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"Arrow's Theorem" published on by Oxford University Press.

In this essay, we contest one of the main arguments for restricting corporate board voting to shareholders. In justifying the limitation of the franchise to shareholders, scholars have repeatedly turned to social choice theory—specifically, Arrow's theorem—to justify the exclusive shareholder franchise. Citing to the theorem, corporate law commentators have argued that lumping different groups of stakeholders together into the electorate would result in a lack of consensus and, ultimately, the lack of coherence that attends intransitive social choices, perhaps even leading the corporation to self-destruct. We contend that this argument is misguided. First, we argue that scholars have greatly overestimated the relative likelihood of cyclical outcomes with an expanded electorate. Second, even if a nascent intransitivity were to occur, there is almost no chance that it would manifest itself in inconsistent corporate decisions, much less ones that would cause a firm to self-destruct. Moreover, the exclusive shareholder franchise, like any other preference aggregation system, may avoid violating one of the conditions of Arrow's theorem only by violating another—a tradeoff that has never been explicitly acknowledged or defended. Ultimately, we argue that Arrow's theorem fails to support the limitation of corporate voting rights to shareholders.

The doctrine of shareholder primacy has received substantial attention from its legions of proponents, its indefatigable opponents, and even its disinterested observers. The notion that a corporation should be run in the interests of its shareholders is the theoretical foundation upon which modern corporate law stands. Almost all empirical study in corporate law is premised on a notion of shareholder primacy, and these results would lose much of their meaning if the theory were somehow disproved. Perhaps most importantly, shareholders do in fact have primacy of place within the corporation, as they alone generally have the right to elect the firm's directors. Despite the importance of shareholder primacy to the American (and increasingly global) corporation, there is one aspect of shareholder primacy theory that has not received sustained scholarly critique. In justifying the limitation of the franchise to shareholders, scholars have repeatedly turned to social choice theory-specifically, Arrow's theorem-to raise concerns about expanding the corporate electorate. Arrow's theorem posits that no social choice function, including any voting procedure, can simultaneously fulfill four conditions of democratic fairness and guarantee a transitive outcome. Citing the theorem, corporate law commentators have argued that combining different stakeholders together into the electorate would result in a lack of consensus and, ultimately, the lack of coherence that attends intransitive social choices. Plagued by these voting pathologies, a corporation with such an electorate could even be led to "self-destruct." This argument from Arrow's theorem, however, overestimates the concerns raised by the theorem about the aggregation of more diverse preferences. Almost any time that different viewpoints are converted into social choices, disparate preferences must be reconciled. In fact, the only way around this would be to assume that shareholders will never disagree-increasingly a flawed premise. More importantly, the argument ...

These are the sheets of a presentation on June 8 2018, at the conference of Dutch and Flemish political science. These sheets give an overview, and see "Voting Theory for Democracy" (VTFD) for precision. Arrow's theorem is that four axioms would be reasonable and morally required each by themselves, but together they result into a contradiction. The deduction stands but the interpretation can be rejected. Arrow confuses voting and deciding. The axiom of "pairwise decision making" can be rejected - and Arrow's label "independence of irrelevant alternatives" is distractive. A method that many would find interesting is Borda Fixed Point. ; This is an update of the sheets of my presentation on March 16 2001 for the Social Choice group in Tilburg, The Politicologenetmaal 2018 has this link: https://politicologenetmaal.eu See Voting Theory for Democracy at https://zenodo.org/record/291985

The two most influential traditions of contemporary theorizing about democracy, social choice theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote these conditions, and hence that social choice theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect.

The two most influential traditions of contemporary theorizing about democracy, social choice theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote these conditions, and hence that social choice theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect.

In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow's theorem, all voting methods must be seriously flawed. Arrow's theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow's result. Parallel to Arrow's ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow's theorem, but rather from restrictions imposed on voters' expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior.

"Rational Choice Theory in Political Decision Making" published on by Oxford University Press.

