scholarly journals Comparing Voting by Committees According to Their Manipulability

2017 ◽  
Vol 9 (4) ◽  
pp. 74-107 ◽  
Author(s):  
R. Pablo Arribillaga ◽  
Jordi Massó
Keyword(s):  
Equivalence Class ◽  
Binary Relation ◽  
Equivalence Classes ◽  
Simple Criterion ◽  
Upper Semilattice ◽  
Set Inclusion ◽  
Full Class ◽  
Voting By Committees

We consider the class of voting by committees to be used by a society to collectively choose a subset from a given set of objects. We offer a simple criterion to compare two voting by committees without dummy agents according to their manipulability. This criterion is based on the set-inclusion relationships between the two corresponding pairs of sets of objects, those at which each agent is decisive and those at which each agent is vetoer. We show that the binary relation “to be as manipulable as” endows the set of equivalence classes of anonymous voting by committees (i.e., voting by quotas) with a complete upper semilattice structure, whose supremum is the equivalence class containing all voting by quotas with the property that the quota of each object is strictly larger than one and strictly lower than the number of agents. Finally, we extend the comparability criterion to the full class of all voting by committees. (JEL D71, D72)

scholarly journals On the finiteness of the derived equivalence classes of some stable endomorphism rings

2020 ◽  
Vol 296 (3-4) ◽  
pp. 1157-1183 ◽  
Author(s):  
Jenny August
Keyword(s):  
Equivalence Class ◽  
Minimal Model ◽  
Equivalence Classes ◽  
Finite Dimensional Algebra ◽  
Derived Equivalence ◽  
Endomorphism Rings ◽  
Dimensional Algebra ◽  
Rigid Objects ◽  
Finite Dimensional ◽  
Frobenius Category

Abstract We prove that the stable endomorphism rings of rigid objects in a suitable Frobenius category have only finitely many basic algebras in their derived equivalence class and that these are precisely the stable endomorphism rings of objects obtained by iterated mutation. The main application is to the Homological Minimal Model Programme. For a 3-fold flopping contraction $$f :X \rightarrow {\mathrm{Spec}\;}\,R$$ f : X → Spec R , where X has only Gorenstein terminal singularities, there is an associated finite dimensional algebra $$A_{{\text {con}}}$$ A con known as the contraction algebra. As a corollary of our main result, there are only finitely many basic algebras in the derived equivalence class of $$A_{\text {con}}$$ A con and these are precisely the contraction algebras of maps obtained by a sequence of iterated flops from f. This provides evidence towards a key conjecture in the area.

Regent Results in Comma-Free Codes

1963 ◽  
Vol 15 ◽  
pp. 178-187 ◽  
Author(s):  
B. H. Jiggs
Keyword(s):  
Equivalence Class ◽  
Cyclic Permutation ◽  
Equivalence Classes ◽  
The Other ◽  
Complete Class

A set D of k-letter words is called a comma-free dictionary (2), if whenever (a1a2 . . . ak) and (b1b2 . . . bk) are in D, the "overlaps" (a2a3 . . . akb1), (a3a4 . . . akb1b2), . . . , (akb1 . . . bk-1) are not in D. We say that two k-letter words are in the same equivalence class if one is a cyclic permutation of the other. An equivalence class is called complete if it contains k distinct members. Comma-freedom is violated if we choose words from incomplete equivalence classes, or if more than one word is chosen from the same complete class.

Scalable l-Diversity

2019 ◽  
Vol 14 (2) ◽  
pp. 27-40
Author(s):  
Udai Pratap Rao ◽  
Brijesh B. Mehta ◽  
Nikhil Kumar
Keyword(s):  
Equivalence Class ◽  
Information Loss ◽  
Equivalence Classes ◽  
Data Publishing ◽  
Programming Paradigm ◽  
Research Areas ◽  
Complete Dataset ◽  
Input Dataset ◽  
Privacy Preserving Data Publishing ◽  
Cost Penalty

