"An obvious alternative is to have the government produce the [public] good and pay for it out of taxes. This may or may not be an improvement. The mechanism we rely on to make the government act in our interest – voting – itself involves the private production of a public good. When you spend time and energy deciding which candidate best serves the general interest and voting accordingly, most of the benefit of your expenditure goes to other people. You are producing a public good: a vote for the better candidate. That is a very hard public good to produce privately, since the public is a very large one: the whole population of the country. Hence it is very badly underproduced. The underproduction of that public good means that people do not find it in their interest to spend much effort deciding who is the best candidate – which in turn means that democracy does not work very well, so we cannot rely on the government to act in our interest."First, the "may or may not be" point is important. Notice economists are usually more willing to point out an externality problem than advocate an intervention. I'm sure almost all economists will acknowledge the public health externality problems associated with eating fast food and large sodas. There is an externality there - no doubt about it. But very few would say that that justifies Bloomberg's solution (although I'm sure there are some out there).
Now on to the point about the trouble with democracy. Friedman may get into this later (I haven't read the book), but I would add that this is exactly why federalism is so critical. Private production of "votes for the better candidate" is still out of reach (and presumably Friedman would go the extra step that I wouldn't), but we are narrowing the scale at which coordination would occur and bringing the consequences of policy choice closer to home, which raises the likelihood of it being an improvement. Currently, most Americans don't care or know all that much about state or local government. However, to a large extent that's a consequence of the erosion of federalism and it would presumably improve if federalism were to be bolstered.
Actually I think the problem is really worse than Friedman puts it here because often we have externalities that extend only relatively locally but that the federal government has taken the initiative in addressing - so not only is one person providing an externalized benefit to the whole country with their vote, but they are voting for a policymaker that is mismatched to the degree of externality he or she is addressing.
Another option besides federalism is the sort of Deweyan option of developing a culture of democratic responsibility. Try to influence people's preferences to make them want to seek out the better candidate and care about a well functioning system. Both, I think, are important. Because ultimately the observation about the public goods properties of a vote doesn't solve any problems. It's not like not having government is guaranteed to be a better option after making this observation. The observation only demonstrates that we cannot be sure one way or another whether government is the better option. We know that no government will underproduce the public good. We know that government may potentially still underproduce, get it right, or overproduce the public good (depending on the quality of the institutions). So what is optimal? It's not clear. What will improve the set of options we have to choose from, though? Federalism and Deweyan dedication to good democratic practice ought to improve the set of options we have to choose from. We may still choose the no-intervention route (that's often the choice, and for good reason), but when we think intervention is justified this ought to improve the outcomes associated with that intervention.