According to Bermúdez, it is rational for Agamemnon to prefer the act of killing Iphigenia (act o) to the act of not killing her (act o′) when the former is framed as following Artemis's will (frame F ₂(o)) and the latter is framed as failing his ships and people (frame F(o′)), while at the same time preferring not to kill her (o′) to killing her (o) when the former is framed as failing his ships and people (frame F(o′)) and the latter is framed as murdering his daughter (frame F ₁(o)). And, Bermúdez says, such preferences are rational even when Agamemnon is fully aware that F ₁(o) and F ₂(o) are frames for the same option. That is, he claims that Agamemnon's preferences are these, and they are rational:

(1)$$F_1( o ) \prec F( {{o}^{\prime}} ) \quad F( {{o}^{\prime}} ) \prec F_2( o ) \quad F_1( o ) \prec F_2( o ) $$

I agree that there are rationally permissible attitudes in the vicinity of (1), but the ones Bermúdez ascribes to Agamemnon aren't them. In this note, I'll describe them and say why I think they better represent Agamemnon's situation.

Bermúdez argues that Agamemnon's quasi-cyclical preferences are rational because two competing reasons are in play: the value of following Artemis's will, on the one hand, and the value of his daughter's life, on the other. Agamemnon cannot settle how he wishes to weigh these two reasons against each other. If he were to give more weight to the former, he'd kill his daughter; if the latter, he would not. But he can't decide which he favours.

Here's another way we might describe Agamemnon's situation. Unable to decide how to weigh the two competing reasons against one another, his preferences are simply incomplete. Knowing that following Artemis's will is the same act as murdering his daughter, he should be indifferent between those two framings. But he neither prefers the act o that these two framings frame to the act o′ of not killing Iphigenia, framed as failing his ships and his people, nor disprefers it, nor is indifferent between the two.

That is, his preferences are as follows:

(2)$$F_1( o ) \; \sim \; F_2( o ) ,\,{\rm and}\,{\rm no}\,{\rm further}\,{\rm comparisons} . $$

Now, how would Agamemnon choose if these were his preferences? When you face a choice between two acts and you prefer neither to the other, you are rationally permitted to choice either. But notably in the cases Bermúdez describes, the agents don't simply choose at random. If the value of following Artemis's will is made salient and the value of his daughter's life is not, Agamemnon will kill Iphigenia; if the value of his daughter's life is made salient and the value of following Artemis's will is not, he will not. So, Agamemnon is different from someone with incomplete preferences between two acts who simply chooses at random when faced with a choice between them. You might think it is an advantage of Bermúdez's account that it captures that.

Whether this is an advantage or not depends on what we take the agent's preference ordering to be. Here are two alternatives: (a) it records the agent's judgments of betterness (cf. Broome, Reference Broome1991); (b) it provides a summary of the agent's actual behaviour or their behavioural dispositions (cf. Samuelson, Reference Samuelson1938, Reference Samuelson1948). If ${\prec}$ records Agamemnon's judgments of betterness, then (2) gives the correct account. After all, Agamemnon knows that it is acts that are better or worse than one another, not framings, so while he might have to define his betterness ordering over framings of acts because he is not able to represent an act to himself without framing it in some way, when he knows that two frames are presentations of the same act, he should be indifferent between them because he knows they are equally good. On the other hand, if ${\prec}$ records his dispositions to behave in certain ways, Bermúdez's proposal (1) is more plausible.

Nonetheless, I think there is a third account that is more plausible than (1) in the cases Bermúdez considers and when the preference ordering is taken to record behaviour. On this account, we say that Agamemnon's preferences are in fact complete at any time, but they change from one time to another depending on which of the two competing reasons is salient to him. So, when the value of following Artemis's will is salient, his preferences are:

(3.1)$$F( {{o}^{\prime}} ) \prec F_1( o ) \quad F( {{o}^{\prime}} ) \prec F_2( o ) \quad F_1( o ) \; \sim \; F_2( o ) $$

But when the value of his daughter's life is salient, his preferences are:

(3.2)$$F_1( o ) \prec F( {{o}^{\prime}} ) \quad F_2( o ) \prec F( {{o}^{\prime}} ) \quad F_1( o ) \; \sim \; F_2( o ) $$

On this account, there is no quasi-cyclicity and yet Agamemnon's pattern of behaviour is recorded, unlike in (2). But it also has the advantage that it highlights something troubling about Agamemnon's preferences from the point of view of rationality. If your preferences change, they are exploitable. Suppose you prefer act o to act o′ at one time and act o′ to act o at a later time. Then I can offer you a choice between o and o′ at the first time, when you'll choose o; then, at the later time, there will be some price such that, if I offer you the option to switch to o′ for that price, you'll take it, because you then prefer o′ to o. So you'll end up with o′ minus the price, when you could have chosen o′ costlessly at the outset and then not switched later. Of course, in order for someone to reliably exploit you like this, your change of preferences must be predictable or manipulable. But that is exactly how things are for Agamemnon. One need only make one or other of the competing reasons salient to him to manipulate his decision.

So I think that (2) is a better account of Agamemnon's preferences than (1) if those preferences give a betterness ordering, while (3) is better than (1) if they give a summary of behaviour.