Decidability and manipulability in social choice

congratulate, very good idea suggest..

Decidability and manipulability in social choice

Skip to search form Skip to main content You are currently offline.

Decidability and manipulability in social choice

Some features of the site may not work correctly. DOI: Maus and H. Peters and T. MausH. PetersT. Abstract Gibbard [Gibbard, A. Manipulation of voting schemes: a general result.

Econometrica 41, —] and Satterthwaite [Satterthwaite, M. Strategy-proofness and Arrow's conditions: existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory 10,—] show that an anonymous social choice function with more than two alternatives in its range must be manipulable. View via Publisher. Save to Library. Create Alert. Launch Research Feed.

Share This Paper. Why does manipulation of social choices matter? Sato Does Incomplete Information Reduce Manipulability? Yuliya A. Veselova Topics from this paper. Citation Type. Has PDF. Publication Type. More Filters. Research Feed. View 1 excerpt. Dictatorship versus manipulability. View 1 excerpt, cites methods.

View 2 excerpts, cites results and methods. Gains from manipulating social choice rules. References Publications referenced by this paper.

Hd designs san jose swing

Minimal manipulability: anonymity and unanimity. Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions. View 2 excerpts, references background.

Assimp tutorial

View 1 excerpt, references results.Social choice theory is the study of collective decision processes and procedures.

It is not a single theory, but a cluster of models and results concerning the aggregation of individual inputs e. Central questions are: How can a group of individuals choose a winning outcome e. What are the properties of different voting systems?

When is a voting system democratic? How can a collective e. How can we rank different social alternatives in an order of social welfare? Social choice theorists study these questions not just by looking at examples, but by developing general models and proving theorems.

decidability and manipulability in social choice

Its influence extends across economics, political science, philosophy, mathematics, and recently computer science and biology. Apart from contributing to our understanding of collective decision procedures, social choice theory has applications in the areas of institutional design, welfare economics, and social epistemology.

The two scholars most often associated with the development of social choice theory are the Frenchman Nicolas de Condorcet — and the American Kenneth Arrow born Condorcet was a liberal thinker in the era of the French Revolution who was pursued by the revolutionary authorities for criticizing them.

After a period of hiding, he was eventually arrested, though apparently not immediately identified, and he died in prison for more details on Condorcet, see McLean and Hewitt In his Essay on the Application of Analysis to the Probability of Majority Decisionshe advocated a particular voting system, pairwise majority voting, and presented his two most prominent insights.

The first, known as Condorcet's jury theoremis that if each member of a jury has an equal and independent chance better than random, but worse than perfect, of making a correct judgment on whether a defendant is guilty or on some other factual propositionthe majority of jurors is more likely to be correct than each individual juror, and the probability of a correct majority judgment approaches 1 as the jury size increases. Suppose, for example, that one third of a group prefers alternative x to y to za second third prefers y to z to xand a final third prefers z to x to y.

Furthermore, no alternative is a Condorcet winneran alternative that beats, or at least ties with, every other alternative in pairwise majority contests. Condorcet anticipated a key theme of modern social choice theory: majority rule is at once a plausible method of collective decision making and yet subject to some surprising problems.

decidability and manipulability in social choice

Resolving or bypassing these problems remains one of social choice theory's core concerns. While Condorcet had investigated a particular voting method majority votingArrow, who won the Nobel Memorial Prize in Economics inintroduced a general approach to the study of preference aggregation, partly inspired by his teacher of logic, Alfred Tarski —from whom he had learnt relation theory as an undergraduate at the City College of New York Suppes Arrow considered a class of possible aggregation methods, which he called social welfare functionsand asked which of them satisfy certain axioms or desiderata.

decidability and manipulability in social choice

He proved that, surprisingly, there exists no method for aggregating the preferences of two or more individuals over three or more alternatives into collective preferences, where this method satisfies five seemingly plausible axioms, discussed below.

This result, known as Arrow's impossibility theoremprompted much work and many debates in social choice theory and welfare economics. William Riker —who inspired the Rochester school in political science, interpreted it as a mathematical proof of the impossibility of populist democracy e.

Others, most prominently Amartya Sen bornwho won the Nobel Memorial Prize, took it to show that ordinal preferences are insufficient for making satisfactory social choices. Commentators also questioned whether Arrow's desiderata on an aggregation method are as innocuous as claimed or whether they should be relaxed. The lessons from Arrow's theorem depend, in part, on how we interpret an Arrovian social welfare function. Sen argued that when a social planner seeks to rank different social alternatives in an order of social welfare thereby employing some aggregation rule as a welfare evaluation methodit may be justifiable to use additional information over and above ordinal preferences, such as interpersonally comparable welfare measurements e.

This view was influenced by neoclassical economics, associated with scholars such as Vilfredo Pareto —Lionel Robbins —John Hicks —co-winner of the Economics Nobel Prize with Arrow, and Paul Samuelson —another Nobel Laureate.

Tractrix horn vs exponential horn

Nowadays most social choice theorists have moved beyond the early negative interpretations of Arrow's theorem and are interested in the trade-offs involved in finding satisfactory decision procedures. Within this approach, Arrow's axiomatic method is perhaps even more influential than his impossibility theorem on the axiomatic method, see Thomson Here the aim is to identify a set of plausible necessary and sufficient conditions that uniquely characterize a particular solution or class of solutions to a given type of collective decision problem.

An early example is Kenneth May's characterization of majority rule, discussed below.A computational voting model ," Economics BulletinAccessEcon, vol.

Enelow, James M. More about this item Keywords Social choice ; agenda ; object construction ; hyperplane arrangement ; directed graphs ; algorithm ; NEP fields This paper has been announced in the following NEP Reports : NEP-MIC Microeconomics Statistics Access and download statistics Corrections All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact:. If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about. If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item.

