Strategy-proof and symmetric social choice functions for public good economies

We study economies with one private good and one pure public good, and cons ider the following axioms of social choice functions. Strategy-proofness sa ys that no agent can benefit by misrepresenting his preferences, regardless of whether the other agents misrepresent or not, and whatever his preferen ces are. Symmetry says that if two agents have the same preference, they mu st be treated equally. Anonymity says that when the preferences of two agen ts are switched, their consumption bundles are also switched. Individual ra tionality says that a social choice function never assigns an allocation wh ich makes some agent worse off than he would be by consuming no public goad and paying nothing. In Theorem 1, we characterize the class of strategy-pr oof, budget-balancing, and symmetric social choice functions, assuming conv exity of the cost function of the public good. In Theorem 2, we characteriz e the class of strategy-proof, budget-balancing, and anonymous social choic e functions. In Theorem 3, we characterize the class of strategy-proof, bud get-balancing, symmetric, and individually rational social choice functions .