Strategy-proof Non-dictatorial Social Choice Functions in Clockwise Circular Domain

Restricting domain had always been an approach to find out strategy proof social choice function in a voting setup where the society would choose one alternative from the individual preferences. By restricting the domain to a single peaked domain, Moulin (1980) found strategy-proof non-dictatorial social choice functions however, Sato (2010) shows that there does not exist any strategy-proof non-dictatorial choice function on a circular domain. Further restricting the circular domain to a clockwise circular domain, here we attempt to find all non-dictatorial social choice functions that are strategy proof on a clockwise circular domain. Many well-known social choice functions like majority rule, plurality rule, Instant runoff, Condorcet winner turns out to be manipulable whereas we find Borda count rule is strategy proof on a such domain for any number of agents and alternatives. We have defined two new SCF pairwise universal winner (PUW) rule and pairwise winner using plurality (PWP) rule which shows interesting properties. Both PUW and PWP are based on pairwise competition between alternatives, but the way a pairwise winner is decided is quite different. We found for two agents, PUW is strategy proof on clockwise circular domain. And PWP satisfies the monotone property on the clockwise circular domain for any number of agents and alternatives.