Lifting Rationality Assumptions in Binary Aggregation
Umberto Grandi, Ulle Endriss
Abstract:
We consider problems where several individuals each need to
make a yes/no choice regarding a number of issues and these
choices then need to be aggregated into a collective choice.
Depending on the application at hand, different combinations
of yes/no may be considered rational. We can describe such
rationality assumptions in terms of a propositional formula.
The question then arises whether or not a given aggregation
procedure will lift the rationality assumptions from the individual
to the collective level, i.e., whether the collective
choice will be rational whenever all individual choices are.
To address this question, for each of a number of simple fragments
of the language of propositional logic, we provide an
axiomatic characterisation of the class of aggregation procedures
that will lift all rationality assumptions expressible in
that fragment.