Arrow's Theorem
In: Oxford Research Encyclopedia of Politics
"Arrow's Theorem" published on by Oxford University Press.
In: Oxford Research Encyclopedia of Politics
"Arrow's Theorem" published on by Oxford University Press.
In: British journal of political science, Band 46, Heft 1, S. 1-9
ISSN: 1469-2112
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: Working Papers on the Profitable Economics No. 341
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Working paper
This paper studies the relationship between the theory of distributive justice based on the concept of envy-freeness and Arrovian social choise theory. We define two conditions of No-envy and study their relationship with Arrow' scondition of independence of irrelevant alternatives, a weakening of this condition called Personal States Independence and the condition of Minimal Equity, that says that each individual must have the power to veto (in a limited sense) at least one alternative (presumably, one alternative which is particularly unfair to him).
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In: British journal of political science, Band 46, Heft 1, S. 1
ISSN: 0007-1234
In: European Journal of Political Economy, Band 65, S. 101936
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.
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In: Mathematics Preprint Archive Vol. 2001, Issue 11, pp 215-243
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Working paper
In: 47 Stan. L. Rev. 295 (1994-1995)
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In: Journal of theoretical politics, Band 3, Heft 3, S. 259-276
ISSN: 1460-3667
The circumstances of the author's discovery of the median voter theorem and the steps which led from there to his Theory of Committees and Elections are set out. His theory is presented in the form of the `statistical thesis' that the best choice procedure selects the option which `on average' is highest on the committee members' schedules. As there is more than one concept of average, so there is more than one acceptable committee procedure. The author's way of proceeding is compared and contrasted with Arrow's.
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 ...
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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
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In: Mathematics of Social Choice, S. 83-91