Abstract
Parfit (Reasons and persons, Clarendon Press, Oxford, 1984) posed a challenge: provide a satisfying normative account that solves the nonidentity problem, avoids the repugnant and absurd conclusions, and solves the mereaddition paradox. In response, some have suggested that we look toward personaffecting views of morality for a solution. But the personaffecting views that have been offered so far have been unable to satisfy Parfit’s four requirements, and these views have been subject to a number of independent complaints. This paper describes a personaffecting account which meets Parfit’s challenge. The account satisfies Parfit’s four requirements, and avoids many of the criticisms that have been raised against personaffecting views.
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Notes
 1.
Parfit (1984, p. 443).
 2.
Of course, many have denied that all of these requirements need to be met, and have gone on to endorse theories which satisfy some subset of these requirements. See Arrhenius et al. (2010) for a comprehensive discussion of the many different responses that have been offered to Parfit’s dilemma.
 3.
 4.
 5.
 6.
 7.
Or, more precisely, “Bob could have been a plumber” is true iff there is some world W, and some counterpart of Bob in W, which is a plumber (see Lewis 1986, pp. 9–10). Similar remarks apply to the example that follows.
 8.
To see the former, note that b may be the individual at b’s world that most closely resembles a, but there may be other individuals at a’s world that more closely resemble b than a does. To see the latter, note that b may be similar enough to a to be its counterpart, and c may be similar enough to b to be its counterpart, but the resemblance gap between c and a may to be too wide for c to be a’s counterpart.
 9.
In the case of Roberts (1998), the similarity is less apparent. But one can think of the HMV as a quantitative version of Roberts’ view. And the prescriptions of the two views are almost identical (though Roberts’ view is silent in some cases in which the HMV is not).
 10.
 11.
 12.
 13.
If one holds the view that all moral agents are moral patients, then this case is, strictly speaking, impossible. I.e., since there is no individual present in all of the outcomes, there couldn’t be an agent who was facing these choices. (Recall that these outcomes include all of the agents who exist, at all times.) However, nothing of substance hangs on this, so I’ll occasionally engage in the simplifying fiction of ignoring the presence of the agent in question.
 14.
 15.
That said, some have argued that this asymmetry is actually counterintuitive. I discuss these arguments in Sect. 8.
 16.
For example, see Lewis (1986).
 17.
On these kinds of questions, Lewis writes: “You could do worse than plunge for the first answer to come into your head, and defend that strenuously. If you did, your answer would be right. For your answer itself would create a context, and the context would select a way of representing, and the way of representing would be such as to make your answer true. ... That is how it is in general with dependence on complex features of context. There is a rule of accommodation: what you say makes itself true, if at all possible, by creating a context that selects the relevant features so as to make it true.” Lewis (1986, p. 251).
 18.
“In parallel fashion, I suggest that those philosophers who preach that origins are essential are absolutely right—in the context of their own preaching. They make themselves right: their preaching constitutes a context in which de re modality is governed by a way of representing (as I think, by a counterpart relation) that requires match of origins.” Lewis (1986, p. 252).
 19.
I use the term “objective” here broadly (if loosely) to cover the rejection of any number of ways in which moral claims might be defective, relative, insubstantial, etc.
 20.
If we understand these as desiderata for counterpart*fixing proposals, it should be clear why we want the first and third desiderata. Why do we want the second desiderata? Because we are, in part, trying to capture personaffecting intuitions. The more a counterpart*fixing proposal diverges from our intuitive judgments regarding how to identify individuals, the less faithful it is to our personaffecting intuitions.
 21.
In relativistic worlds we can instead consider what it is for two individuals to be indiscernableuptor, where r is the spatiotemporal region the agent occupies at the moment of decision. We can say that two individuals are indiscernableuptor iff they are alike with respect to all of the properties and relations that supervene on the qualitative state of the world in the backwards light cone of r. (I’m assuming here that there aren’t closed timelike curves; some other strategy needs to be employed if there are.)
 22.
My use of the term “maps” should be understood to imply only that there is a multivalued function (or “multimap”) from individuals in W _{ i } to individuals in W _{ j }, not that there is a function (or “map”) from the former to the latter. The first condition below will, in fact, require there to be such a function. But we want all of the substantive constraints on the counterpart relation to appear in the list of conditions, not to be smuggled in by our setup.
