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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.

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.

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.

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