Browsing by Subject "Social choice."

Now showing 1 - 10 of 10

Open Access
Essays in social choice theory
(2009) Erol, Selman
In this thesis, we investigate several issues concerning the class of Maskin monotonic social choice rules. Firstly, given a set of profiles, we find out which Maskin monotonic social choice rules adopt this set as a center. Then we introduce an algorithmic approach to find the self-monotonicities of a Maskin monotonic social choice rule. Moreover, we characterize all binary set operations that preserve Maskin monotonicity. Then we pass to investigating social choice functions, and determine the the domains of impossibility and possibility around a center with respect to a modified Manhattan metric. Finally, we try to reach a necessary and sufficient condition for Nash-implementability of a social choice in terms of neutrality
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 on monotonicity in social choice theory
(2007) Doğan, Battal
Due to Maskin (1977), Maskin-monotonicity is known to be a necessary condition for Nash-implementability. Once one classifies social choice rules as the ones which are Maskin-monotonic and those which are not, a natural question one may ask is whether it is possible to further classify the Maskinmonotonic social choice rules according to how strongly monotonic they are. This study utilizes two key notions , namely self-monotonicity and center, which enable us to compare Maskin-monotonic social choice rules among themselves according to the strength of their monotonicities. Moreover, Nashimplementable two-person social choice rules are now characterized via the notion of center, in line with the conjecture that Implementation Theory can be rewritten in terms of monotonicity
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
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
Party implementation
(2009) Apakan, Hasan Tahsin
In this study party implementation concept is introduced. Party implementation is an extension of classical implementation allowing different parties to have group-specific choice rules. Members of a party are assumed to act cooperatively according to a common preference. In this context, a choice rule is said to be party implementable if it is robust to co-operative manipulation. In this thesis some necessity and sufficiency results for party implementation are proven. In particular, it is shown that under some restrictions if the societies choice rule is party implementable, an alternative that is chosen by any group should also be chosen by the society. Conversely, it is shown that if the collective choice can be represented by the union of different groups’ choice, then the social choice rule should be party implementable.
Open Access
Stability of covers under different rights structures
(2012) Akbulut, Çiğdem
A countryís social welfare depends on Örmsí proÖts and consumersí surplus. Given unions of countries, a countryís aim is to maximize its own social welfare when it decides to enter or exit a union. For examining unions, we use the notion of a cover as elaborated in Koray (2007).We utilize the Öndings of Ilk¨l¨Á · (2010) about the Cournot equilibrium in our setting to examine core stability and e¢ ciency of covers of countries.We adapt di§erent rightsístructures based on; free exit, free entry, approved exit and approved entry introduced by Sertel (1992) to the context of covers, along with introducing some stronger structures and study how stability of covers varies when linkage costs are imposed upon countries.
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.