 23.
If we take counterpart relations to be similarity relations, then this condition is a bit too strong. Problems arise in cases in which there are multiple indiscernable individuals at a world—individuals who share all of their intrinsic and extrinsic qualitative properties. Because these individuals are indiscernable, a qualitative counterpart relation can’t assign them different counterparts, or take them to be counterparts of different individuals. So in these cases both parts of condition 1 can fail. There are a couple of different ways to handle such cases. One approach is to shift the qualitative requirement from the counterpart relations themselves to what counterpart relations a context can pick out. Then we could allow counterpart relations to be more finegrained (and so allow them to be onetoone functions even in cases with multiple indiscernable individuals), but require contexts to deliver multiple counterpart relations—all of the counterpart relations that are ‘precisifications’ of the coarse counterpart relation the original theory employed. Then, when assessing personaffecting views like HMV, one could employ any or all of these finegrained counterpart relations, since they’ll all deliver the same results.
 24.
All of an agent’s outcomes will be identical up to t. So if there are multiple individuals that are indiscernableuptot at one available world, there will be the same number of individuals who are indiscernableuptot at every other available world. Thus there may be looseness regarding which of these indiscernableuptot individuals are mapped to which other indiscernableuptot individuals. (Even this looseness will sometimes be removed by the fourth condition, if the individuals end up having different levels of wellbeing due to their experiences after t, and this ends up impacting the harm assigned to the world.)
 25.
Parfit (1984, p. 359).
 26.
One might suggest that we understand the assertion that “this girl’s decision... will probably be worse for her child” as a de dicto, not a de re claim (see Hare 2007). If so, then this is not a personaffecting judgment, and talk of counterpart relations is besides the point. I think the second half of this assertion—“if she waited, she would probably give him a better start in life”—suggests a de re reading. But in any case, not much hangs on this. SHMV delivers the correct prescription regardless of what story we end up deciding on.
 27.
A similar response to the nonidentity problem is suggested by Wrigley (2006), who employs counterpart theory to assess the moral status of genetic selection.
 28.
If we employ counterpart* relations we may have to hedge this claim a bit, since there are contexts in which the counterpart and counterpart* relations can come apart.
 29.
Parfit (1984, p. 388).
 30.
Strictly speaking, Parfit is talking about assessments of which worlds are better than one another, not assessments of what one ought to do. But I take the interesting question to be the one concerning obligation; questions regarding which world is better are only interesting insofar as they relate to what we ought to do. So this is how I’ll understand the problems Parfit raises. (See also the discussion in Sect. 7.)
 31.
Of course, nothing much hangs on this explanation. SHMV yields the right result regardless of whether this explanation of our intuitions is correct.
 32.
Interesting questions arise regarding how to understand conditional deontic claims if we reject IIA_{ d }. (Thanks to Ted Sider here.) Although these are interesting issues, I won’t attempt to address them here.
 33.
 34.
A number of results demonstrating the incompatibility of several normative theses that yield these three judgments have been given in the literature; see Ng (1989), Blackorby and Donaldson (1991), and Arrhenius (2000). The result stated here, and proved in the appendix, is both weaker and stronger than these results. It is stronger in that it makes no assumptions about the normative theses that justify our intuitive judgments in these three cases, and thus applies regardless of how one tries to justify these verdicts. It is weaker in that it doesn’t directly yield conclusions regarding which kinds of normative theses are mutually inconsistent. (Though one can use this result to generate such conclusions by finding sets of principles that yield the three verdicts in question.)
 35.
Another principle along these lines that personaffecting views conflict with is the Pareto plus principle (PPP): if a W _{1}option is permissible, a W _{2}option is available, and W _{2} is the same as W _{1} except that it contains an additional happy person, then the W _{2}option must be permissible. I don’t think this conflict raises any additional interesting issues, however. Rather, I think that the conflict between personaffecting views and PPP is just the conflict between personaffecting views and IIA_{ d } in disguise.