If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation. Please note that corrections may take a couple of weeks to filter through the various RePEc services. Economic literature: papersarticlessoftwarechaptersbooks. FRED data. Decidability and manipulability in social choice. Registered: Luigi Marengo. We present a geometric model of social choice among bundles of interdependent elements, that we will call objects.

We show that the outcome of the social choice process is highly dependent on the way these bundles are formed. By bundling and unbundling the same set of constituent elements an authority enjoys a vast power of determining the social outcome, as locally or globally stable social optima can be created or eliminated.

At the same time, by bundling and unbundling elements, it is also possible to greatly increase or decrease decidability both because the likelihood of intransitive cycles varies and because the time required to reach a social optimum varies. In this paper we present a rigorous framework which allows us to study this trade-off between decidability and non-manipulability.

Corrections All material on this site has been provided by the respective publishers and authors. Louis Fed. Help us Corrections Found an error or omission? RePEc uses bibliographic data supplied by the respective publishers.In this paper, we develop on a geometric model of social choice among bundles of interdependent elements objects.

Social choice can be seen as a process of search for optima in a complex multidimensional space and objects determine a decomposition of such a space into subspaces. We present a series of numerical and probabilistic results which show that such decompositions in objects can greatly increase decidability, as new kind of optima called local and u-local are very likely to appear also in cases in which no generalized Condorcet winner exists in the original search space.

This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Springer, New York. Amendola G, Settepanella S Optimality in social choice.

Undecidability

J Math Sociol — Arrow K Social choice and individual values. Wiley, New York. Google Scholar. Banks J Sophisticated voting outcomes and covering relation. Soc Choice Welf — Oxford University Press, London.

Bernholz P Logrolling, arrow paradox and decision rules. Kyklos — University of Michigan Press, Ann Arbor. Q J Polit Sci — Condorcet de Caritat, J. Imprimerie Royale, Paris. Am J Polit Sci — Dutta B Covering sets and a new Condorcet choice correspondence.

Social Choice Theory

J Econ Theory — Am Polit Sci Rev — Fey M Choosing from a large tournament. Fryer R, Jackson M A categorical model of cognition and biased decision making.

Press J Theor Econ 8, Article 6. Cambridge University Press, Cambridge. Kramer GH Sophisticated voting over multidimensional choice spaces.

Gödel's Incompleteness Theorem - Numberphile

Lang J Vote and aggregation in combinatorial domains with structured preferences. Marengo L, Pasquali C The construction of choice.Dutta, Bhaskar, Enelow, James M. Peter Bernholz, Full references including those not matched with items on IDEAS More about this item Keywords Social choice ; object construction ; hyperplane arrangement ; probability ; tournament ; algorithm ; Statistics Access and download statistics Corrections All material on this site has been provided by the respective publishers and authors.

You can help correct errors and omissions. See general information about how to correct material in RePEc. For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact:. If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form. If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services. Economic literature: papersarticlessoftwarechaptersbooks. FRED data. Decidability in complex social choices. Registered: Luigi Marengo Davide Pirino. In this paper we develop on a geometric model of social choice among bundles of interdependent elements objects.

Social choice can be seen as a process of search for optima in a complex multi- dimensional space and objects determine a decomposition of such a space into subspaces. We present a series of numerical and proba- bilistic results which show that such decompositions in objects can greatly increase decidability, as new kind of optima called local and u-local are very likely to appear also in cases in which no generalized Condorcet winner exists in the original search space.

More about this item Keywords Social choice ; object construction ; hyperplane arrangement ; probability ; tournament ; algorithm ; Statistics Access and download statistics. Corrections All material on this site has been provided by the respective publishers and authors. Louis Fed. Help us Corrections Found an error or omission?

RePEc uses bibliographic data supplied by the respective publishers.We present a geometric model of social choice among bundles of interdependent elements, that we will call objects.

We show that the outcome of the social choice process is highly dependent on the way thesebundlesareformed. By bundlingandunbundlingthesameset of constituent elements an authority enjoys a vast power of determining the social outcome, as locally or globally stable social optima can be created or eliminated.

At the same time, by bundling and unbundling elements, it is also possible to greatly increase or decrease decidability both because the likelihood of intransitive cycles varies and because the time required to reach a social optimum varies. In this paper we present a rigorous framework which allows us to study this trade-off between decidability and non-manipulability.

Keywords: Social choice, agenda, object construction, hyperplane arrangement, directed graphs, algorithm.

Eaton m45 pulley

Documents: Advanced Search Include Citations. Abstract We present a geometric model of social choice among bundles of interdependent elements, that we will call objects. Powered by:.Please wait while the activity loads. If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled. If loading fails, click here to try again. Question 1. Question 1 Explanation:. Second and third will be undecidable. Hence, option D is Correct.

Question 2. Which of the following problems are decidable?

W204 crankcase breather

Question 2 Explanation:. Question 3. Which of the following are decidable? Whether the intersection of two regular languages is infinite II. Whether a given context-free language is regular III. Whether two push-down automata accept the same language IV. Whether a given grammar is context-free. Question 3 Explanation:.

A Intersection of two regular languages is regular and checking if a regular language is infinite is decidable. B Deciding regularity of a context free language is undecidable.

If so, L CFG is infinite otherwise it is finite. C Equality problem is undecidable for all languages except in case of finite automata i.

D We have to check if the grammar obeys the rules of CFG. If, it obeys such rules then it is decidable.


Yozshukinos

thoughts on “Decidability and manipulability in social choice

Leave a Reply

Your email address will not be published. Required fields are marked *

Back to top