Privacy preserving data publishing is one of the most demanding research areas in the recent few years. There are more than billions of devices capable to collect the data from various sources. To preserve the privacy while publishing data, algorithms for equivalence class generation and scalable anonymization with k-anonymity and l-diversity using MapReduce programming paradigm are proposed in this article. Equivalence class generation algorithms divide the datasets into equivalence classes for Scalable k-Anonymity (SKA) and Scalable l-Diversity (SLD) separately. These equivalence classes are finally fed to the anonymization algorithm that calculates the Gross Cost Penalty (GCP) for the complete dataset. The value of GCP gives information loss in input dataset after anonymization.

scholarly journals Bipolar Fuzzy Relations

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1044 ◽  
Author(s):  
Jeong-Gon Lee ◽  
Kul Hur
Keyword(s):  
Equivalence Class ◽  
Level Set ◽  
Equivalence Relation ◽  
Level Sets ◽  
Equivalence Classes ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Transitive Relation ◽  
Fuzzy Partition

We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

scholarly journals The binomial equivalence classes of finite words

2020 ◽  
Vol 30 (07) ◽  
pp. 1375-1397
Author(s):  
Marie Lejeune ◽  
Michel Rigo ◽  
Matthieu Rosenfeld
Keyword(s):  
Nilpotent Group ◽  
Equivalence Class ◽  
Free Monoid ◽  
Equivalence Classes ◽  
Single Element ◽  
Free Nilpotent Group ◽  
Context Free ◽  
Abelian Equivalence

Two finite words [Formula: see text] and [Formula: see text] are [Formula: see text]-binomially equivalent if, for each word [Formula: see text] of length at most [Formula: see text], [Formula: see text] appears the same number of times as a subsequence (i.e., as a scattered subword) of both [Formula: see text] and [Formula: see text]. This notion generalizes abelian equivalence. In this paper, we study the equivalence classes induced by the [Formula: see text]-binomial equivalence. We provide an algorithm generating the [Formula: see text]-binomial equivalence class of a word. For [Formula: see text] and alphabet of [Formula: see text] or more symbols, the language made of lexicographically least elements of every [Formula: see text]-binomial equivalence class and the language of singletons, i.e., the words whose [Formula: see text]-binomial equivalence class is restricted to a single element, are shown to be non-context-free. As a consequence of our discussions, we also prove that the submonoid generated by the generators of the free nil-[Formula: see text] group (also called free nilpotent group of class [Formula: see text]) on [Formula: see text] generators is isomorphic to the quotient of the free monoid [Formula: see text] by the [Formula: see text]-binomial equivalence.

Transfer of Social Attributions in Stimulus Equivalence Classes by Preschool Children

1997 ◽  
Vol 80 (1) ◽  
pp. 3-21 ◽  
Author(s):  
Mark Egli ◽  
Beth Joseph ◽  
Travis Thompson
Keyword(s):  
Preschool Children ◽  
Antisocial Behavior ◽  
Equivalence Class ◽  
Stimulus Equivalence ◽  
Computer Game ◽  
Equivalence Classes ◽  
Antisocial Behaviors ◽  
Conditional Discriminations ◽  
Response Options ◽  
Social Attributions

The transfer of social attributions within stimulus-equivalence classes comprised of photographs of children was examined. Five children (mean age: 4 yr., 2 mo.) were taught conditional discriminations sufficient for the emergence of two 3-member equivalence classes (A1-B1-C1 and A2-B2-C2). Social attributions were established by using two photographs to identify fictional children who could facilitate (B1) or prevent (B2) the participant's reinforcement on a computer game. Transfer of attribution was assessed by asking the participants questions regarding predicted social behaviors by children in all six photographs. One set of questions pertained explicitly to the response-options of the computer game; a second set referred to other prosocial and antisocial behaviors. Three children chose photographs in response to questions consistent with their experience with members B1 and B2 of the shared equivalence class when the questions pertained to the computer game. One subject also selected photographs in response to questions about predicted prosocial and antisocial behavior which reflected her experience with the B1 and B2 photographs.