To see why, consider the restricted Pareto plus principle (RPPP), which applies solely to cases in which there are only two options available. I suggest that RPPP captures the distinctive intuition behind PPP. And personaffecting views like SHMV won’t conflict with RPPP. But we can derive PPP from RPPP if we assume IIA_{ d }. And personaffecting views like SHMV will conflict with PPP. So it isn’t until we add IIA to RPPP that we get a conflict with SHMV. This suggests that the conflict between personaffecting views like SHMV and PPP stems from the implicit IIAlike assumptions built into the formulation of PPP, not from anything distinctive regarding PPP per se. (See Roberts 2003b for another argument for why proponents of personaffecting views should reject PPP.)
 36.
 37.
What if one thinks that it’s analytic that an “all things considered better than” relation will satisfy (i)–(iii)? Then proponents of personaffecting views will follow proponents of intransitivity in denying that there is such a relation.
 38.
Likewise, our moral intuitions may distinguish between things like preventing harms and providing benefits, something that typical wellbeingfocused theories won’t be sensitive too. (Thanks to Elizabeth Harman here.)
 39.
 40.
I say this because I’m sympathetic to these kinds of utilitarian apologetics. Indeed, I think something like utilitarianism may well be correct.
 41.
I owe this case to James Patten.
 42.
The six possibilities this rules out are: (α: W _{1}, β: W _{2}), (α: W _{1}, β: both), (α: W _{2}, β: W _{1}), (α: W _{2}, β: both), (α: both, β: W _{1}), (α: both, β: W _{2}).
 43.
The four additional possibilities this rules out are: (α: W _{1}, β: W _{1}), (α: both, β: W _{1}), (α: both, β: both), (α: neither, β: both).
 44.
The two additional possibilities this rules out are: (α: W _{2}, β: W _{1}), (α: W _{2}, β: both).
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Acknowledgments
I’d like to thank Phil Bricker, Maya Eddon, Fred Feldman, Peter Graham, Elizabeth Harman, Julia Markovits, James Patten, Melinda Roberts, Ted Sider, Dennis Whitcomb, members of 2011 Bellingham Summer Philosophy Conference, and an anonymous referee, for helpful comments and discussion.
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Appendix
Appendix
Proof: a normative theory satisfies IIA_{ d } iff it meshes with IIA
Here we’ll prove that a normative theory satisfies IIA_{ d } iff it meshes with IIA.
Definitions
Let’s begin with the definitions required to make the meaning of this claim precise. I’ll say that the choice of an option A in a decision situation is in accordance with normative theory T iff T takes A to be permissible in that decision situation. I’ll say that the choice of an option A in a decision situation is in accordance with preference function f iff, for all available options X, A ≥ X. And I’ll say that a set of choices S is in accordance with f/T iff all and only the choices in that set are in accordance with f/T. Finally, I’ll say that a normative theory T meshes with preference constraint C iff the set S of choices that are in accordance with T is also in accordance with some preference function f that satisfies C.
We can characterize IIA and IIA_{ d } as follows:
 IIA::

If there is a W _{1} W _{2}situation in which the W _{1}option ≥ the W _{2}option, then in all W _{1} W _{2}situations the W _{1}option ≥ the W _{2}option.
 IIA_{ d }::


(i)
If there exists a W _{1} W _{2}situation in which both the W _{1}option and the W _{2}option are permissible, then in all W _{1} W _{2}situations the W _{1}option is permissible iff the W _{2}option is permissible.

(ii)
If there exists a W _{1} W _{2}situation in which the W _{1}option is permissible and the W _{2}option is impermissible, then in all W _{1} W _{2}situations the W _{2}option is impermissible.

(i)
Proof
With this terminology in place, we can make sense of the result to be proved: a normative theory T satisfies IIA_{ d } iff it meshes with IIA.
Part I: If a normative theory T violates IIA_{ d }, then it will not mesh with IIA.
We’ll demonstrate this in two steps. First (I.A), we’ll show that if a normative theory T violates the first clause of IIA_{ d }, then the set of choices in accordance with T will only be in accordance with preference functions that violate IIA. Second (II.B), we’ll show that if a normative theory T violates the second clause of IIA_{ d }, then the set of choices in accordance with T will only be in accordance with preference functions that violate IIA.
