In a recent paper (Okasha, Mind 120:83–115, 2011), Samir Okasha uses Arrow’s theorem to raise a challenge for the rationality of theory choice. He argues that, as soon as one accepts the plausibility of the assumptions leading to Arrow’s theorem, one is compelled to conclude that there are no adequate theory choice algorithms. Okasha offers a partial way out of this predicament by diagnosing the source of Arrow’s theorem and using his diagnosis to deploy an approach that circumvents it. In (...) this paper I explain why, although Okasha is right to emphasise that Arrow’s result is the effect of an informational problem, he is not right to locate this problem at the level of the informational input of a theory choice rule. Once the informational problem is correctly located, Arrow’s theorem may be dismissed as a problem. (shrink)

The purpose of this article is to introduce a Cartesian product structure into the social choice theoretical framework and to examine if new possibility results to Gibbard’s and Sen’s paradoxes can be developed thanks to it. We believe that a Cartesian product structure is a pertinent way to describe individual rights in the social choice theory since it discriminates the personal features comprised in each social state. First we define some conceptual and formal tools related to the Cartesian product structure. (...) We then apply these notions to Gibbard’s paradox and to Sen’s impossibility of a Paretian liberal. Finally we compare the advantages of our approach to other solutions proposed in the literature for both impossibility theorems. (shrink)

In this paper we consider several ways in which voting systems can be manipulated and we pose some related ethical questions. Our focus is on the recent phenomenon of vote trading or vote swapping that was invented in 2000 and used in the 2000 and 2004 U.S. Presidential elections. Vote trading is an Internet-based technique that sought to allow Democrats in heavily Republican states (like Texas) to effectively vote in swing states (like Florida), where their votes would have more impact. (...) We also look at some other new ways that voting systems can be manipulated and we consider the general question of whether there exist voting systems that cannot be manipulated. (shrink)

Sen’s Liberal paradox describes a conflict between weak Pareto, minimal liberalism, and either transitivity or a best element over a domain of individual preferences. This paper examines variants of that paradox with varying amounts of unconditional preferences. We define a notion of unconditional preferences under which, in the absence of Pareto, there can be no cycles. We then define a stronger condition, that makes an individual’s preferences for her own private attributes independent of all other attributes. Under this assumption, there (...) can be no cycles with or without Pareto. We also show there exists a social decision function satisfying those conditions. We then determine the probability of a cycle assuming a much weaker independence condition that does not restrict the domain. This probability converges to one as the number of non-private attributes within the social states increases. Finally, we use simulations to determine the probability that liberalism and Pareto conflict with best elements, maximal elements, and transitivity separately. (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.

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)