Browsing by Subject "Social choice--Mathematical models."

Now showing 1 - 14 of 14

Open Access
Cloning-proof social choice correspondences
(2011) Öztürk, Zeliha Emel
In this thesis study, we provide axiomatic characterizations of the well-known Condorcet and Plurality rules via consistency axioms when the alternative set is endogeneous, namely hereditariness and cloning-proofness. Cloningproofness is the requirement that the social choice rule be insensitive to the replication of alternatives, whereas hereditariness requires insensitivity to withdrawal of alternatives.
Open Access
Consistency
(1998) Özgür, Onur
In this study, we introduce a different mechanism with a hybrid ownership definition lying in between public and private ownership. Agents have claims over the endowments and the total production of the economy instead of having absolute ownership rights. We define social desirability as the following: an alternative x is socially preferred to an alternative y if the majority of the agents prefer x to y. In this context, we investigate whether the competitive equilibrium outcome is socially the most desirable outcome and whether there are other efficient outcomes socially preferred to the competitive equilibrium outcome. We use a voting scheme where agents vote on the production alternatives of the economy. We investigate if there is a voting rule that leads to the competitive equilibrium outcome and what kind of a rule this latter is. The central finding of the study is that, for a class of production and utility functions, there is a voting rule that leads to the competitive equilibrium outcome. Moreover, this is a weighted voting rule where agents’ votes are their initial claims. A second important contribution is the analysis of the process of candidate nomination, which is most of the time, neglected by social choice problems. Finally, we consider the transfer problem where agents make transfers to other agents to make them vote on specific alternatives.
Open Access
Do impossibility results survive in historically standard domains?
(2008) Gürer, Ebru
One of the major assumptions common to all impossibility results in social choice theory is that of ”full” or rich enough domain. Thus, a major stream of attempts has focused on how to restrict the domains of social choice functions in order to escape impossibilities, without paying much attention to the question of whether there exist actual societies with such restricted domains of preference profiles, however. The notion of an unrestricted domain is based on the assumption that the individuals form their preferences independent of each other. If one replaces this assumption by one under which individual preferences are clustered around a ”social norm” in a unipolar standard society, the question of how this kind of restricted domain restriction influences the existence of a Maskin monotonic, surjective and nondictatorial social choice function becomes important. We employ the so-called Manhattan metric to measure the degree of how clustered a society around a social norm is. We then try to characterize what degrees of clustering around a social norm allow us to escape impossibility results, in an attempt to shed some light on the question of whether impossibilities in social choice theory arise from assuming the existence of historically impossible societies.
Open Access
Essays on implementability and monotonicity
(2009) Pasin, Pelin
In this thesis we study the implementation problem with regard to the relation between monotonicity and implementability. Recent work in the field has shown that the implementability of a social choice rule strongly depends upon the compatibility between the monotonicity structures of the social choice rule and of the solution concept according to which implementation takes place. Different degrees of monotonicity of the social choice rules and game theoretic solution concepts can be determined via a generalized monotonicity function, strongest of which is called self-monotonicity. In this study, we determine the unique self-monotonicity of the Nash equilibrium concept and show that the monotonicities of a social choice rule are inherited from the unique selfmonotonicity of the Nash equilibrium concept via the mechanisms that implement it. In particular, we show that the essential monotonicity is inherited via the Maskin-Vind type mechanism which is widely used in the characterization results. We also give a new characterization of strong Nash implementable social choice rules via critical profiles. We show that coalitional monotonicity when conjoined with three more conditions is both necessary and sufficient for implementability. Finally we determine a subset of subgame perfect Nash implementable social choice rules that satisfies conditions defined obtained by critical profiles. The results that are obtained in this thesis strongly support the view that implementation theory can be rewritten in terms of monotonicity and that this provides a better understanding of the theory.
Open Access
Explorations of self-selective social choice functions
(1999) Ünel, Bülent
In this study, we analyze self-selective social choice functions focusing on whether one can escape dictatoriality. Two ways are examined: In the first attempt, the set of social choice functions is restricted to tops only. With this restriction, selfselectivity turns out to be equivalent to dictatoriality. In the second, the set of prefence profiles restricted to single-peaked ones. Here we show that there are some self-selective social choice functions which are not dictatorial.
Open Access
Implementation in dominant strategy equilibrium
(1995) Kıbrıs, Özgür
A social choice rule is any proposed solution to the problem of collective decision making and it embeds the normative features that can be attached to the mentioned problem. Implementation of social choice rules in dominant strategy equilibrium is the decentralization of the decision power among the agents such that the outcome that is a priori recommended by the social choice rule can be obtained as a dominant strategy equilibrium outcome of the game form which is endowed with the preferences of the individuals. This work has two features. First, it is a survey on the literature on implementation in dominant strategy and its link with the economic theory. Second, it constructs some new relationships among the key terms of the literature. In this framework, it states and proves a slightly generalized version of the Gibbard-Satterthwaite impossibility theorem. Moreover, it states and proves that the cardinality of a singlepeaked domain converges to zero as the number of alternatives increase to infinity.