I.A. The First Clause: First suppose a theory violates the first clause of IIA_{ d }: there are W _{1} W _{2}situations in which both the W _{1}option and the W _{2}option are permissible according to T, and other W _{1} W _{2}situations in which one is permissible and the other not. Consider the set S of choices in accordance with T. Any preference function f in accordance with S must be such that, (i) in the W _{1} W _{2}situations in which both the W _{1}option and the W _{2}option are permissible, the W _{1}option ≥ the W _{2}option and the W _{2}option ≥ the W _{ a }option, and (ii) in W _{1} W _{2}situations in which (say) the W _{1}option is permissible and the W _{2}option is not, the W _{2}option \(\ngeq\) the W _{1}option. This violates IIA.
I.B. The Second Clause: Suppose a theory violates the second clause of IIA_{ d }: there are W _{1} W _{2}situations in which (say) the W _{1}option is permissible and the W _{2}option impermissible according to T, and other W _{1} W _{2}situations in which the W _{2}option is permissible. Consider the set S of choices in accordance with T. Any preference function f in accordance with S must be such that, (i) in the W _{1} W _{2}situations in which the W _{1}option is permissible and the W _{2}option impermissible, the W _{1}option ≥ the W _{2}option and the W _{2}option \(\ngeq\) the W _{1}option, and (ii) in the W _{1} W _{2}situations in which the W _{2} option is permissible, the W _{2}option ≥ the W _{1}option. This violates IIA.
Part II: If a normative theory T satisfies IIA_{ d }, then the set of choices in accordance with T will mesh with IIA. (I.e., there will be some preference function f that’s in accordance with this set of choices that meshes with IIA.)
Consider the preference functions f that are in accordance with the set S of choices that’s in accordance with a normative theory T that satisfies IIA_{ d }. Any such preference function f will either (i) mesh with IIA or (ii) not mesh with IIA. If f satisfies IIA, then we’re done. If f doesn’t satisfy IIA, then we’ll show (II.A) that there’s always a nearby preference function in accordance with S which does satisfy IIA. So no matter what, a comprehensive strategy in accordance with an IIA_{ d }satisfying theory T will be in accordance with some preference function f which satisfies IIA. So any normative theory T that satisfies IIA_{ d } meshes with IIA.
II.A. The Key Result: Let S be the set of choices in accordance with a normative theory T that satisfies IIA_{ d }, and let f be a preference function in accordance with S. If f violates IIA, then there is a always a nearby preference function in accordance with S which does satisfy IIA.
Take any two W _{1} W _{2}situations in which f yields a violation of IIA with respect to it’s rankings of W _{1} and W _{2} in these situations. Since f violates IIA, it must be the case that the W _{1}option ≥ the W _{2}option in one situation, and the W _{1}option \(\ngeq\) the W _{2}option in the other. Call the first α and the second β.
Let’s consider what set S of choices f could be in accordance with, given these constraints. In particular, let’s consider the choices with respect to the W _{1} and W _{2}options in α and β that f could be in accordance with. To start, we have 16 possibilities: in each situation, α and β, S could contain (i) the W _{1}option (and not the W _{2}option), (ii) the W _{2}option (and not the W _{1}option), (iii) both options or (iv) neither option.
Let’s narrow this down.
First, S needs to be in accordance with a theory T that satisfies IIA_{ d }. This rules out 6 possibilities, leaving us with 10 possibilities.^{Footnote 42}
Second, S needs to be in accordance with f. Since f maintains at β that the W _{1}option \(\ngeq\) the W _{2}option, it follows that S can’t include the W _{1}option at β. This rules out 8 possibilities, 4 of which have already been ruled out, leaving us with 6 possibilities.^{Footnote 43} Likewise, since f maintains at α that the W _{1}option ≥ the W _{2}option, it follows that S can’t include the W _{2}option at α without also including the W _{1}option. This rules out 4 possibilities, 2 of which have already been ruled out, leaving us with 4 possibilities.^{Footnote 44}
These are the four possible ways that S could treat the W _{1} and W _{2}options in α and β that are compatible with the constraints we’ve imposed: (α: W _{1}, β: neither), (α: neither, β: W _{2}), (α: both, β: neither), (α: neither, β: neither).
