In this comment on Francesco Guala's Understanding Institutions, I express my admiration for the book but I also raise some critical criticisms: His general account of institutions as rules-in-equilibrium seems to get their ontology wrong by disregarding their material side - their concrete realizations. It also diregards social institutions whose rules are not (and are not meant to be) in equilibrium. Finally, his suggestion that institutional equilibria necessarily involve correlation devices appers to lack justification.
Abstract in UndeterminedThe point of departure in my story is the contrast between two models of democratic voting process: popular democracy and what might be called committee democracy. On one interpretation, voting in popular democracy is a procedure whose function is to aggregate the individuals' preferences to something like a collective preference, while in committee democracy what is being aggregated are committee members' judgments. The relevant judgments on the agenda often address an evaluative question. It is such value judgments that this paper focuses on. The question is how their aggregation differs from aggregation of preferences.I focus on the case in which the two aggregation scenarios exhibit a far-reaching structural similarity: more precisely, the case in which, in the judgment aggregation scenario, the individual inputs are value rankings. This means that, formally, the individual judgments in this case have the same structure as preference rankings over a given set of alternatives, but while in a preference ranking the alternatives are ordered in accordance with one's preferences, a value ranking expresses one's comparative evaluation of the alternatives: say, this alternative is best, those two alternatives are second-best, that alternative is third-best, etc. I suggest that this difference in the nature of individual inputs in two aggregation scenarios has important implications for the task of aggregation. In particular, distance-based methods that look fine for the aggregation of judgments turn out to be inappropriate for the aggregation of preferences: Minimization of distance from individual inputs violates the Pareto condition.When applied to judgment aggregation, distance-based methods can also be approached from the epistemic standpoint: the questions canl be posed concerning their advantages as a truth-tracker. In this context, what matters is not only the probability of the outcome of the aggregation procedure being true, but also the expected verisimilitude of the outcome: its expected distance from truth.
The Puzzle of the Hats is a betting arrangement which appears to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players' rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and betting rates diverge. Second, there is an analogy between ways of dealing with situations of this kind and different policies for sequential choice. Third, there is an analogy with strategic voting, showing that the common interest is not always served by expressing how things seem to you in social decision-making. And fourth, our analysis of the Puzzle of the Hats casts light on a recent controversy about the Dutch book argument for the Sleeping Beauty Problem.
Distribute white and black hats in a dark room to a group of three rational players with each player having a fifty-fifty chance of receiving a hat of one colour or the other. Clearly, the chance that, as a result of this distribution, (A) "Not all hats are of the same colour" is 3/4. The light is switched on and all players can see the hats of the other persons, but not the colour of their own hats. Then no matter what combination of hats was assigned, at least one player will see two hats of the same colour. For her the chance that not all hats are of the same colour strictly depends on the colour of her own hat and hence equals 1/2. On Lewis's principal principle, a rational player will let her degrees of belief be determined by these chances. So before the light is switched on, all players will assign degree of belief of 3/4 to (A) and after the light is turned on, at least one player will assign degree of belief of 1/2 to (A). Suppose a bookie offers to sell a single bet on (A) with stakes $4 at a price of $3 before the light is turned on and subsequently offers to buy a single bet on (A) with stakes $4 at a price of $2 after the light is turned on. If, following Ramsey, the degree of belief equals the betting rate at which the player is willing to buy and to sell a bet on a given proposition, then any of the players would be willing to buy the first bet and at least one player would be willing to sell the second bet. Whether all hats are of the same colour or not, the bookie can make a Dutch book - she has a guaranteed profit of $1. However, it can be shown that a rational player whose degree of belief in (A) equals 1/2 would not volunteer to sell the second bet on (A), neither when her aim is to maximise her own payoffs, nor when she wants to maximise the payoffs of the group. The argument to this effect shares a common structure with models (i) for the tragedy of the commons and (ii) for strategic voting in juries.
A committee has to address a complex question, the answer to which requires answering several sub-questions. Two different voting procedures can be used. On one procedure, the committee members vote on each sub-question and the voting results then are used as premises for the committee's conclusion on the main issue. This premise-based procedure (pbp) can be contrasted with the conclusion-based procedure (cbp). On that procedure, the members directly vote on the conclusion, with the vote of each member being guided by her views on the relevant sub-questions. These procedures are by no means equivalent, which has been pointed out in legal theory in connection with jury votes (cf. Kornhauser and Sager 1986, 1993, Kornhauser 1992a, 1992b, and Chapman 1998a, 1998b). There may be a majority of voters supporting each premise, but if these majorities do not significantly overlap, there will be a majority against the conclusion. Pettit (2001) connects the choice between the two procedures with general political theory, in particular, with the discussion of deliberative democracy. However, the problem we want to examine concerns the relative advantages and disadvantages of the two procedures from the epistemic point of view. In some cases one can assume that the question before the committee has the right answer. In cases like this, is one of the two procedures better when it comes to tracking the truth? As it turns out, the answer to this query is not univocal. On the basis of Condorcet's jury theorem, we show that the premise-based procedure is clearly superior if the objective is reach truth for the right reasons, i.e. without making any mistakes on the way. However, if the goal instead is to reach truth for whatever reasons, right or wrong, there will be cases in which using the conclusion-based procedure turns out to be more reliable, even though, for the most part, the premise-based procedure will retain its superiority. Our results partly confirm and partly disconfirm the tentative conjectures that have been put forward in Pettit and Rabinowicz (2001).
