Group belief

Suppose we wanted our epistemology to apply not just to individuals, but to “group agents” like committees, governments, companies, and so on. Such agents may be made up of members who disagree. Levi (1986, 1999) has argued that representation of such conflict is better handled with sets of probabilities than with precise probabilities. There is a rich literature on combining or aggregating the (probabilistic) opinions of members of groups (Genest and Zidek 1986) but the outcome of such aggregation does not adequately represent the disagreement among the group. Some forms of aggregation also fail to respect plausible constraints on group belief. For example, if every member of the group agrees that [ltr]X[/ltr] and [ltr]Y[/ltr] are probabilistically independent, then it seems plausible to require that the group belief respects this unanimity. It is, however, well known that linear pooling—a simple and popular form of aggregation—does not respect this desideratum. Consider two probability functions [ltr]p[/ltr], [ltr]q[/ltr] such that [ltr]p(X)=p(Y)=1/3[/ltr] and [ltr]p(X∣Y)=p(X)[/ltr] while [ltr]q(X)=q(Y)=2/3[/ltr] and [ltr]q(X∣Y)=q(X)[/ltr]. Consider aggregating these two probabilities by taking an unweighted average of them: [ltr]r=p/2+q/2[/ltr]. Now, calculation shows that [ltr]r(X∩Y)=5/18[/ltr] while [ltr]r(X)r(Y)=1/4[/ltr], thus demonstrating that [ltr]r[/ltr]does not consider [ltr]X[/ltr] and [ltr]Y[/ltr] to be independent. So such an aggregation method does not satisfy the above desideratum (Kyburg and Pittarelli 1992; Cozman 2012). For more on judgement aggregation in groups, see List and Pettit (2011), especially chapter 2.
If committee members have credences and utilities that differ among the group, then no precise probability-utility pair distinct from the probabilities and utilities of the agents can satisfy thePareto condition (Seidenfeld, Kadane, and Schervish 1989). The Pareto condition requires that the group preference respect agreement of preference among the group. That is, if all members of the group prefer [ltr]A[/ltr] to [ltr]B[/ltr] (that is, if each group member finds that [ltr]A[/ltr] has higher expected utility than [ltr]B[/ltr]) then the aggregate preference (as determined by the aggregate probability-utility pair) should satisfy that preference. Since this “consensus preservation” is a reasonable requirement on aggregation, this result shows that precise models of group agents are problematic. Walley discusses an example of a set of probabilities where each probability represents the beliefs of a member of a group, then [ltr]P[/ltr] is an incomplete description of the beliefs of each agent, in the sense that if all members of [ltr]P[/ltr] agree on something, then that thing is something each agent believes. Sets of probabilities allow us to represent an agent who is conflicted in their judgements (Levi 1986, 1999).

اقتباس :: Ideally rational agents may face choices where there is no best option available to them. Indeterminacy in probability judgement and unresolved conflicts between values lead to predicaments where at the moment of choice the rational agent recognizes more than one such preference ranking of the available options in [the set of available choices] to be permissible. (Levi 1999: 510)

Levi also argued that individual agents can be in conflict in the same way as groups, and thus that individuals’ credal states are also better represented by sets of probabilities. (Levi also argued for the convexity of credal states, which brings him into conflict with the above argument about independence (see historical appendix section 3).) One doesn’t need to buy the claim that groups and individuals must be modelled in the same way to take something away from this idea. One merely needs to accept the idea that an individual can be conflicted in such a way that a reasonable representation of her belief state—or belief and value state—is in terms of sets of functions.Bradley (2009) calls members of such sets “avatars”. This suggests that we interpret an individual’s credal set as a credal committee made up of her avatars. This interpretation of the representor is due to Joyce (2011), though Joyce attributes it Adam Elga. This committee represents all the possible prior probabilities you could have that are consistent with the evidence. Each credal committee member is a fully opinionated Jamesian voluntarist. The committee as a whole, collectively, is a Cliffordian objectivist.

Group belief

Group belief :: تعاليق

Group belief