This paper continues the recent tradition of investigating iterated AGM revision by reasoning directly about the dynamics for total pre-order (“implausibility ordering”) representations of AGM revision functions. We reorient discussion, however, by proving that symmetry considerations, almost by themselves, suffice to determine a particular, AGM-friendly implausibility ordering dynamics due to Spohn 1988, which we call “J-revision”. After exploring the connections between implausibility ordering dynamics and the social choice theory of Arrow 1963, we provide symmetry arguments in the social choice-theoretic framework (...) for an interesting generalization of J-revision due to Nayak 1994. We conclude by arguing that the symmetry principles that uniquely favor J-revision and its generalizations are importantly expressive of the purely qualitative framework for representing beliefs that distinguishes the AGM program. Our results therefore comprehensively vindicate Spohn's 1988 conjecture that essentially J-revision is the best that can be done by way of a purely qualitative model of belief revision. (shrink)

It is argued in this paper that amalgamating confirmation from various sources is relevantly different from social-choice contexts, and that proving an impossibility theorem for aggregating confirmation measures directs attention to irrelevant issues.

It has become accepted that social choice is impossible in the absence of interpersonal comparisons of well-being. This view is challenged here. Arrow obtained an impossibility theorem only by making unreasonable demands on social choice functions. With reasonable requirements, one can get very attractive possibilities and derive social preferences on the basis of non-comparable individual preferences. This new approach makes it possible to design optimal second-best institutions inspired by principles of fairness, while traditionally the analysis of optimal second-best institutions was (...) thought to require interpersonal comparisons of well-being. In particular, this approach turns out to be especially suitable for the application of recent philosophical theories of justice formulated in terms of fairness, such as equality of resources. (shrink)

This paper aims to reexamine the axiom of the independence of irrelevant alternatives in the theory of social choice. A generalized notion of independence is introduced to clarify an informational requirement of binary independence which is usually imposed in the Arrovian framework. We characterize the implication of binary independence.

Arrow's Independence of Irrelevant Alternatives Condition is examined. It is shown why the standard rationale for (or against) the condition tends to be inconclusive as it fails to consider the basic ‘game’ issue in social choice. Specifically it is explained how some recent results (Gibbard-Satterthwaite) on the general non-existence of strategy-proof voting procedures provide the strongest rationale for the independence condition. Also, it is shown that this rationale was exactly the one used by Condorcet in his work on decision rules (...) for juries and elections. (shrink)

Kirjasymposio Eerik Lagerspetzin Social Choice and Democratic Values – kirjasta. Kenneth Arrowia seuraten Lagerspetz pitää sosiaalisen valinnan teorian suurimpana vahvuutena sitä, että sen tuloksia voidaan käyttää monissa erilaisissa yhteyksissä. Minä taas pidän teorian suurimpana heikkoutena sen vaikeutta: tutkijat eivät ole päässeet yhteisymmärrykseen erityisesti ns. epärelevanttien vaihtoehtojen riippumattomuusehdon tulkinnasta ja muotoilusta. Lagerspetz hyväksyy kirjassaan nähdäkseni seuraavat väitteet: kaikki demokraattiset äänestyssäännöt rikkovat riippumattomuusehtoa, mutta että tuo ehto on silti normatiivisesti perusteltu. Arrow’n ehdot ovat intuitiivisesti ottaen hyväksyttävissä. Koska riippumattomuusehdon rikkoutumisesta seuraa strategista äänestämistä (...) ja strateginen äänestäminen on normatiivisesti katsottuna ei-toivottavaa tai jopa moraalisesti kyseenalaista, strategisen äänestämisen poissulkeminen olisi paras mahdollinen argumentti riippumattomuusehdon puolesta. Lisäksi säännöt jotka toteuttavat riippumattomuusehdon ovat immuuneja strategiselle käyttäytymiselle. Hyvin toimiva äänestyssääntö luo puhtaasti mekaanisen yhteyden yksilöiden mielipiteiden ja kollektiivisen valinnan välille. Tämän kirjoituksen ensisijainen tavoite on kumota jokainen edellisessä kappaleessa esitetty väite. (shrink)

Arrow's Independence of Irrelevant Alternatives (IIA) has been under criticism for decades for not taking account of preference intensities. Computer-simulation results by Aki Lehtinen concerning strategic voting under various voting rules show that this intensity argument does not need to rest on mere intuition. Voters may express intensities by voting strategically, and that this has beneficial aggregate-level consequences: utilitarian efficiency is higher if voters engage in strategic behaviour than if they always vote sincerely. Strategic voting is thus unambiguously beneficial under (...) a utilitarian evaluation of outcomes. What has been considered the main argument for IIA turns out to be one against it. This paper assesses the implications of these results for interpretations of Arrow's theorem and the Gibbard-Satterthwaite theorem in a discussion on the methodological and philosophical arguments concerning preference intensities and IIA. (shrink)

Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, it is (...) basically impracticable to maintain logic–and–metalogic without paying heed to cognitive theorizing. For it is cognitively irrelevant whether possible conclusions are deduced from some premises before the premises are determined to be true or whether the premises themselves are determined to be true first and, then, the conclusions are deduced from them. In this paper we consider the term metalogic as inherently embodied under the framework referred to as cognitive science and mathematics. We propose a metalogical interpretation of Arrow’s impossibility theorem and, to that end, choice theory is understood as a mental course of action dealing with logic and metalogic issues, in which a possible mathematical approach to model a mental course of action is adopted as a systematic operating method. Nevertheless, if we look closely at the core of Arrow’s impossibility theorem in terms of metalogic, a second fundamental contribution to this framework is represented by the Nash equilibrium. As a result of the foregoing, therefore, we prove the metalogical equivalence between Arrow’s impossibility theorem and the existence of the Nash equilibrium. More specifically, Arrow’s requirements correspond to the Nash equilibrium for finite mixed strategies with no symmetry conditions. To demonstrate this proof, we first verify that Arrow’s set and Nash’s set are isomorphic to each other, both sets being under stated conditions of non–symmetry. Then, the proof is completed by virtue of category theory. Indeed, the two sets are categories that correspond biuniquely to one another and, thus, it is possible to define a covariant functor that preserves their mutual structures. According to this, we show the proof–dedicated metalanguage as a precursor to a special equivalence theorem. (shrink)

This paper provides a generalized characterization of the family of independence conditions which are equivalent to independence of irrelevant alternatives by proposing a pair-based refinement of S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {S}$$\end{document}-independence. Equipped with the new result, the relation between external independence conditions and independence of irrelevant alternatives is explored.