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Since Sen's insightful analysis of Arrow's Impossibility Theorem, Arrow's theorem is often interpreted as a consequence of the exclusion of interpersonal information from Arrow's framework. Interpersonal comparability of either welfare levels or welfare units is known to be sufficient for circumventing Arrow's impossibility result. But it is less well known whether one of these types of comparability is also necessary or whether Arrow's conditions can already be satisfied in much narrower informational frameworks. This note explores such a framework: the assumption of (ONC + 0), ordinal measurability of welfare with the additional measurability of a "zero‐line", is shown to point towards new, albeit limited, escape routes from Arrow's theorem. Some existence and classification results are established, using the condition that social orderings be transitive as well as the condition that social orderings be quasi‐transitive.

In 1951, Kenneth Arrow published his now celebrated book Social Choice and Individual Values. Although not the first book to be written on social choice, Arrow's work ushered in a voluminous literature mostly produced by economists but by philosophers and political scientists as well. Arrow's chief result was a proof of the impossibility of a social welfare function (hereafter "SWF"). He showed that there could be no decision procedure for aggregating individual preference orderings into a grand, overall social preference ordering. The result has been hailed by some as a sort of Godel Theorem of economics. It has seemed to many to have, if not the complexity of the Godel Theorem, at least the same astonishing counter‐intuitiveness. On the other hand, some social choice theorists, while conceding the validity of the Arrow Theorem, have challenged its soundness by quarreling with one or more of its presuppositions.

We develop a geometric approach to identify all possible profiles that support specified votes for separate initiatives or for a bundled bill. This disaggregation allows us to compute the likelihood of different scenarios describing how voters split over the alternatives and to offer new interpretations for pairwise voting. The source of the problems—an unanticipated loss of available information—also explains a variety of other phenomena, such as Simpson's paradox (a statistical paradox in which the behavior of the "parts" disagrees with that of the "whole") and Arrow's theorem from social choice.

We develop a geometric approach to identify all possible profiles that support specified votes for separate initiatives or for a bundled bill. This disaggregation allows us to compute the likelihood of different scenarios describing how voters split over the alternatives & to offer new interpretations for pairwise voting. The source of the problems -- an unanticipated loss of available information -- also explains a variety of other phenomena, such as Simpson's paradox (a statistical paradox in which the behavior of the "parts" disagrees with that of the "whole") & Arrow's theorem from social choice. 6 Tables, 4 Figures, 1 Appendix, 23 References. Adapted from the source document.

Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- List of Figures and Tables -- Preface and Acknowledgements -- Introduction: The Social Choice Approach to Institutional Planning Theory -- Part I: Democracy, Rationality, and Planning: Applying Arrow's Theorem -- 1 Paradox of Dialogical Decision-making -- 2 Evaluation and Arguments: Balancing the Procedural Values of Priority Setting Techniques -- 3 Institutions of Communicative-calculative Synthesis: Structured Group Processes -- 4 Decision Cycles in Two Transport Planning Cases -- Part II: Public Interest and Protected Spheres: Applying Sen's Theorem -- 5 Democratic Planning and the Liberal Paradox -- 6 Loyalty Dilemmas in Advocacy Planning -- 7 Privacy as a Planning Problem: Transport-related Examples -- 8 Equality and Planning with Protected Spheres -- Part III: Manipulation in Planning: Applying Gibbard and Satterthwaite's Theorem -- 9 Power Concentration or Manipulation in the Planning Process -- 10 Planning Style and Agency Properties -- 11 Agency Profiles Applied to Positive Planning Theory -- 12 Economics of Dialogue: Hard Trade-offs in Communicative Planning -- Epilogue: Challenge and Response -- Bibliography -- Glossary of Social Choice Terms -- Index.