Now consider two preference functions, f _{1} and f _{2}, which are the same as f in every respect except for their preference rankings of the W _{1} and W _{2}options in α and β. While f maintains that the W _{1}option ≥ the W _{2}option in α and the W _{1}option \(\ngeq\) the W _{2}option in β, f _{1} maintains that the W _{1}option ≥ the W _{2}option in both, and f _{2} maintains that the W _{1}option \(\ngeq\) the W _{2}option in both. In each of the four possibilities for S compatible with the constraints, either f _{1} or f _{2} will be in accordance with S. (f _{1} is in accordance with (α: W _{1}, β: neither), f _{2} is in accordance with (α: neither, β: W _{2}), and both are in accordance with (α: both, β: neither) and (α: neither, β: neither).) And both f _{1} and f _{2} are compatible with IIA with respect to the W _{1} and W _{2}options in α and β.
These nearby preference functions only ‘fix’ f with respect to one violation of IIA. But by iterating this process, we can transform any f in accordance with S which fails to satisfy IIA into a nearby alternative which is also in accordance with S and which does satisfy IIA.
Proof: given IIA_{ d } and that some option is permissible, the three judgments yield a contradiction
Here we’ll see that given IIA_{ d } and the assumption that some option is always permissible, our intuitive judgments in the three cases that comprise the mereaddition paradox lead to a contradiction.
The intuitive judgments that are reported with respect to these three cases leave a bit of wiggle room. It is usually left open in the first case whether both options are intuitively permissible or whether only the W _{2}option is permissible. Likewise, it is usually left open in the third case whether both options are intuitively permissible or whether only the W _{1}option is permissible. This gives us four permutations. We’ll show that all four of these possible prescriptions lead to contradictions.
First, consider the most natural judgments: suppose that both options are permissible in case one, and that only the W _{1}option is permissible in case three. And consider the case in which the agent has a choice between all three of the outcomes:
Given the judgment in the first case, IIA_{ d } entails that in W _{1} W _{2}situations the W _{1}option is permissible iff the W _{2}option is permissible. Given the second judgment, IIA_{ d } entails that in W _{2} W _{3}situations the W _{2}option is impermissible. It follows that in W _{1} W _{2} W _{3}situations, both the W _{1} and W _{2}options are impermissible. Given the third judgment, IIA_{ d } entails that in W _{1} W _{3}situations the W _{3}option is impermissible. It follows that in W _{1} W _{2} W _{3}situations like this one, all three options are impermissible. But there must always be a permissible option available. Contradiction.
Second, suppose that only the W _{2}option is permissible in case one, and only the W _{1}option is permissible in case three. Then this will change what the first judgment and IIA_{ d } entail in the initial case: they will now entail that in W _{1} W _{2}situations (and a fortiriori W _{1} W _{2} W _{3}options) the W _{1}option is impermissible. Since the second and third judgments and IIA_{ d } entail that the W _{2} and W _{3}options are also impermissible in these situations, we again get the result that all three options are impermissible. But there must be a permissible option. Contradiction.
Third, suppose that both options are permissible in both cases one and three. Then this will change what the third judgment and IIA_{ d } entail in the initial case: they will now entail that in W _{1} W _{2} W _{3}situations, the W _{1}option is permissible iff the W _{3}option is permissible. Since the first judgment and IIA_{ d } entail that the W _{1}option is permissible iff the W _{2}option is permissible in these situations, it follows that all three options are either permissible or impermissible. And since the second judgment and IIA_{ d } entail that the W _{2}option is impermissible in these situations, we get the result that all three options are impermissible. But there must be a permissible option. Contradiction.
Fourth, suppose that only the W _{2}option is permissible in case one, and both options are permissible in case three. Then in W _{1} W _{2} W _{3}situations, the first judgment and IIA_{ d } will entail that the W _{1}option is impermissible, the second judgment and IIA_{ d } will entail that the W _{2}option is impermissible, and the third judgment and IIA_{ d } will entail that the W _{3}option is permissible iff the W _{1}option is permissible. Together this entails that all three options are impermissible. But there must be a permissible option. Contradiction.
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Meacham, C.J.G. Personaffecting views and saturating counterpart relations. Philos Stud 158, 257–287 (2012). https://doi.org/10.1007/s1109801298849
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Keywords
 Repugnant conclusion
 Nonidentity problem
 Mereaddition paradox
 Personaffecting view
 Parfit
 Counterpart