scholarly journals Roberts’ weak welfarism theorem: a minor correction

2021 ◽  
Author(s):  
Peter J. Hammond
Keyword(s):  
Euclidean Space ◽  
Social Welfare ◽  
Utility Function ◽  
Weak Continuity ◽  
Strict Preference ◽  
Counter Example ◽  
Independence Of Irrelevant Alternatives ◽  
Unrestricted Domain ◽  
A Minor ◽  
Minor Correction

AbstractRoberts’ “weak neutrality” or “weak welfarism” theorem concerns Sen social welfare functionals which are defined on an unrestricted domain of utility function profiles and satisfy independence of irrelevant alternatives, the Pareto condition, and a form of weak continuity. Roberts (Rev Econ Stud 47(2):421–439, 1980) claimed that the induced welfare ordering on social states has a one-way representation by a continuous, monotonic real-valued welfare function defined on the Euclidean space of interpersonal utility vectors—that is, an increase in this welfare function is sufficient, but may not be necessary, for social strict preference. A counter-example shows that weak continuity is insufficient; a minor strengthening to pairwise continuity is proposed instead and its sufficiency demonstrated.

The Compressibility of Rubber

1930 ◽  
Vol 3 (4) ◽  
pp. 555-562 ◽  
Author(s):  
L. H. Adams ◽  
R. E. Gibson
Keyword(s):  
High Pressures ◽  
Sulfur Compound ◽  
Reliable Estimate ◽  
Total Sulfur ◽  
Tetramethylthiuram Disulfide ◽  
Three Samples ◽  
Inorganic Fillers ◽  
A Minor ◽  
Low Pressures ◽  
Minor Correction

Abstract Although many of the elastic properties of rubber have been investigated with very interesting results, no measurements have been made, so far as we know, of its cubic compressibility at high pressures. Those measurements which have been made at low pressures yield results varying from 93×10−6 obtained by Clapeyron to an estimate of the order of the compressibility of bronze (about 1×10−6) given by Amagat. As the compressibility of rubber enters as a minor correction into most compressibility measurements at high pressures, it is very desirable to have a reliable estimate of its value. In this communication we propose to give the results of experimental determinations of the compressibility at 25° of three samples of rubber which were furnished to us by H. L. Curtis and A. H. Scott of the U. S. Bureau of Standards. The samples are described as follows: Sample A.—Hard rubber from panel made by the Goodrich Company. It is a rubber-sulfur compound containing no inorganic fillers. The total sulfur amounts to 27.4 per cent, of which 0.21 per cent, is free sulfur. The density is 1.149 at 27° C. Sample B.—A rubber-sulfur compound containing 90 per cent. smoked rubber and 10 per cent. sulfur and vulcanized 105 minutes at 300° F. Density = 0.990 at 25°. Sample C consists of pale crepe rubber 90.75 per cent., zinc oxide 5 per cent., sulfur 4 per cent., tetramethylthiuram disulfide 0.25 per cent. It was vulcanized for 30 minutes at 260° F. Density = 0.990 at 27°.

scholarly journals Condorcet's Theory of Voting

1988 ◽  
Vol 82 (4) ◽  
pp. 1231-1244 ◽  
Author(s):  
H. P. Young
Keyword(s):  
Social Welfare ◽  
Social Welfare Function ◽  
Optimal Choice ◽  
Simple Majority ◽  
Independence Of Irrelevant Alternatives ◽  
Correct Rule

Condcrcet's criterion states that an alternative that defeats every other by a simple majority is the socially optimal choice. Condorcet argued that if the object of voting is to determine the “best” decision for society but voters sometimes make mistakes in their judgments, then the majority alternative (if it exists) is statistically most likely to be the best choice. Strictly speaking, this claim is not true; in some situations Bordas rule gives a sharper estimate of the best alternative. Nevertheless, Condorcet did propose a novel and statistically correct rule for finding the most likely ranking of the alternatives. This procedure, which is sometimes known as “Kemeny's rule,” is the unique social welfare function that satisfies a variant of independence of irrelevant alternatives together with several other standard properties.

scholarly journals Homogeneous Premium Calculation Principles

1984 ◽  
Vol 14 (2) ◽  
pp. 123-133 ◽  
Author(s):  
Axel Reich
Keyword(s):  
Utility Function ◽  
General Theorem ◽  
Random Variables ◽  
Continuity Condition ◽  
Weak Continuity ◽  
Local Homogeneity ◽  
Diophantine Approximations ◽  
Premium Calculation

AbstractA premium calculation principle π is called positively homogeneous if π(cX) = cπ(X) for all c > 0 and all random variables X. For all known principles it is shown that this condition is fulfilled if it is satisfied for two specific values of c only, say c = 2 and c = 3, and for only all two point random variables X. In the case of the Esscher principle one value of c suffices. In short this means that local homogeneity implies global homogeneity. From this it follows that in the case of the zero utility principle or Swiss premium calculation principle, the underlying utility function is of a very specific type.A very general theorem on premium calculation principles which satisfy a weak continuity condition, is added. Among others the proof uses Kroneckers Theorem on Diophantine Approximations.

