Rights Systems and Aggregation Functions on Property Spaces

The notion of a decisive coalitions of voters with different grades of decisiveness is a part of the mathematical framework for many models in social choice theory. More generally we study aggregation problems in which subgroup of decision-makers have the right to determine the properties of the aggregate. Then we introduce property spaces and rights to properties and characterise aggregation operators that are consistent with rights to properties. Moreover we define congruences in property spaces, and we propose a generalization of Sugeno integral in our framework.