Paradoxes, if they do not define a field, render its problems intriguing and often perplexing, especially insofar as the paradoxes remain unresolved. Voting theory, for example, has been greatly stimulated by the Condorcet paradox, which is the discovery by the Marquis de Condorcet that there may be no alternative that is preferred by a majority to every other alternative, producing so-called cyclical majorities. Its modern extension and generalization is Arrow's theorem, which says, roughly speaking, that a certain set of reasonable conditions for aggregating individuals' preferences into some social choice are inconsistent. In the last fifty years, hundreds of books and thousands of articles have been written about these and related social-choice paradoxes and theorems, as well as their ramifications for voting and democracy. Hannu Nurmi provides a good survey and classification of voting paradoxes and also offers advice on "how to deal with them." There is also an enormous literature on fairness, justice, and equality, and numerous suggestions on how to rectify the absence of these properties or attenuate their erosion. But paradoxes do not frame the study of fairness in the same way they have inspired social-choice theory.

Cover -- Half Title -- Dedication -- Title Page -- Copyright Page -- Table of Contents -- Acknowledgements -- 1 Education and the state -- Introduction -- West's 'market model' -- 2 Equality of opportunity -- Introduction -- West on equality of opportunity -- Williams on equality of opportunity -- Rawls on equality of opportunity -- Why Dworkin cares about equality -- For 'equality of opportunity' read 'an adequate education for all' -- 3 Education for democracy -- Introduction -- West on education for democracy -- Education for participation in democracy -- State versus nonstate education for democracy: contingent arguments -- State versus nonstate education for democracy: noncontingent arguments -- Justifications for democracy and fitness tests for participation -- 'Education for democracy': markets and the state -- 4 Education for autonomy -- Introduction -- White on a compulsory curriculum for autonomy -- Raz on the state promotion of autonomy: negative arguments -- Raz on the state promotion of autonomy -- Challenging Raz's 'contingent objection' -- The epistemic argument and the curriculum -- Against state promotion of education for autonomy -- 5 Democratic control of education -- Introduction -- Democratic control of the curriculum: an argument from political equality -- Improving democracy by improving voting systems -- Riker and Nathan on the limitations of democracy -- Questioning the conditions of Arrow's theorem -- Logrolling and democratic control of education -- Democracy versus markets -- Fleshing out West's 'minimum adequate education for all' -- 6 Education as a public good -- Introduction -- Grace on education as a public good -- Education and the 'public goods dilemma' -- West's market model and externalities -- West's market model and the 'public goods dilemma' -- 7 Education and the state revisited -- Bibliography

During the 1996 term, the United States Supreme Court made a candid confession about its voting practices. In Seminole Tribe of Florida v. Florida, the Court overruled Pennsylvania v. Union Gas Co. and recognized that when a justice defers to the majority against his or her own reasoning inconclusive precedent results. Union Gas was particularly unusual because Justice White switched his vote to assure a result in a three-remedy case where none of the three remedies had the support of a majority. In Seminole Tribe, the Court admitted Union Gas "has, since its issuance, been of questionable precedential value, largely because a majority of the Court expressly disagreed with the rationale of the plurality." Accordingly, the Court recognized the problems created when a justice votes against his or her own reasoning to ensure a result. While scholars frequently have analyzed the strategic voting practices of legislators, similar analysis of voting on judicial panels is relatively new. Frank Easterbrook was the first scholar to apply Arrow's Theorem systematically to the Supreme Court's voting practice, and several scholars followed his lead. After Justice White's vote in Union Gas, Professor John Rogers warned the Court against abdicating its role as a reasoned decision maker. He concluded, however, that the contradictory vote in Union Gas was aberrational. More recently, Professors David Post and Steven Salop published an article encouraging multimember courts to abandon their traditional practice of outcome voting and instead to adopt a system of issue voting.' Shortly thereafter, Professors Lewis Kornhauser and Lawrence Sager urged appellate courts to adopt neither outcome voting nor issue voting as a rule. Rather, they suggested appellate courts should take a metavote on whether outcome or issue voting should control each case." Professor Maxwell Stearns advanced the debate over appellate court voting in a trilogy of articles published over the past two years. These articles apply social choice theory to the ...