A note on rigidity of spacelike self-shrinkers

2020 ◽  
Vol 31 (05) ◽  
pp. 2050035
Author(s):  
Yong Luo ◽  
Hongbing Qiu
Keyword(s):  
Euclidean Space ◽  
Growth Condition ◽  
Fundamental Form ◽  
Mean Curvature ◽  
Integral Method ◽  
Acta Math ◽  
Second Fundamental Form ◽  
The Second Fundamental Form ◽  
The Mean ◽  
A Minor

By using the integral method, we prove a rigidity theorem for spacelike self-shrinkers in pseudo-Euclidean space under a minor growth condition in terms of the mean curvature and the second fundamental form, which generalizes Theorem 1.1 in [H. Q. Liu and Y. L. Xin, Some Results on Space-Like Self-Shrinkers, Acta Math. Sin. (Engl. Ser.) 32(1) (2016) 69–82].

scholarly journals A Comprehensive Approach to Revealed Preference Theory

2017 ◽  
Vol 107 (4) ◽  
pp. 1239-1263 ◽  
Author(s):  
Hiroki Nishimura ◽  
Efe A. Ok ◽  
John K.-H. Quah
Keyword(s):  
Euclidean Space ◽  
Utility Function ◽  
Revealed Preference ◽  
Consumer Theory ◽  
Choice Data ◽  
Preference Theory ◽  
Positive Orthant ◽  
Intertemporal Consumption ◽  
Afriat’S Theorem ◽  
Revealed Preference Theory

We develop a version of Afriat's theorem that is applicable in a variety of choice environments beyond the setting of classical consumer theory. This allows us to devise tests for rationalizability in environments where the set of alternatives is not the positive orthant of a Euclidean space and where the rationalizing utility function is required to satisfy properties appropriate to that environment. We show that our results are applicable, amongst others, to choice data on lotteries, contingent consumption, and intertemporal consumption. (JEL D11, D81)

A correction to Lewis and Langford's Symbolic logic

1940 ◽  
Vol 5 (4) ◽  
pp. 149-149
Author(s):  
J. C. C. McKinsey
Keyword(s):  
The Other ◽  
Symbolic Logic ◽  
Minor Error ◽  
Counter Example ◽  
Other Hand ◽  
Image Position ◽  
A Minor

The purpose of this note is to call attention to a minor error in Lewis and Langford's Symbolic logic. On page 221, in discussing the Tarski-Łukasiewicz three-valued logic, the authors make the following assertion: “Let T(p) be any proposition, involving only one element, whose analogue holds in the two-valued system; if T(p) does not hold in the Three-valued Calculus, then pC.T(p) and Np.C.T(p) both hold.”I shall show, by means of a counter-example, that this assertion is not true. Let T(p) be the sentence:It is then easily verified that T(0) = T(1) = 1, and that T(½) = 0. Thus T(p) holds in the two-valued calculus, but not in the three-valued calculus. On the other hand, pC.T(p) does not hold, since ½.CT(½) = ½C0 = ½; similarly, Np.C.T(p) does not hold, since N½.C.T(½) = ½C0 = ½.

A counter-example to ‘Wagner's conjecture’ for infinite graphs

1988 ◽  
Vol 103 (1) ◽  
pp. 55-57 ◽  
Author(s):  
Robin Thomas
Keyword(s):  
Graph Theory ◽  
Planar Graphs ◽  
Infinite Sequence ◽  
Infinite Graphs ◽  
Famous Theorem ◽  
Finite Graphs ◽  
Counter Example ◽  
Excluded Minor ◽  
A Minor ◽  
Forbidden Minors

Wagner made the conjecture that given an infinite sequence G1, G2, … of finite graphs there are indices i < j such that Gi is a minor of Gj. (A graph is a minor of another if the first can be obtained by contraction from a subgraph of the second.) The importance of this conjecture is that it yields excluded minor theorems in graph theory, where by an excluded minor theorem we mean a result asserting that a graph possesses a specified property if and only if none of its minors belongs to a finite list of ‘forbidden minors’. A widely known example of an excluded minor theorem is Kuratowski's famous theorem on planar graphs; one of its formulations says that a graph is planar if and only if it has neither K5 nor K3, 3 as a minor. But several other excluded minor theorems have been discovered by now (see e.g. [7–9]).

scholarly journals Gradient of mean mass of a star in the field of globular clusters

2007 ◽  
pp. 47-52
Author(s):  
A. Valjarevic
Keyword(s):  
Density Profile ◽  
Surface Density ◽  
Globular Clusters ◽  
Surface Brightness ◽  
Star Clusters ◽  
Segregation Phenomenon ◽  
Mass Segregation ◽  
A Minor ◽  
Minor Correction

Based on the relevant available data, the distributions of masses and apparent magnitudes of stars belonging to globular star clusters are simulated. The simulations are aimed at examining the influence of the mass-segregation phenomenon on the surface-density profile. It is found that a minor correction should be introduced in order to infer the profile of the surface density from that of the surface brightness. .

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