Optimization of apportionments

Abstract

The situations in practice, which lead to apportionments, are multiple, including distribution of goods between benefits, elections, etc. In this monograph, the known results regarding mono-option and apportionment mono-criteria decision-making are systematized and developed. Along with those known in the field, the work includes: new indicators of disproportiona litity and apportionment methods; analytical expressions regarding the disproportionality of optimal solutions; conditions, in which some known methods do not allow obtaining the solution and their improvements; mathematical expectation of the values ​​of parameters of optimal solutions; new properties and quantitative estimation of apportionment methods regarding the disproportionality, compliance with the Quota rule, fav g the benefit, immunity to paradoxes, monotony, partitioning, and creation of coalitions; recommendations for the application of disproportionality indicators and apportionment methods in specific situations. The book can be useful to researchers and practitioners interested in current information on mono - option and apportionment decision-making, including collective.