A survey of partial degrees

1975 ◽  
Vol 40 (2) ◽  
pp. 130-140 ◽  
Author(s):  
Leonard P. Sasso
Keyword(s):  
Equivalence Classes ◽  
Turing Machines ◽  
Systems Of Equations ◽  
Partial Functions ◽  
Enumeration Degrees ◽  
Upper Semilattice ◽  
Enumeration Reducibility ◽  
Turing Reducibility ◽  
Recursive Operators ◽  
Relative Enumerability

Partial degrees are equivalence classes of partial natural number functions under some suitable extension of relative recursiveness to partial functions. The usual definitions of relative recursiveness, equivalent in the context of total functions, are distinct when extended to partial functions. The purpose of this paper is to compare the upper semilattice structures of the resulting degrees.Relative partial recursiveness of partial functions was first introduced in Kleene [2] as an extension of the definition by means of systems of equations of relative recursiveness of total functions. Kleene's relative partial recursiveness is equivalent to the relation between the graphs of partial functions induced by Rogers' [10] relation of relative enumerability (called enumeration reducibility) between sets. The resulting degrees are hence called enumeration degrees. In [2] Davis introduces completely computable or compact functionals of partial functions and uses these to define relative partial recursiveness of partial functions. Davis' functionals are equivalent to the recursive operators introduced in Rogers [10] where a theorem of Myhill and Shepherdson is used to show that the resulting reducibility, here called weak Turing reducibility, is stronger than (i.e., implies, but is not implied by) enumeration reducibility. As in Davis [2], relative recursiveness of total functions with range ⊆{0, 1} may be defined by means of Turing machines with oracles or equivalently as the closure of initial functions under composition, primitive re-cursion, and minimalization (i.e., relative μ-recursiveness). Extending either of these definitions yields a relation between partial functions, here called Turing reducibility, which is stronger still.

Representations of Well-Founded Preference Orders

1983 ◽  
Vol 35 (3) ◽  
pp. 496-508 ◽  
Author(s):  
Douglas Cenzer ◽  
R. Daniel Mauldin
Keyword(s):  
Utility Function ◽  
Binary Relation ◽  
Linear Order ◽  
Equivalence Classes ◽  
Preference Order ◽  
Real Numbers ◽  
Order Preserving Map ◽  
Preference Orders ◽  
Reasonable Sense ◽  
Natural Relation

A preference order, or linear preorder, on a set X is a binary relation which is transitive, reflexive and total. This preorder partitions the set X into equivalence classes of the form . The natural relation induced by on the set of equivalence classes is a linear order. A well-founded preference order, or prewellordering, will similarly induce a well-ordering. A representation or Paretian utility function of a preference order is an order-preserving map f from X into the R of real numbers (provided with the standard ordering). Mathematicians and economists have studied the problem of obtaining continuous or measurable representations of suitably defined preference orders [4, 7]. Parametrized versions of this problem have also been studied [1, 7, 8]. Given a continuum of preference orders which vary in some reasonable sense with a parameter t, one would like to obtain a continuum of representations which similarly vary with t.

A Micro-Aggregation Algorithm Based on Density Partition Method for Anonymizing Biomedical Data

2019 ◽  
Vol 14 (7) ◽  
pp. 667-675 ◽  
Author(s):  
Xiang Wu ◽  
Yuyang Wei ◽  
Tao Jiang ◽  
Yu Wang ◽  
Shuguang Jiang
Keyword(s):  
Equivalence Class ◽  
Real Life ◽  
Equivalence Classes ◽  
Biomedical Data ◽  
Clustering Method ◽  
Data Utility ◽  
Density Based Clustering ◽  
High Utility ◽  
Partition Method

Objective: Biomedical data can be de-identified via micro-aggregation achieving privacy. However, the existing micro-aggregation algorithms result in low similarity within the equivalence classes, and thus, produce low-utility anonymous data when dealing with a sparse biomedical dataset. To balance data utility and anonymity, we develop a novel microaggregation framework. Methods: Combining a density-based clustering method and classical micro-aggregation algorithm, we propose a density-based second division micro-aggregation framework called DBTP . The framework allows the anonymous sets to achieve the optimal k- partition with an increased homogeneity of the tuples in the equivalence class. Based on the proposed framework, we propose a k − anonymity algorithm DBTP − MDAV and an l − diversity algorithm DBTP − l − MDAV to respond to different attacks. Conclusion: Experiments on real-life biomedical datasets confirm that the anonymous algorithms under the framework developed in this paper are superior to the existing algorithms for achieving high utility.

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