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

A Constrained Object Model for Configuration Based Workflow Composition

Automatic or assisted workflow composition is a field of intense research for applications to the world wide web or to business process modeling. Workflow composition is traditionally addressed in various ways, generally via theorem proving techniques. Recent research observed that building a composite workflow bears strong relationships with finite model search, and that some workflow languages can be defined as constrained object metamodels . This lead to consider the viability of applying configuration techniques to this problem, which was proven feasible. Constrained based configuration expects a constrained object model as input. The purpose of this document is to formally specify the constrained object model involved in ongoing experiments and research using the Z specification language.Comment: This is an extended version of the article published at BPM'05, Third International Conference on Business Process Management, Nancy Franc

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;