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No it doesn't invalidate it, but it means that such an assertion is unjustified. You say that private provision will be less than the optimal amount. But you don't know wether this is neceassarily less or more than the level provided publicly. If the level of free riding increased while defence spending increased, it would be a non issue. Free riding leads to the problem of sub optimnal provision, but in itself is not the problem. Since the role of the ADF is to obstensibly reduce coercion, why provide a second best (to private provision) and sub optimal level of defence through a coercive system of funding? Saying that free riding is the problem is like analysing poverty traps and noting the rationality of welfare recipients is the problem.
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