The sociological explanation of altruistic behaviour often encounters serious difficulties. This essay attempts to solve the altruism enigma through the presentation of an alternative explanation to Arrow's Possibility Theorem as well as to Berlin's serious objections to rational calculus in political behaviour. Bestowing charisma and/or sacredness to certain values often proves the solution to the puzzle by providing a rational criterion for action which cancels out other criteria and calculations. The Possibility Theorem which is put forward here solves the problem of the rationality of the supposedly irrational in rational choice situations and dilemmas. The Possibility Theorem is a contribution to the issue of the rationality of charisma and, therefore, to the analytical explanation of altruistic behaviour. ; La explicación sociológica del altruismo presenta serias dificultades. El presente ensayo propone resolver el enigma del altruismo mediante la presentación de una explicación alternativa al Teorema de Imposibilidad de Arrow así como a las objeciones de Berlin al cálculo racional en política. La atribución de carisma o sacralidad a ciertos valores genera, frecuentemente, la solución. Tal atribución suministra un criterio racional de acción que supera y descarta otros cálculos. El Teorema de Posibilidad que aquí se postula resuelve el problema de la racionalidad de lo supuestamente irrracional en las trías o elecciones racionales de conducta. El Teorema propuesto es una aportación a la cuestión de la racionalidad del carisma y, por ende, a la explicación analítica del altruismo.

May's celebrated theorem (1952) shows that, if a group of individuals wants to make a choice between two alternatives (say x and y), then majority voting is the unique decision procedure satisfying a set of attractive minimal conditions. The conditions are (i) universal domain: the decision procedure should produce an outcome (x, y or tie) for any logically possible combination of individual votes for x and y; (ii) anonymity: the collective choice should be invariant under permutations of the individual votes, i.e. all individual votes should have equal weight; (iii) neutrality: if the individual votes for x and y are swapped, then the outcome should be swapped in the same way, i.e. the labels of the alternatives should not matter; (iv) positive responsiveness: supposing all other votes remain the same, if one individual changes his or her vote in favour of a winning alternative, then this alternative should remain the outcome; if there was previously a tie, a change of one individual vote should break the tie in the direction of that change. May's theorem is often interpreted as a vindication of majoritarian democracy when a collective decision between two alternatives is to be made. Many collective decision problems are, however, more complex. They may not be confined to a binary choice between two alternatives, or between the acceptance or rejection of a single proposition. Suppose there are three or more alternatives (say x, y and z). In that case, it may seem natural to determine an overall collective preference ranking of these alternatives by applying majority voting to each pair of alternatives. But, unfortunately, pairwise majority voting may lead to cyclical collective preferences. Suppose person 1 prefers x to y to z, person 2 prefers y to z to x, and person 3 prefers z to x to y. Then there are majorities of two out of three for x against y, for y against z, and for z against x, a cycle. This is Condorcet's paradox. But a greater number of alternatives is not the only way in which a collective decision problem may deviate from the single binary choice framework of May's theorem. A collective decision problem may also involve simultaneous decisions on the acceptance or rejection of multiple interconnected propositions. For instance, a policy package or a legal decision may consist of multiple propositions which mutually constrain each other. To ensure consistency, the acceptance or rejection of some of these propositions may constrain the acceptance or rejection of others. Once again, a natural suggestion would be to apply majority voting to each proposition separately. As we will see in detail below, however, this method also generates a paradox, sometimes called the 'doctrinal paradox' or 'discursive dilemma': propositionwise majority voting over multiple interconnected propositions may lead to inconsistent collective sets of judgments on these propositions. We have thus identified two dimensions along which a collective decision problem may deviate from the single binary choice framework of May's theorem: (a) the number of alternatives, and (b) the number of interconnected propositions on which simultaneous decisions are to be made. Deviations along each of these dimensions lead to a breakdown of the attractive properties of majority voting highlighted by May's theorem. Deviations along dimension (a) can generate Condorcet's paradox: pairwise majority voting over multiple alternatives may lead to cyclical collective preferences. And deviations along dimension (b) can generate the 'doctrinal paradox' or 'discursive dilemma': propositionwise majority voting over multiple interconnected propositions may lead to inconsistent collective sets of judgments on these propositions. In each case, we can ask whether the paradox is just an artefact of majority voting in special contrived circumstances, or whether it actually illustrates a more general problem. Arrow's impossibility theorem (1951/1963) famously affirms the latter for dimension (a): Condorcet's paradox brings to the surface a more general impossibility problem of collective decision making between three or more alternatives. But Arrow's theorem does not apply straightforwardly to the case of dimension (b). List and Pettit (2001) have shown that the 'doctrinal paradox' or 'discursive dilemma' also illustrates a more general impossibility problem, this time regarding simultaneous collective decisions on multiple interconnected propositions. The two impossibility theorems are related, but not identical. Arrow's result makes it less surprising to find that an impossibility problem pertains to the latter decision problem too, and yet the two theorems are not trivial corollaries of each other. The aim of this paper is to compare these two impossibility results and to explore their connections and dissimilarities. Sections 2 and 3 briefly introduce, respectively, Arrow's theorem and the new theorem on the aggregation of sets of judgments. Section 4 addresses the question of whether the two generalizations of May's single binary choice framework -- the framework of preferences over three or more options and the framework of sets of judgments over multiple connected propositions -- can somehow be mapped into each other. Reinterpreting preferences as ranking judgments, section 5 derives a simple impossibility theorem on the aggregation of preferences from the theorem on the aggregation of sets of judgments, and compares the result with Arrow's theorem. A formal proof of the result is given in an appendix. Section 6 discusses escape-routes from the two impossibility results, and indicates their parallels. Section 7, finally, explores the role of two crucial conditions underlying the two impossibility theorems -- independence of irrelevant alternatives and systematicity --, and identifies a unifying mechanism generating both impossibility problems.

