Optimizing group judgmental accuracy in the presence of interdependencies

Abstract

Consider a group of people confronted with a dichotomous choice (for example, a yes or no decision). Assume that we can characterize each person by a probability, pi, of making the 'better' of the two choices open to the group, such that we define 'better' in terms of some linear ordering of the alternatives. If individual choices are independent, and if the a priori likelihood that either of the two choices is correct is one half, we show that the group decision procedure that maximizes the likelihood that the group will make the better of the two choices open to it is a weighted voting rule that assigns weights, wi, such that Pi wi ~ log 1-ffi "We then examine the implications for optimal group choice of interdependencies among individual choices.

Information theoretic combination of pattern classifiers

“…Considering a MV combination scheme, the probability PðĈ ¼ yÞ thatĈ outputs y is related to each voter classifier by [37] PðĈ ¼ yÞ r X KÀ1…”

“…Then, the following theorem gives the relationship between the ensemble accuracy and the individual accuracies as a function of the numbers of voters: Theorem 4.1 (Shapley and Grofman [37]). Consider a group of odd size K with any distribution of individual accuracies (p 1 ,y,p K ), where p i 40:5 8i.…”

Beyond Condorcet: optimal aggregation rules using voting records

“…By the main result in Nitzan and Paroush (1982) and Shapley and Grofman (1984), if voter skills { } i p are known, a linear aggregation rule is optimal, that is, yields the maximal collective probability of making the correct decision, if w i = log(p i /1-p i ).…”

“…Given such probability assignments, we can compute the probability that some judgment aggregation rule (such as a majority rule) will actually yield the correct decision. In fact, given such probability assignments, the optimal aggregation rule can be identified (Nitzan and Paroush (1982), Shapley and Grofman (1984), Ben-Yashar and Nitzan (1997)). …”

The Swing Voter's Curse in Social Networks

“…) (e.g., Shapley and Grofman, 1984). Hence, a set of voters S is better informed than another set S if and only if i∈S log(…”