Some new domain restrictions in social choice, and their consequences

Restricting the domains of definition of social choice functions is a classical method to test the robustness of impossibility results and to find conditions under which attractive methods to reach collective decisions can be identified, satisfying different sets of desirable properties. We survey a number of domains that we have recently explored, and exhibit results emerging for functions defined on them. In particular, we have identified a condition called top monotonicity under which the core of voting rules is non-empty, a second one called sequential inclusion where individual and group strategy-proofness become equivalent, and still a third condition called intertwinedness where the strategy-proofness of social choice functions is guaranteed as soon as they satisfy very simple monotonicity and invariance requirements.