Some background: I previously appealed to such rooted preferences as an objection to Caspar Hare's morphing argument, suggesting that a decent person might reasonably prefer a world where a counterpart of Dale exists over a world where a slightly better-off counterpart of that counterpart, but who no longer qualifies as a counterpart of Dale, exists instead. Hare now responds by running his argument in terms of "active favoring", which is basically a special kind of counterfactual preference where we ask what the agent would prefer if she were agnostic about which world is actual.
There are a couple of different ways we could imagine this going.
(1) Suppose Amy retains all her (apparent) memories, etc., but just loses confidence in their veridicality. Perhaps an evil demon tells her that there's a 50% chance that she's been massively deluded, and has actually led a very different life raising Hamish instead of Dale. If so, she will soon have her "true" memories restored, etc. Should Amy hope that her memories of life with Dale are a delusion, and that she will wake up to a happier Hamish instead? I think the partialist can reasonably claim: No. Given her apparent memories, providing grounds for a reasonable attachment to a child like Dale, Amy may (and perhaps even should) prefer Dale's existence over Hamish's, even though she is unsure which is her actual son. So, on this interpretation of "active favoring", it does not help Hare's argument: it can be reasonably "rooted" in particular attachments just as old-fashioned preferences can.
(2) Suppose instead that Amy is a total amnesiac. Not only is she unsure which world is actual, but we've also purged any memory traces (etc.) that the actual world had imprinted upon her. Perhaps what Hare means by "active favoring" is what such a total amnesiac would prefer. If all Amy knows is that she either has a deaf child called 'Dale', or a slightly better-off non-deaf child named 'Hamish', then it seems prima facie plausible that minimal benevolence requires that she prefer to have the better-off child. After all, what basis could she have for preferring the worse-off child?
Well, let's develop the story a little further. Recall that, prior to her amnesia, Amy loved her deaf son Dale very much. She came to value his particular personality and way of life, including his deafness. And let's suppose, more specifically, that she came to value Dale's personality and way of life in itself, and not just under the superficial guise of "being Dale's". She comes to deeply value the deaf life, because her son is deaf; but what she ends up valuing here just is the deaf life and not the deaf life insofar as my son is deaf. The causal condition need not, and we now suppose does not, become embedded in the intentional content of what is valued. Amy thus has a rooted preference for a deaf child, and one that seemingly could survive her amnesia. If she no longer remembers Dale, then she won't fully understand why she came to have this preference for a deaf child. But suppose she has it nonetheless, as a causal consequence of her forgotten attachment to Dale. Is she unreasonable, or in violation of minimal benevolence or moral decency? It seems harsh to say so. But that is what Hare is committed to, if he is to rule out the permissibility of actively favoring the impartially worse outcome.
I'm less confident that rooted preferences are reasonable in the case of total amnesia (compared to the unreliable memory case). Maybe the rooted amnesiac is unreasonable. One reason to think so is that it would seem clearly unreasonable for someone to just out of the blue prefer to have the worse-off child. But Amy the Amnesiac might be an internal duplicate of such an unreasonable person: there is nothing internal to her current mental state to establish that her preference was in fact causally "rooted" in concern for an actual person. So if we are a certain sort of "internalist" about rationality, thinking that it supervenes upon the internal qualities of a person's mind at a moment, then it seems we're committed to thinking Amy unreasonable too. (On the other hand, you might just take this case to constitute a counterexample to such an internalist view!)
I'm sympathetic to this form of "internalism", so perhaps the thing to say is that (i) Amy the rooted amnesiac is irrational to prefer a deaf child -- her amnesia stripped her of the grounds for her reasonably rooted preference, so its persistence in the absence of those grounds is no longer reasonable; but (ii) she has an excuse for this rational error, insofar as it is a natural continuance of what was a reasonable preference, with a respectable causal history. So Amy thus doesn't warrant the kind of negative assessments that we might make of a person who arbitrarily, "out of the blue", prefers a deaf child.
Does that seem right?