  A collective choice problem is a finite set of social alternatives and a
finite set of economic agents with vNM utility functions. We associate a public
goods economy with each collective choice problem and establish the existence
and efficiency of (equal income) Lindahl equilibrium allocations. We interpret
collective choice problems as cooperative bargaining problems and define a
set-valued solution concept, {\it the equitable solution} (ES). We provide
axioms that characterize ES and show that ES contains the Nash bargaining
solution. Our main result shows that the set of ES payoffs is the same a the
set of Lindahl equilibrium payoffs. We consider two applications: in the first,
we show that in a large class of matching problems without transfers the set of
Lindahl equilibrium payoffs is the same as the set of (equal income) Walrasian
equilibrium payoffs. In our second application, we show that in any discrete
exchange economy without transfers every Walrasian equilibrium payoff is a
Lindahl equilibrium payoff of the corresponding collective choice market.
Moreover, for any cooperative bargaining problem, it is possible to define a
set of commodities so that the resulting economy's utility possibility set is
that bargaining problem {\it and} the resulting economy's set of Walrasian
equilibrium payoffs is the same as the set of Lindahl equilibrium payoffs of
the corresponding collective choice market.
