Arrow's Theorem, Weglorz' Models and the Axiom of Choice
نویسندگان
چکیده
Applying Weglorz’ models of set theory without the axiom of choice, we investigate Arrow-type social welfare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying “finite discrimination”, if and only if in Weglorz’ model there is a free ultrafilter on a set representing the individuals. AMS-subject classification. 03E35 (Consistency and Independence Proofs), 90A08 (Social Choice)
منابع مشابه
On Tychonoff's type theorem via grills
Let ${X_{alpha}:alphainLambda}$ be a collection of topological spaces, and $mathcal {G}_{alpha}$ be a grill on $X_{alpha}$ for each $alphainLambda$. We consider Tychonoffrq{}s type Theorem for $X=prod_{alphainLambda}X_{alpha}$ via the above grills and a natural grill on $X$ related to these grills, and present a simple proof to this theorem. This immediately yields the classical theorem...
متن کاملArrow's Axiom and Full Rationality for Fuzzy Choice Functions
A classical result for crisp choice functions shows the equivalence between Arrow axiom and the property of full rationality. In this paper we study a fuzzy form of Arrow axiom formulated in terms of the subsethood degree and of the degree of equality (of fuzzy sets). We prove that a fuzzy choice function verifies Fuzzy Arrow Axiom if and only if it is (fuzzy) full rational. We also show that t...
متن کاملOn characterizations of the fully rational fuzzy choice functions
In the present paper, we introduce the fuzzy Nehring axiom, fuzzy Sen axiom and weaker form of the weak fuzzycongruence axiom. We establish interrelations between these axioms and their relation with fuzzy Chernoff axiom. Weexpress full rationality of a fuzzy choice function using these axioms along with the fuzzy Chernoff axiom.
متن کاملArrow theorems in the fuzzy setting
Throughout this paper, our main idea is to analyze the Arrovian approach in a fuzzy context, paying attention to different extensions of the classical Arrow's model arising in mathematical Social Choice to aggregate preferences that the agents define on a set of alternatives. There is a wide set of extensions. Some of them give rise to an impossibility theorem as in the Arrovian classical mod...
متن کاملRational Choice Theory: A Cultural Reconsideration
Economists have heralded the formulation of the expected utility theorem as a universal method of choice under uncertainty. In their seminal paper, Stigler and Becker (Stigler & Becker, 1977) declared that “human behavior can be explained by a generalized calculus of utility-maximizing behavior” (p.76). The universality of the rational choice theory has been widely criticized by psychologists, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Log. Q.
دوره 46 شماره
صفحات -
تاریخ انتشار 2000