949 research outputs found
The measurement of opportunity inequality: a cardinality-based approach
We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on agents' preferences over individual opportunity sets, we formulate the analogues ofthe notions ofthe Lorenz partial ordering, equalizing Dalton transfers, and inequality averse social welfare functionals -concepts which play a central role in the literature on income inequality. For the particular case in which agents rank opportunity sets on the basis of their cardinalities, we establish an analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of equalizing transfers, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functionals. In addition, we characterize the smallest monotonic and transitive extension of the cardinality-based Lorenz inequality ordering
The measurement of opportunity inequality: a cardinality-based approach.
We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on agents' preferences over individual opportunity sets, we formulate the analogues ofthe notions ofthe Lorenz partial ordering, equalizing Dalton transfers, and inequality averse social welfare functionals -concepts which play a central role in the literature on income inequality. For the particular case in which agents rank opportunity sets on the basis of their cardinalities, we establish an analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of equalizing transfers, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functionals. In addition, we characterize the smallest monotonic and transitive extension of the cardinality-based Lorenz inequality ordering.Opportunity Inequality; Equalizing Transfers; Lorenz Domination;
Feat: Functional Enumeration of Algebraic Types
In mathematics, an enumeration of a set S is a bijective function from (an initial segment of) the natural numbers to S. We define "functional enumerations" as efficiently computable such bijections. This paper describes a theory of functional enumeration and provides an algebra of enumerations closed under sums, products, guarded recursion and bijections. We partition each enumerated set into numbered, finite subsets.
We provide a generic enumeration such that the number of each part corresponds to the size of its values (measured in the number of constructors). We implement our ideas in a Haskell library called testing-feat, and make the source code freely available. Feat provides efficient "random access" to enumerated values. The primary application is property-based testing, where it is used to define both random sampling (for example QuickCheck generators) and exhaustive enumeration (in the style of SmallCheck). We claim that functional enumeration is the best option for automatically generating test cases from large groups of mutually recursive syntax tree types. As a case study we use Feat to test the pretty-printer of the Template Haskell library (uncovering several bugs)
Triple-loop networks with arbitrarily many minimum distance diagrams
Minimum distance diagrams are a way to encode the diameter and routing
information of multi-loop networks. For the widely studied case of double-loop
networks, it is known that each network has at most two such diagrams and that
they have a very definite form "L-shape''.
In contrast, in this paper we show that there are triple-loop networks with
an arbitrarily big number of associated minimum distance diagrams. For doing
this, we build-up on the relations between minimum distance diagrams and
monomial ideals.Comment: 17 pages, 8 figure
Notes on cardinals that are characterizable by a complete (Scott) sentence
This is part I of a study on cardinals that are characterizable by Scott
sentences. Building on [3], [6] and [1] we study which cardinals are
characterizable by a Scott sentence , in the sense that
characterizes , if has a model of size , but no models
of size . We show that the set of cardinals that are characterized by
a Scott sentence is closed under successors, countable unions and countable
products (cf. theorems 2.3, 3.4, and corollary 3.6). We also prove that if
is characterized by a Scott sentence, at least one of
and is homogeneously characterizable (cf.
definition 1.3 and theorem 2.9). Based on Shelah's [8], we give counterexamples
that characterizable cardinals are not closed under predecessors, or
cofinalities.Comment: Version 2 replaces version 1 of the same paper (with the same title),
but version 2 contains only half of the content of version 1. The second half
of version 1 will be posted by itsel
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