Thanks, everyone, for suggestions on my proposal below, and I'm especially honored that seasoned bettor Bryan offered a few suggestions (I also got a nice email with suggestions from EconLog friend Fabio Rojas, who noted that the selection biases in evaluations of homeschooling are considerable). What Bryan proposes would, I think, be excellent.
I should've phrased the last post not as an offer of a bet but perhaps rather as a call for bet proposals. As stated, the "bet" doesn't have clear terms because I'm not really sure of the measurable standards critics of homeschooling would cite as evidence against it apart from the obvious ones like ACT/SAT scores. I'm mostly interested in engaging people who are of the view that homeschooling is in some sense a bad idea--the people who ask "don't you worry about whether they'll be too sheltered?"
From my experience with homeschoolers, they bristle at the notion that they and their kids are inadequately socialized or inadequately exposed to diverse opinions because they forsake traditional education. Possible? Yes. Plausible? Perhaps. Probable? I doubt it, which is why I'm willing to bet. Perhaps I'm overestimating public skepticism about homeschooling, but I'm inclined to think not given existing skepticism about charter schools and vouchers.
So here's something a bit more specific, to be settled on April 9, 2033: the consensus in the literature on homeschooling will find that relative to people who attend public and private schools, the homeschooled will have mixes of friends of different races, religions, and socioeconomic backgrounds that are either statistically indistinguishable (insignificant at conventional levels) or statistically more diverse (significant at conventional levels). Here's one way to find this out: I would suspect that enough data will accumulate over the next two decades that we would be able to construct Herfindahl-Hirschman Indexes measuring the diversity of people's social networks. I suspect it's only a matter of time before people get access to data from Facebook, Google, and other websites that will help us arrive at clear answers to these questions.
Some were less than impressed with the stakes I offered ($100, nominal), so Iet's raise it to $500, real, adjusted for inflation with the CPI (I'm willing to go higher). I would also be interested in finding out whether there is an independent and nonpartisan organization out there that might be willing to commission such a study.