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

Arrow's Impossibility Theorem and Sen's Minimal Liberalism example impose 'impossibility' roadblocks on progress. A reinterpretation explained in this article exposes what causes these negative conclusions, which permits the development of positive resolutions that retain the spirit of Arrow's and Sen's assumptions. What precipitates difficulties is surprisingly common, and it affects most disciplines. This insight identifies how to analyze other puzzles such as conflicting laws or controversies over voting rules. An unexpected bonus is that this social science issue defines a research agenda to address the 'dark matter' mystery confronting astronomers.

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 ...

Riker (Liberalism against populism, Waveland, New York, 1982) famously argued that Arrow's impossibility theorem undermined the logical foundations of "populism", the view that in a democracy, laws and policies ought to express "the will of the people". In response, his critics have questioned the use of Arrow's theorem on the grounds that not all configurations of preferences are likely to occur in practice; the critics allege, in particular, that majority preference cycles, whose possibility the theorem exploits, rarely happen. In this essay, I argue that the critics' rejoinder to Riker misses the mark even if its factual claim about preferences is correct: Arrow's theorem and related results threaten the populist's principle of democratic legitimacy even if majority preference cycles never occur. In this particular context, the assumption of an unrestricted domain is justified irrespective of the preferences citizens are likely to have.

Abstract
Arrow (1950) famously showed the impossibility of aggregating individual preference orders into a social preference order (together with basic desiderata). This paper shows that it is possible to aggregate individual choice functions, that satisfy almost any condition weaker than WARP, into a social choice function that satisfy the same condition (and also Arrow's desiderata).