{"product_id":"9781441950796","title":"Arrovian Aggregation Models","description":"\u003ch1\u003eArrovian Aggregation Models\u003c\/h1\u003e \u003ch2\u003e\u003c\/h2\u003e \u003cp\u003eAggregation of individual opinions into a social decision is a  problem widely observed in everyday life. For centuries people tried  to invent the `best' aggregation rule. In 1951 young American  scientist and future Nobel Prize winner Kenneth Arrow formulated the  problem in an axiomatic way, i.e., he specified a set of axioms which  every reasonable aggregation rule has to satisfy, and obtained that  these axioms are inconsistent. This result, often called Arrow's  Paradox or General Impossibility Theorem, had become a cornerstone of  social choice theory. The main condition used by Arrow was his famous  Independence of Irrelevant Alternatives. This very condition  pre-defines the `local' treatment of the alternatives (or pairs of  alternatives, or sets of alternatives, etc.) in aggregation  procedures. \u003cbr\u003e  Remaining within the framework of the axiomatic approach and based on  the consideration of local rules, \u003cem\u003eArrovian Aggregation Models\u003c\/em\u003e  investigates three formulations of the aggregation problem according  to the form in which the individual opinions about the alternatives  are defined, as well as to the form of desired social decision. In  other words, we study three aggregation models. What is common between  them is that in all models some analogue of the Independence of  Irrelevant Alternatives condition is used, which is why we call these  models Arrovian aggregation models. \u003cbr\u003e  Chapter 1 presents a general description of the problem of axiomatic  synthesis of local rules, and introduces problem formulations for  various versions of formalization of individual opinions and  collective decision. Chapter 2 formalizes precisely the notion of  `rationality' of individual opinions and social decision. Chapter 3  deals with the aggregation model for the case of individual opinions  and social decisions formalized as binary relations. Chapter 4 deals  with Functional Aggregation Rules which transform into a social choice  function individual opinions defined as choice functions. Chapter 5  considers another model \u0026amp;endash; Social Choice Correspondences when  the individual opinions are formalized as binary relations, and the  collective decision is looked for as a choice function. Several new  classes of rules are introduced and analyzed.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2010-12-07\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003e ISBN-10: 9781441950796\u003c\/p\u003e \u003cp\u003eISBN-13: 9781441950796\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4757-4542-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 244\u003c\/p\u003e ","brand":"Springer","offers":[{"title":"Default Title","offer_id":44358909886604,"sku":"9781441950796","price":99.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781441950796.jpg?v=1755096716","url":"https:\/\/lateknightbooks.com\/products\/9781441950796","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}