## Working Papers,

Lund University, Department of Economics

# No 2005:3: Strategy-Proof Allocation of Multiple Public Goods

*Lars-Gunnar Svensson*
() and *Pär Torstensson*

Additional contact information

Lars-Gunnar Svensson: Department of Economics, Lund University, Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund, Sweden

Pär Torstensson: Department of Economics, Lund University, Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund, Sweden

**Abstract:** We characterize the set of strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. The set of feasible alternatives is a subset of a product set with a finite number of elements. We do not require the SCFs to be ‘onto’, but instead impose the weaker requirement that every element in each category of public goods is attained at some preference profile. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. We find that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial in each component of the range. If the range cannot be decomposed at all, the SCF is dictatorial in spite of the separability assumption on preferences, and a form of the Gibbard-Satterthwaite theorem with a restricted preference domain is obtained.

**Keywords:**
Strategy-proof; multiple public goods; decomposability; weakly onto; component-wise dictatorial.

**JEL-codes:**
D71; D78; H41

16 pages, First version: January 19, 2005.
Revised: February 2, 2007.

**Note:** The paper is forthcoming in "Social Choice and Welfare".

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