On strategy-proof social choice between two alternatives

We study strategy-proof rules for choosing between two alternatives. We consider the full preference domain which allows for indifference. In this framework, for strategy proof rules, ontoness does not imply efficiency. We weaken the requirement of efficiency to ontoness and characterizes the class of strategy-proof rules. We argue that the notion of effciency is not desirable always. Our main result provides a simple characterization of the class of onto, anonymous and strategy-proof rules in this framework. Our analysis can help policy makers choose among these rules.