Munich Center for Mathematical Philosophy (MCMP)

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Talk: Jason Alexander (LSE)

Location: Ludwigstr. 31, ground floor, Room 021.

19.06.2019 16:00  – 18:00 


Group Agency and the Dynamics of Intragroup Deliberation (with Julia Morley)


Recent attempts to understand group agency have investigated conditions required for the formation of group attitudes using axiomatic methods from the judgement aggregation literature (List and Pettit, 2011). In particular, a number of impossibility results have been appealed as a way of defending a non-reductive theory of group agency. The specific claim defended by List and Pettit is somewhat open to debate: in some parts of Group Agency, they claim only that it is possible that there exists a non-reductive group agent. (Indeed, that is one implication of the subtitle of their book.) In other places, though, they appear to claim that all group agents are such that they cannot be reduced. One such passage can be seen in the quote below (italics added for emphasis):

“While the agency achieved by a group supervenes on the contributions of its members — while it is not ontologically autonomous — it is autonomous in another, related sense. The agency of the group relates in such a complex way to the agency of individuals that we have little chance of tracking the dispositions of the group agent, and of interacting with it as an agent to contest or interrogate, persuade or coerce, if we conceptualize its doing at the individual level. [. . . ] In view of these considerations, we must think of group agents as relatively autonomous entities — agents in their own right, as it is often said, groups with minds of their own.” (List and Pettit, 2011, 76–77)

Given that both claims state something about the real world, this raises the following question: how, and what, can we learn about the real world from an impossibility theorem?

To begin, consider how impossibility results can be used to draw inferences about actual practice. In particular, consider two instances of impossibility results with powerful intellectual legacies: Gödel’s incompleteness theorems and the Arrow impossibility theorem. Gödel’s incompleteness theorems are credited, correctly, as leading to the demise of Hilbert’s programme in the foundations of mathematics. Why? Because Gödel showed that there were true state- ments of arithmetic which were impossible to prove from the Peano axioms. What’s important, here, is that Gödel’s impossibility result showed the exis- tence of true but unprovable statements using an idealized formal model that was recognised by mathematicians as, in principle, a descriptively accurate characterisation of the social practice of mathematical proof. Hence Gödel’s result said something about fundamental limitations in the actual practice of mathematicians constructing proofs. In contrast, Arrow’s impossibility theorem showed that it was impossible to have a social welfare function that satisfied certain intuitive fairness criteria. What’s important, here, is that Arrow’s impossibility result showed that some normatively desireable criteria to impose upon a voting scheme were not simultaneously satisfiable. Hence, Arrow’s result said something about the fundamental limitations faced by people designing certain kinds of electoral systems.

Which, if any, of these two senses are we supposed to approach the underlying theorem from judgement aggregation which draws upon an impossibility result for legitimising group nonreductionism? Are the four axioms imposed upon the aggregation function supposed to be interpreted as an attempt to pro- vide a descriptive characterisation of group deliberation? Or, alternatively, are those axioms to be interpreted as stating normatively desireable requirements for group deliberation?

We argue that there are good reasons, both empirically and conceptually, for disputing either interpretation of the axioms. But note that this then makes the whole endeavour a bit mysterious, for if the requirements are neither to be understood as descriptive or normative, what relationship exists between the formal model and its target, the actual practice of group deliberation? With no obvious candidate relationship existing between the two, the link between the formal model and its target is severed, thereby inhibiting our ability to draw meaningful conclusions about how to understand the practice of real-world group deliberation from the formal model and its associated impossibility result. In particular, our empirical case study shows how it is possible for all four axioms to be violated in ways compatible with a straightforward, individualist, aggregative understanding of group deliberation. The upshot, then, is that while we may charitably grant that List and Pettit do succeed in providing an argument for the logical possibility of nonreductive group agents, it is not the case that the stronger interpretation of their impossibility result — namely that all group agents are nonreductive — holds.