Open Access
Implementation via code of rights
(2008) Yıldız, Kemal
Implementation of a social choice rule can be thought of as a design of power (re)distribution in the society whose ”equilibrium outcomes” coincide with the alternatives chosen by the social choice rule at any preference profile of the society. In this paper, we introduce a new societal framework for implementation which takes the power distribution in the society, represented by a code of rights, as its point of departure. We examine and identify how implementation via code of rights (referred to as gamma implementation) is related to classical Nash implementation via mechanism. We characterize gamma implementability when the state space on which the rights structure is to be specified consists of the alternatives from which a social choice is to be made. We show that any social choice rule is gamma implementable if it satisfies pivotal oligarchic monotonicity condition that we introduce. Moreover, pivotal oligarchic monotonicity condition combined with Pareto optimality is sufficient for a non-empty valued social choice rule to be gamma implementable. Finally we revisit liberal’s paradox of A.K. Sen, which turns out to fit very well into the gamma implementation framework.
Open Access
Majority voting rule and oligarchic social choice rules
(2001) Pasin, Pelin
In the first part of this study majority voting rule for two alternatives and continuum agents is characterized. As in the finite agent case, symmetry among agents, neutrality between alternatives and positive responsiveness characterize majority voting rule. In the second part, the relation between T-monotonicity and the group which acts as the oligarchy in an oligarchic social choice rule, is analyzed. It is shown that the minimal coalition for which the social choice rule is monotonic constitutes the oligarchy.
Open Access
Measuring self-selectivity via generalized Condorcet rules
(2011) Altuntaş, Açelya
In this thesis, we introduce a method to measure self-selectivity of social choice functions. Due to Koray [2000], a neutral and unanimous social choice function is known to be universally self-selective if and only if it is dictatorial. Therefore, in this study, we confine our set of test social choice functions to particular singleton-valued refinements of generalized Condorcet rules. We show that there are some non-dictatorial self-selective social choice functions. Moreover, we define the notion of self-selectivity degree which enables us to compare social choice functions according to the strength of their selfselectivities. We conclude that the family of generalized Condorcet functions is an appropriate set of test social choice functions when we localize the notion of self-selectivity.
Open Access
Median rule and majoritarian compromise
(2013) Polat, Ali Oğuz
In this thesis, we analyze the relationship between Majoritarian Compromise (Sertel & Yılmaz, 1984) and the Median Rule (Basset & Persky, 1999). We show that, for the populations with odd size, these two rules are equivalent and we describe the relationship for the case where population size is even. Then, we explore some axiomatic properties of Median Rule. It turns out that Median Rule satisfies all properties that Majoritarian Compromise satisfies in Sertel and Yılmaz (1999) and it fails all properties that Majoritarian Compromise fails in Sertel and Yılmaz (1999). We, then, introduce two axioms which differentiate these rules. We conclude that, the Median Rule can be considered as a viable alternative to Majoritarian Compromise, as it satis- fies all axioms that Majoritarian Compromise is known to satisfy except one particular axiom.
Open Access
Preservation of implementability under algebraic operations
(2011) Doğan, Serhat
In this thesis, we investigate whether union and intersection preserve Nash and subgame perfect implementability. Nash implementability is known to be preserved under union. Here we first show that, under some reasonably mild assumptions, Nash implementability is also preserved under intersection. The conjunction of these two results yields an almost lattice-like structure for Nash implementable social choice rules. Next, we carry over these results to subgame perfect implementability by employing similar arguments. Finally, based on the fact that Nash implementable social choice rules are closed under union, we provide a new characterization of Nash implementability, which also exemplifies the potential use of our findings for further research.
Open Access
Some results on monotonicity
(2010) Dindar, Hayrullah
In this thesis, we investigate several issues concerning social choice rules which satisfy different degrees of Maskin type monotonicities. Firstly, we introduce g −monotonicity and monotonicity region notions which enable one to compare monotonicity properties of non Maskin monotonic social choice rules. We compare self-monotonicities of standard scoring rules and study monotonicity of Majoritarian compromise. Secondly we determine domains of impossibility and possibility when the individual preferences are clustered around two opposing norms and the degree of clustering is measured via the M anhattan metric. In the last chapter we investigate the relation between monotonicity and dictatoriality when agents are allowed to have thick indifference classes.
Open Access
Two essays in social choice theory
(2000) Kaya, Ayça
Solution concepts which implement only monotonic social choice rules are characterized in terms of a new notion of monotonicity pertaining to solution concepts. For any given class G of mechanisms, it turns out that a solution concept a implements only monotonic social choice rules via mechanisms in G if and only if a is G-monotonic. Moreover, with each solution concept a, we associate a class G^ of mechanisms such that each a-implementable onto social choice function which takes on at least three different values is dictatorial if and only if a is Go-monotonic. Oligarchic social choice rules are characterized by the conjunction of unanimity and a monotonicity condition, oligarchic monotonicity, which is stronger than Maskin monotonicity. Given an oligarchic social choice rule, the coalition acting as the oligarchy turns out to be the minimal set T of agents such that the social choice mle is Maskin monotonic when the restriction of each profile to T is considered. Finally, the solution concepts which implement only oligarchic social choice rules are characterized in terms of oligarchic monotonicity modified for solution concepts.
Open Access
Universally selection-closed families of social choice functions
(2009) Şenocak, Talat
In this thesis, we introduce a new notion of consistency for families of social choice functions, called selection-closedness. This concept requires that every member of a family of social choice functions that are to be employed by a society to make its choice from an alternative set it faces, should choose a member of the given family, when it is also employed to choose the social choice function itself in the presence of other rival such functions along with the members of the initial family. We show that a proper subset of neutral social choice functions is universally selection-closed if and only if it is a subset of the set of dictatorial and anti-dictatorial social choice functions. Finally, we introduce a weaker version of selection-closedness and conclude that a “rightextendable scoring correspondence” is strict if and only if the set consisting of its singleton valued refinements is universally weakly selection-closed.