Securely implementable social choice rules with partially honest agents

We study a social choice model with partially honest agents, and we show that strategy-proofness is a necessary and sufficient condition to achieve secure implementation. This result provides a behavioral foundation for the rectangularity property; and it offers as a by-product a revelation principle for secure implementation with partial honesty. We apply the implementation concept to a single-crossing voting environment, and we prove that it characterizes, in combination with unanimity, the family of augmented representative voter schemes.