I doubt, in any event, that a more elaborate model will change the basic conclusion: that the deliberative prediction market provides at least some increased incentive to reveal information. I’ll let interested readers look at the original paper for a more developed argument (including math), but it boils down to a very simple point. A prediction market, as Robin and I both note, already provides some incentives to reveal information. But if a trader’s payoff depends on whether the trader actually succeeds at persuading others rather than on whether the trader turns out in the long run to be correct, the trader will have an additional incentive to reveal that information.

Relaxing the assumptions that Robin questions will not undermine this point. First, Robin notes that a trader may get more than one package of information. It’s possible that the deliberative market might lead someone to reveal first one package of information (pointing, say, to a higher value), wait to profit on that, and then reveal another package of information (pointing to a lower value), and cash in on that too.

So, the deliberative market could on occasion delay the release of some information packages. But those information packages might not have been released at all in the standard prediction market. Suppose that a trader in a standard prediction market conducts research that reveals two information packages that cancel each other out. The trader has no incentive to trade at all, let alone to reveal the two packages of information.

The bottom line is that I can’t think of any scenario in which the deliberative prediction market would result in less information revelation, and it might well result in more information revelation. Allowing private information exchange doesn’t undermine this either. Private information exchange can also allow a trader to cash out a position or, in the deliberative market, to make sure that the market does not move too much after the trader’s initial prediction.

Finally, I’m making a straightforward comparison in my paper (see p. 17), assessing the effect of two different possible compensation regimes in the same environment. Robin argues that the assumptions about this environment are unrealistic and that I would reach a different conclusion relaxing the assumptions (though I disagree above). But I just don’t see how I change either the explicit or implicit assumptions underlying the two regimes. Admittedly, I don’t explicitly model the information revelation incentives that already would exist in both markets, but I hold those constant in the two settings.

Robin’s post is valuable and helps point in the direction of useful research, even though Robin does not include a robust formal model to justify his claim that "we can easily get the same info revelation advantages" in the standard prediction market as in the deliberative market. I hope that Robin will agree that the concept of a deliberative market also is valuable and points in the direction of useful research, even though I support it with only three pages of math.

I’ll use this opportunity to respond briefly to his criticism (while gratefully accepting his praise). I agree that it’s best when technical designs for prediction markets can be supported by mathematical models or empirical evidence. At the same time, I didn’t want to scare away readers by including math. Meanwhile, I agree that field experiments can be helpful, and I am developing a web site that will test some of the ideas of the book (subject, of course and unfortunately, to legal restrictions). While recognizing the contributions of experimental economics, I doubt that laboratory experiments will be of much use in persuading skeptics that prediction markets can be useful in real-world institutions.

Nonetheless, almost all of the market designs that I describe in the book already have some support of the kind that Robin recommends (in some cases by Robin himself). For example, I previously offered a mathematical elaboration of “deliberative markets,” which seek to encourage participants to seek to persuade others that their predictions are correct.

Admittedly, there are a few exceptions. The incentives provided by two of my technical proposals (the decentralized subsidy approach and the nobody-loses prediction market) are sufficiently straightforward to me that math seems superfluous to me, though I agree that field tests comparing these with alternatives would be useful. Two of the proposals (the text-authoring market and the market web) could certainly benefit from experimentation, but the software needed to implement them would be considerably more complicated than what is needed for existing prediction markets.

A concluding thought: Robin’s articles are generally ridiculously underplaced in comparison to both their quality and their influence. But certainly I’m glad that Robin didn’t wait to publish his articles on science claims and futarchy until he had developed mathematical models or laboratory experiments. I don’t think that they would have added much. Academia may well be biased against articles whose primary thrust is to propose new institutions; I’ve also generally had better luck in placing more conventional articles. But I still think that such articles perform a useful function, and while they should include support, there may be an efficient division of labor between those who sketch out broad ideas and those who elaborate them (with or without mathematical models) or test them (in laboratory and field experiments). This is particularly so when the practical reality is that many different forms of elaboration and confirmation will be necessary before new institutions can be adopted.