Paul Hewitt and I had an unproductive conversation a while back on the subject of labor productivity differentials (or the question of their existence, to be more precise). He referenced it at Overcoming Bias more recently and mentioned that he had posed a riddle for me at Unqualified Reservations. I found his comment here, but it was for an old post, so I will respond at my own blog.
I will work backward from the original issue to more recent ones. As stated earlier, my question was an empirical one about productivity. Signaling theory is irrelevant. Any misunderstanding of said theory on my part or even yours is irrelevant. Only productivity data (and I’m fine with mere proxies) is relevant.

Regarding prayer: by assuming that God is vindictive, I presume that also means God exists. Since we are also assuming that it is possible to regulate prayer, I presume that means the question of whether an omniscient God can hear verbally unspoken prayers is moot (either he can’t or we have brain police who can regulate thoughts). If indeed (as we appear to be assuming) “bad” prayers lead to disasters like the Great Flood (which I recall not having anything to do with prayers in the Bible, man-derived curses being more associated with rival Gods & religions), it makes sense to regulate them. I don’t see the relevance of signaling theory. God is either omniscient or like an automatic prayer-response machine, who does not try to separate noise from signal (according to the book of Job it may be completely fruitless for humans to try to speculate on God’s reasoning at all). Humans can signal to each other, but we are interested here in disasters caused by prayers rather than information about people gleaned from their prayers.

Finally, I agree that we already subsidize & require vaccination, and I think in that case there is sound economic reasoning behind it. I don’t think that characterizes the majority of medical spending or explains much of our policies. I don’t resort to the rational voter explanation in the assumption that they must explain all our policies, many of them have no sensible basis. People all across the political spectrum can agree on that, though they may disagree on particulars (though intellectual elites on different sides often have particulars they agree on as well). I can’t think of any externality/public-good arguments for education similar to those mentioned for medicine. I invite you to provide it here.

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