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.

Voting systems aggregate preferences efficiently and are often used for deciding conservation priorities. Desirable characteristics of voting systems include transitivity, completeness, and Pareto optimality, among others. Voting systems that are common and potentially useful for environmental decision making include simple majority, approval, and preferential voting. Unfortunately, no voting system can guarantee an outcome, while also satisfying a range of very reasonable performance criteria. Furthermore, voting methods may be manipulated by decision makers and strategic voters if they have knowledge of the voting patterns and alliances of others in the voting populations. The difficult properties of voting systems arise in routine decision making when there are multiple criteria and management alternatives. Because each method has flaws, we do not endorse one method. Instead, we urge organizers to be transparent about the properties of proposed voting systems and to offer participants the opportunity to approve the voting system as part of the ground rules for operation of a group.

International audience ; Is social justice congruent with democracy? Are utilitarianism and welfare economics compatible with political liberalism? Salient disagreements between welfare economics and political philosophy focus upon the choice of principles of justice in a democratic society, and sustainability thereof remains an open question. Arrow's theorem establishes the impossibility of grounding a social welfare function upon individual preferences. Harsanyi's rule-utilitarianism builds a welfare function upon Bayesian expected utility. Rawls's contractarian theory of justice upholds the priority of the right over the good. Sen's theory of social choice rejects the compatibility of the Pareto principle with political liberalism. ; La justice sociale est-elle congruente avec la démocratie ? L'utilitarisme et l'économie du bien-être sont-ils compatibles avec le libéralisme politique ? Des désaccords saillants entre économie du bien-être et philosophie politique concernent le choix des principes de justice d'une société démocratique, et la pérennité de celle-ci demeure une question ouverte. Le théorème d'Arrow établit l'impossibilité d'une fonction de bien-être social issue des préférences individuelles. L'utilitarisme de la règle d'Harsanyi fonde la fonction de bien-être sur l'utilité espérée. La théorie contractualiste de la justice de Rawls affirme la priorité du juste sur le bien. La théorie du choix social de Sen récuse la compatibilité du principe de Pareto avec le libéralisme politique.

International audience ; Is social justice congruent with democracy? Are utilitarianism and welfare economics compatible with political liberalism? Salient disagreements between welfare economics and political philosophy focus upon the choice of principles of justice in a democratic society, and sustainability thereof remains an open question. Arrow's theorem establishes the impossibility of grounding a social welfare function upon individual preferences. Harsanyi's rule-utilitarianism builds a welfare function upon Bayesian expected utility. Rawls's contractarian theory of justice upholds the priority of the right over the good. Sen's theory of social choice rejects the compatibility of the Pareto principle with political liberalism. ; La justice sociale est-elle congruente avec la démocratie ? L'utilitarisme et l'économie du bien-être sont-ils compatibles avec le libéralisme politique ? Des désaccords saillants entre économie du bien-être et philosophie politique concernent le choix des principes de justice d'une société démocratique, et la pérennité de celle-ci demeure une question ouverte. Le théorème d'Arrow établit l'impossibilité d'une fonction de bien-être social issue des préférences individuelles. L'utilitarisme de la règle d'Harsanyi fonde la fonction de bien-être sur l'utilité espérée. La théorie contractualiste de la justice de Rawls affirme la priorité du juste sur le bien. La théorie du choix social de Sen récuse la compatibilité du principe de Pareto avec le libéralisme politique.