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Patrick, 
 
I would disagree that it is by mathematics that 
Samuelson carries out his "pigeonholing."  He does 
the pigeonholing first and then derives the mathematical 
implications for Pareto Optimality.  One can dispute 
the validity of the latter procedures (use of calculus 
to study optimization), but that is a distinct problem from 
what is at issue here. 
 
The real issue is the nature of "collective consumption 
goods."  Now, you are correct that Samuelson provided 
very little analysis of the property rights issues or possible 
alternative arrangements or specific aspects of non- 
excudability, etc. in his original papers, beyond simply 
asserting the likelihood of a non-optimal outcome from a 
vaguely specified laissez-faire outcome. 
 
However, subsequent discussions have made it clear 
that in the real world we see a spectrum between "pure 
private"and "pure public" goods.  For this intermediate 
spectrum, a variety of alternative arrangements along 
Coasian lines may be manageable. 
 
But, Samuelson was dealing with pure cases, food 
as a private good and national defense as a collective 
consumption good.  The hard fact is that when one is 
dealing with a pure collective consumption good, it is 
very hard if not impossible to assign any kind of individual 
property rights in any meaningful way.  That is what Samuelson 
showed, even if he did not draw out the argument fully. 
 
I think a reasonable response to this is to argue that there 
are in fact very few such pure collective consumption goods, 
rather than to dismiss Samuelson's analysis for having failed 
to deal with all the possible intermediate cases. 
 
Barkley Rosser 
 
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