The "efficiency" of a solution depends entirely on people's valuations. And people's valuations can only be revealed by honest sacrifice. Dishonest sacrifice is correlated with inefficient solutions. The free-rider problem is when shortages are the consequence of people's allocations (how much they spend/sacrifice) being less than their valuations.
I derived some positive value from reading this blog entry that Katja Grace took the time and made the effort to produce. But, I haven't allocated any money to her which means that my allocation is less than my valuation. Is this the free-rider problem? It's a problem if it results in a shortage of her blog entries. The more of her readers who are dishonest (allocation < valuation) with her... and the greater their dishonesty.... the more likely it is that a shortage will occur. Dishonest sacrifice is inaccurate communication and suboptimal incentive.
If you truly understand the problem with dishonesty... then you should understand the problem with democracy. Other than the opportunity costs, voting doesn't require sacrifice... but you're only going to vote for things that you positively value. This means that your allocation will always be less than your valuation. Democracy is dishonesty... it's inaccurate communication and suboptimal incentive.
You think democracy helps the poor but in reality, it hurts everybody... especially the poor. Poverty would be eliminated if people truly understood the importance of honesty.
With a Coasian system, I have no idea how much money the poor would be willing to pay for progressive taxation. But if we actually implemented coasianism it would mean that people understood the importance of honesty... which would mean that taxpayers would also be able to choose where their taxes go. If, via coasianism, the wealthy managed to win a more regressive system... then this would logically give them less influence over public goods. Would the wealthy really want less influence over public goods?
Personally, I'm guessing that if people understood the importance of honesty that the tax rate would increase and the public sector would expand to include digital goods (ie music, videos, blogs). We'd have no reason to be dishonest with Katja Grace.
Regarding coasianism and speculation...
It is impossible for anyone, even if he be a statesman of genius, to weigh the whole community's utility and sacrifice against each other. - Knut Wicksell, A New Principle of Just Taxation
If it would be easy to predict which side would win then coasianism would be a waste of everybody's time.