Perspectival Act Utilitarianism

Abstract

This paper explores a problem involved in defining the act utilitarian notion of a “right action” within the framework of stit semantics. The problem is there seem to be two different, and conflicting, ways of defining this idea, both intuitively attractive. Previous work has addressed this problem by developing separate theories to account for our conflicting intuitions. This paper shows that the problem can also be addressed through a single theory that allows actions to assessed from different perspectives.

Appendix: Act Utilitarianism for Groups

This appendix shows how perspectival act utilitarianism can be extended from individual actions to group actions , and how the relation between the right actions available to groups and individuals can then be seen to depend on the standpoint from which these actions are evaluated.

The extension of perspectival act utilitarianism to group actions is straightforward, involving nothing more than a generalization of several of our previous notions. We have already seen, in the text, how the set Choice _Γ ^m of actions available to the group Γ at the moment m can be defined, with each group action identified as a pattern of actions available to the individuals from that group. The states confronting the group Γ at m can then be defined as the patterns of actions available at m to all agents except those from that particular group :

$$State_{\varGamma}^{m} = Choice_{\hbox{Agent} - \varGamma}^{m}$$

And where X is some proposition, weak and strong dominance relations under the condition X can be defined among the actions available to a group in a way exactly parallel to the definition for individual actions.

Conditional dominance ordering on group actions : Let Γ be a group of agents and m a moment, and let K and K′ be members of Choice _Γ ^m, and X a proposition. Then $K \preceq_X K'$ (K′ weakly dominates K under the condition X) if and only if $K \cap X \cap S \leq K'\cap X \cap S$ for each state $S \in State_{\varGamma}^{m}$; and $K \prec_X K'$ (K′ strongly dominates K under the condition X) if and only if $K \preceq_X K'$ and it is not the case that $K' \preceq_X K$.

The set of actions available to the group Γ under the condition X can be defined as those among the available actions that are consistent with this condition :

$$Choice_{\varGamma}^{m}/X = \{ K \in Choice_{\varGamma}^{m}\!: K \cap X \not= \emptyset \}.$$

And the optimal actions available to the group under this condition can then be defined as the actions available under this condition that are not dominated under this condition by any other such actions:

$$Optimal_{\varGamma}^{m}/X \!= \! \{ K \! \in \! Choice_{\varGamma}^{m}/X\! : \neg \exists K' \in Choice_{\varGamma}^{m}/X \, (K \prec_X K') \}.$$

Finally, the set of states confronting Γ at m that are consistent with the proposition X can be represented just as before:

$$State_{\varGamma}^{m}/X = \{ K \in State_{\varGamma}^{m}\! : K \cap X \not= \emptyset \}.^{14}$$

¹⁴ And likewise the proposition that one of these states holds:

$$State_{\varGamma}^{m}(X) = \bigcup State_{\varGamma}^{m}/X.$$

Given these materials, we can now introduce a form a perspectival act utilitarianism for groups, according to which an action available to the group Γ at a moment m is right from the standpoint of the moment m′ just in case that action is optimal under the conditions in which the group Γ finds itself at m, where these conditions are judged from the standpoint of m′:

Perspectival act utilitarianism for groups: Let Γ be a group of agents and m and m′ moments such that either $m < m'$ or $m' < m$ or $m = m'$, and suppose $K \in Choice_{\varGamma}^{m}$. Then the action K is right at m from the standpoint of m′ if and only if $K \in Optimal_{\varGamma}^{m}/State_{\varGamma}^{m}(H_{m'})$, and wrong otherwise.

As with individual actions, this perspectival account supports the orthodox intuitions concerning group actions when the moment m′ of evaluation is later than the moment m of action, while the dominance intuitions are supported when m′ is earlier than or identical with m.

Now that the perspectival account has been extended from individuals to groups, let us turn briefly to two of the most central questions concerning the relation between individual and group act utilitarianism. First, if each individual belonging to a group performs a right action, does that entail that the group itself performs a right action? And second, if a group performs a right action, does that entail that the individuals belonging to the group do so?