It is not uncommon to be frustrated by the outcome of an election or a decision in voting, law, economics, engineering, and other fields. Does this 'bad' result reflect poor data or poorly informed voters? Or does the disturbing conclusion reflect the choice of the decision/election procedure? Nobel Laureate Kenneth Arrow's famed theorem has been interpreted to mean 'no decision procedure is without flaws'. Similarly, Nobel Laureate Amartya Sen dashes hope for individual liberties by showing their incompatibility with societal needs. This highly accessible book offers a new, different interpretation and resolution of Arrow's and Sen's theorems. Using simple mathematics, it shows that these negative conclusions arise because, in each case, some of their assumptions negate other crucial assumptions. Once this is understood, not only do the conclusions become expected, but a wide class of other phenomena can also be anticipated

Wulf Gaertner provides a comprehensive account of an important and complex issue within social choice theory: how to establish a social welfare function while restricting the spectrum of individual preferences in a sensible way. Gaertner's starting point is K. J. Arrow's famous 'Impossibility Theorem', which showed that no welfare function could exist if an unrestricted domain of preferences is to be satisfied together with some other appealing conditions. A number of leading economists have tried to provide avenues out of this 'impossibility' by restricting the variety of preferences: here, Gaertner provides a clear and detailed account, using standardized mathematical notation, of well over forty theorems associated with domain conditions. Domain Conditions in Social Choice Theory will be an essential addition to the library of social choice theory for scholars and their advanced graduate students

Coalition Formation and Social Choice provides a unified and comprehensive study of coalition formation and collective decision-making in committees. It discusses the main existing theories including the size principle, conflict of interest theory, dominant player theory, policy distance theory and power excess theory. In addition, the book offers new theories of coalition formation in which the endogenous formation of preferences for coalitions is basic. Both simple game theory and social choice theory are extensively applied in the treatment of the theories. This combined application not only leads to new theories but also offers a new and fresh perspective on coalition formation and collective decision-making in committees. The book covers the fundamental concepts and results of social choice theory including Arrow's Impossibility Theorem. Furthermore, it gives a coherent treatment of the theory of simple games. Besides more traditional topics in simple game theory like power indices, it also introduces new aspects of simple games such as the Chow parameter, the Chow vector and the notion of similar games

Aggregation of individual opinions into a social decision is a problem widely observed in everyday life. For centuries people tried to invent the `best' aggregation rule. In 1951 young American scientist and future Nobel Prize winner Kenneth Arrow formulated the problem in an axiomatic way, i.e., he specified a set of axioms which every reasonable aggregation rule has to satisfy, and obtained that these axioms are inconsistent. This result, often called Arrow's Paradox or General Impossibility Theorem, had become a cornerstone of social choice theory. The main condition used by Arrow was his famous Independence of Irrelevant Alternatives. This very condition pre-defines the `local' treatment of the alternatives (or pairs of alternatives, or sets of alternatives, etc.) in aggregation procedures. Remaining within the framework of the axiomatic approach and based on the consideration of local rules, Arrovian Aggregation Models investigates three formulations of the aggregation problem according to the form in which the individual opinions about the alternatives are defined, as well as to the form of desired social decision. In other words, we study three aggregation models. What is common between them is that in all models some analogue of the Independence of Irrelevant Alternatives condition is used, which is why we call these models Arrovian aggregation models. Chapter 1 presents a general description of the problem of axiomatic synthesis of local rules, and introduces problem formulations for various versions of formalization of individual opinions and collective decision. Chapter 2 formalizes precisely the notion of `rationality' of individual opinions and social decision. Chapter 3 deals with the aggregation model for the case of individual opinions and social decisions formalized as binary relations. Chapter 4 deals with Functional Aggregation Rules which transform into a social choice function individual opinions defined as choice functions. Chapter 5 considers another model &endash; Social Choice Correspondences when the individual opinions are formalized as binary relations, and the collective decision is looked for as a choice function. Several new classes of rules are introduced and analyzed