the sum of the utilities u of the alternative possible outcomes of the prospect, each weighted by the probability that the outcome will occur. Thus, for example, the utility of a lottery yielding either a trip to London with probability p or a payment of $2,000 with probability (1 p) is given by − (u(trip to London) p) (u($2,000) (1 p)). According to expected utility × + × − theory, the decision maker will choose among these risky prospects, or lotteries, and will choose the one with the highest expected utility. This theory dominated the economic analysis of individual decision-making under risk from the early 1950s to the 1990s. Beginning in the late 1970s, the accumulation of robust experi- mental evidence against the expected utility hypothesis prompted decision theorists ■ Ivan Moscati is Associate Professor of Economics, University of Insubria, Varese, Italy. He also teaches History of Economics at Bocconi University, Milan, Italy. His email address is [email protected]. -
A Phase Transition in Arrow's Theorem
A Phase Transition in Arrow's Theorem Frederic Koehler∗ Elchanan Mossely Abstract Arrow's Theorem concerns a fundamental problem in social choice theory: given the individual preferences of members of a group, how can they be aggregated to form rational group preferences? Arrow showed that in an election between three or more candidates, there are situations where any voting rule satisfying a small list of natural \fairness" axioms must produce an apparently irrational intransitive outcome. Fur- thermore, quantitative versions of Arrow's Theorem in the literature show that when voters choose rankings in an i.i.d. fashion, the outcome is intransitive with non-negligible probability. It is natural to ask if such a quantitative version of Arrow's Theorem holds for non-i.i.d. models. To answer this question, we study Arrow's Theorem under a natural non-i.i.d. model of voters inspired by canonical models in statistical physics; indeed, a version of this model was previously introduced by Raffaelli and Marsili in the physics literature. This model has a parameter, temperature, that prescribes the correlation between different voters. We show that the behavior of Arrow's Theorem in this model undergoes a striking phase transition: in the entire high temperature regime of the model, a Quantitative Arrow's Theorem holds showing that the probability of paradox for any voting rule satisfying the axioms is non-negligible; this is tight because the probability of paradox under pairwise majority goes to zero when approaching the critical temperature, and becomes exponentially small in the number of voters beyond it. -
Stop Me Before I Quantify Again: the Role of Political Science in the Study of Election Law
University at Buffalo School of Law Digital Commons @ University at Buffalo School of Law Journal Articles Faculty Scholarship 1999 Stop Me Before I Quantify Again: The Role of Political Science in the Study of Election Law James A. Gardner University at Buffalo School of Law Follow this and additional works at: https://digitalcommons.law.buffalo.edu/journal_articles Part of the Election Law Commons, and the Political Science Commons Recommended Citation James A. Gardner, Stop Me Before I Quantify Again: The Role of Political Science in the Study of Election Law, 32 Loy. L.A. L. Rev. 1141 (1999). Available at: https://digitalcommons.law.buffalo.edu/journal_articles/225 This Article is brought to you for free and open access by the Faculty Scholarship at Digital Commons @ University at Buffalo School of Law. It has been accepted for inclusion in Journal Articles by an authorized administrator of Digital Commons @ University at Buffalo School of Law. For more information, please contact [email protected]. STOP ME BEFORE I QUANTIFY AGAIN: THE ROLE OF POLITICAL SCIENCE IN THE STUDY OF ELECTION LAW James A. Gardner* I. INTRODUCTION One of the most striking recent developments in the academic study of law is its increasingly interdisciplinary character. Histori- ans, of course, have long found the legal academy a congenial home, but these days scholars from what seems like every department on the university campus have begun to descend, as it were, upon the law and to stake claims to pieces of the field. Sociologists, statisti- cians, psychologists, economists, linguists, literary analysts of every stripe, and even a few theoretical scientists have quite deliberately begun to sally forth beyond the traditional boundaries of their disci- plines and to bring their insights to the analysis of law.