The answer to the first question is No. This fact is well-known and can be illustrated with the Whiff and Poof example from Fig. 11.6, which was originally formulated to make exactly this point. Still, it is useful to consider the question separately from the dominance and orthodox perspectives, since the contours of this negative answer differ.

Suppose, first, that we evaluate the actions available at the moment m in Fig. 11.6 from the standpoint of m itself, adopting the dominance perspective. Then it is easy to verify that each action available to either agent is classified as right from the standpoint of m. So suppose that Whiff pushes his button, performing the action K ₁, while Poof refrains, performing K ₄ – each agent therefore performing an action that is classified as right. Then the group $\varGamma = \{\alpha, \beta \}$ containing both Whiff and Poof performs the action $K_1 \cap K_4$, which is clearly non-optimal, leading to a utility of 0 while 10 is possible, and so classified as wrong from the standpoint of m. Indeed the group action $K_1 \cap K_4$ is not even in equilibrium: each agent would be better off with a different choice, given the action chosen by the other. Individual satisfaction of dominance act utilitarianism, then, not only fails to guarantee group satisfaction , but has the even more depressing consequence that the pattern of actions chosen, each right from an individual perspective, may not be an equilibrium pattern .

Next, suppose Whiff and Poof both refrain from pushing their buttons, performing the individual actions K ₂ and K ₄. The outcome of this pair of actions is the history h ₄. So let us evaluate these actions from the standpoint of some later moment along this history, thus adopting the orthodox perspective. It is easy to see that both of these actions are then classified as right from the standpoint of this later moment, and also that the pair of actions is in equilibrium : each agent is performing a best available action, given the actions performed by the other.

This example illustrates the general rule: whenever each individual member of a group of agents performs an action that is right from the standpoint of a later moment – and so right from the orthodox perspective – the pattern of actions performed by the entire group is in equilibrium . However, this does not mean that the group action is itself right. In this case, the group action $K_2 \cap K_4$ is non-optimal, and so wrong, since it yields a utility of 6 while the available group action $K_1 \cap K_3$ yields a utility of 10. If each member of a group performs an action that is right from the standpoint of a later moment, then, the overall pattern of actions will be in equilibrium , but it still may not be a right action for that group to perform, since there may be better equilibrium patterns.

Fig. 11.8

Group action right, individual action wrong

Now to the second question: if a group action is right , does it follow from this that the actions of the individuals belonging to that group are also right? The standard answer to this question is Yes. Regan, for example, writes that “for any group of agents in any situation, any pattern of behaviour by that group of agents in that situation which produces the best consequences possible is a pattern in which the members of the group all satisfy AU” (Regan 1980, p. 54). And Jackson, that “if the right group action is actually performed, then that group action’s constituent individual actions must be right” (Jackson 1988, p. 264). In the case of this question, however, the dominance and orthodox perspectives yield different answers.

Both Regan and Jackson adopt the orthodox perspective, evaluating actions from the standpoint of a later moment, and from that perspective what they say is right. In our current language, it can be put like this: if a group action performed at m is right from the standpoint of a later moment m′, then the actions performed by the individual members of that group are also right from the standpoint of m′.

However, the implication fails if we consider the matter from the dominance perspective, evaluating actions from the standpoint of a moment at or before the moment of their performance: where m′ is identical with or earlier than m, it might well be possible that a group action performed at m is right from the standpoint of m′, while the individual action of some member of that group is wrong from the standpoint of m′. This possibility is illustrated in Fig. 11.8. Here, it is easy to see that the action $K_2 \cap K_3$ performed at the moment m by the group $\varGamma = \{\alpha,\beta\}$ is right from the standpoint of the moment m itself, since this group action leads to an outcome of utility 1, the highest available, and is therefore optimal. But the component action K ₂ by the agent α is wrong from the standpoint of m, since it is dominated by K ₁. Of course, from the standpoint of some future moment along the history h ₃, we can see the action K ₂ by α was performed under circumstances in which β performed the action K ₃, so that an outcome of utility 1 was achieved; from this later standpoint, the action K ₂ is therefore right. But at the moment m itself, while it is still unclear which action β will perform, the choice of K ₂ allows for an outcome of utility 0, and is therefore dominated by K ₁, which guarantees an outcome of utility of 1.