Strategic Requirements with Indifference: Single-Peaked versus Single-Plateaued Preferences

• Authors: Dolors Berga and Bernardo Moreno.
• BSE Working Paper: 325 | September 15
• Keywords: Strategy-proof , Single-plateaued preferences , Single-peaked prefer-ences , Maskin monotonicity , Non-bossyness , Plateau-invariance.
• JEL codes: D71
• Strategy-proof
• Single-plateaued preferences
• Single-peaked prefer-ences
• Maskin monotonicity
• Non-bossyness
• Plateau-invariance.

We concentrate on the problem of the provision of one pure public good whenever agents that form the society have either single-plateaued preferences or single-peaked preferences over the set of alternatives. We are interested in comparing the relationships between different nonmanipulability notions under these two domains. On the single-peaked domain, under strategy-proofness, non-bossyness is equivalent to convex range. Thus, minmax rules are the only strategy-proof non-bossy rules. On the single-plateaued domain, only constant rules are non-bossy or Maskin monotonic; but strategy-proofness and weak non-bossy are equivalent to strict Maskin monotonicity. Moreover, strategy-proofness and plateau-invariant guarantee convexity of the range.