Arrows Impossibility Theorem In Practice

Seminar paper from the year 2018 in the subject Politics - General and Theories of International Politics, grade: 1,7, University of Bayreuth, language: English, abstract: Accurately figuring out the cumulative ordering of preferences of an entire society as an aggregation of the orderings of preferences of many individuals would inherently simplify democratic decision processes. However, the social preference ordering is contingent on the specific procedure, or voting rule, used to aggregate the individual preference orderings. This means that different voting rules can lead to different social preference orderings under the input of the same individual preference orderings. This issue effectuates the questions which of the different possible outcomes is the most legitimate, and by extension which voting rule should be used. Arrow sought to answer these questions by demanding that voting rules satisfy a particular set of democratically desirable qualities – these are referred to as axioms or conditions. A voting rule that succeeds in complying with all the conditions could be considered democratically legitimate. The emerging issue is that no voting rule can possibly satisfy all theconditions simultaneously. The blatant preliminary conclusion of this impossibility theorem is somewhat bleak: our faith in democratic voting procedures might be entirely misguided. The aim of this paper is to ascertain, whether the implications of this impossibility theorem constitute an actual issue for the practical application of preference aggregation – or voting – in a democratic political system. Having argued that certain evasions of the impossibility can be practically justified in most cases, the paper will conclude that the impossibility is only relevant for a negligible number of scenarios. Thus, inferring that in most cases Arrow’s impossibility theorem, albeit theoretically relevant, does not constitute a profound issue for voting procedures in a democratic political system.

Arrow Impossibility Theorems is a 10-chapter text that describes existing impossibility theorems. This book explores a number of formalizations of ethical constraints of the theorems. After an introduction to the framework and notation for Arrow impossibility theorems, this book goes on discussing some concepts and an apparatus of relations among those concepts which are important for the theorems. Other chapters present some impossibility results that serve to point out serious difficulties in some plausible escape routes from the theorems of earlier chapters. The final chapter describes important areas of research that have arisen in the collective choice field in the transition away from studying the conditions of Arrow's theorem alone to the totality of all impossibility theorems. This book is intended primarily for economists.

Kenneth Arrow's pathbreaking Òimpossibility theoremÓ was a watershed in the history of welfare economics, voting theory, and collective choice, demonstrating that there is no voting rule that satisfies the four desirable axioms of decisiveness, consensus, nondictatorship, and independence. In this book, Amartya Sen and Eric Maskin explore the implications of ArrowÕs theorem. Sen considers its ongoing utility, exploring the theoremÕs value and limitations in relation to recent research on social reasoning, while Maskin discusses how to design a voting rule that gets us closer to the idealÑgiven that achieving the ideal is impossible. The volume also contains a contextual introduction by social choice scholar Prasanta K. Pattanaik and commentaries from Joseph E. Stiglitz and Kenneth Arrow himself, as well as essays by Sen and Maskin outlining the mathematical proof and framework behind their assertions.

Originally published in 1951, "Social Choice and Individual Values" introduced "Arrow's Impossibility Theorem" and founded the field of social choice theory in economics and political science. This new edition, including a new foreword by Nobel laureate Eric Maskin, reintroduces Arrow's seminal book to a new generation of students and researchers."Far beyond a classic, this small book unleashed the ongoing explosion of interest in social choice and voting theory. A half-century later, the book remains full of profound insight: its central message, 'Arrow's Theorem, ' has changed the way we think."--Donald G. Saari, author of "Decisions and Elections: Explaining the Unexpected "