1 Transitional Consequentialism and the Mere Addition Paradox Suppose that at some particular time only two courses of action are available. Performing either act will change the world. The first act will produce one state of the world, W1, while the second will produce a distinct state of the world, W2. All else is equal, many will claim that we should perform the act that has the best consequences. And if that’s right, then it seems like what we should do depends on the relative value of W1 and W2. For traditional act consequentialism— what to do would be wholly determined by the relative value of W1 and W2. And even most non- consequentialists grant that an act’s actual or expected consequences can at least bear on its moral status—it’s natural to think that, if an act will have catastrophically bad consequences then it’s wrong to do it, at least all else being equal. Beyond actions, we often assess other things— institutions, laws, social rules, policies, motives, or character traits—in light of their actual or expected consequences; and many contemporary use these assessments to “indirectly” rank actions—e.g. an action is right when it conforms to the set of social rules that (when followed) produces better consequences than any other possible set. So we tend to suppose that consequences can be better or worse than others—and that these assessments are important for determining what is to be done —let’s simply call this familiar assessment of outcomes/effects/consequences “consequentialist value.” Traditionally, we’ve thought of consequentialist value in terms of the value (or comparative value) of the states of affairs an act
Transcript
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Transitional Consequentialism and the Mere Addition Paradox
Suppose that at some particular time only two courses of action are available. Performing
either act will change the world. The first act will produce one state of the world, W1, while the
second will produce a distinct state of the world, W2. All else is equal, many will claim that we
should perform the act that has the best consequences. And if that’s right, then it seems like what
we should do depends on the relative value of W1 and W2. For traditional act consequentialism—
what to do would be wholly determined by the relative value of W1 and W2. And even most non-
consequentialists grant that an act’s actual or expected consequences can at least bear on its moral
status—it’s natural to think that, if an act will have catastrophically bad consequences then it’s
wrong to do it, at least all else being equal. Beyond actions, we often assess other things—
institutions, laws, social rules, policies, motives, or character traits—in light of their actual or
expected consequences; and many contemporary use these assessments to “indirectly” rank
actions—e.g. an action is right when it conforms to the set of social rules that (when followed)
produces better consequences than any other possible set. So we tend to suppose that
consequences can be better or worse than others—and that these assessments are important for
determining what is to be done —let’s simply call this familiar assessment of
outcomes/effects/consequences “consequentialist value.” Traditionally, we’ve thought of
consequentialist value in terms of the value (or comparative value) of the states of affairs an act
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(social rule, etc.) will produce.1 Call this view “the standard account” (hereafter, “SA”). On its
face, SA is simple and powerful. But the effects of our actions are not merely realizations of states
of affairs: our acts also produce changes, or what we will call state transitions. For example, in the
case given above we don’t merely realize W1 or W2, we also make it the case that the world
transitions from its actual state to W1 or W2. A transition, in this sense, is any shift from one state of
the world to another. When we realize a state of the world Wn we also realize a state transition
from the actual world to Wn. If we symbolize the actual world as “Wa” we may symbolize such a
transition as [Wa»Wn]. Thus, for any set of available outcomes, there is a corresponding set of
available transitions. This suggests an alternative to SA that computes the consequentialist value of
an act (etc.) not by the value of the states of affairs that would result but by the value of the state
transitions that would result. Call this “the transitional account” (hereafter, “TA”). According to
TA, the question to ask is not whether W1 is better than W2, but instead whether [Wa »W1] is
better than [Wa »W2]. On TA, it is not states of affairs or events that have consequentialist value; it
is transitions, or changes, that do.
Insofar as TA maintains that it is transitions or changes that have value rather than states of
affairs, it is more in line with the findings of empirical psychology. For it is well established that as a
matter of fact people evaluate changes, or transitions, rather than states of affairs. Most famously,
Daniel Kahneman and Amos Tversky conducted experiments that establish what they call the
reflection effect, according to which value is assigned to gains and losses rather than final assets, with
1 This assumes that the outcomes of actions are certain, when ordinarily choice is complicated by uncertainty,
requiring summing the expected value. However, for simplicity, we will assume throughout that the outcomes of
actions are certain, as the points we aim to make are unchanged if there were uncertainty.
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losses having greater disvalue than the value of equivalent gains.2 More recently, Jonathan Haidt has
gathered evidence for what he calls the adaptation principle, according to which people evaluate their
current state based on whether it is better or worse than the state to which they are accustomed.
Indeed, he notes, this practice has a neurological basis, as nerve cells (neurons) respond vigorously
to new stimuli and fire less in response to stimuli which they have become used to. It is, he
concludes, “change that contains vital information, not steady states.”3 Of course the fact that
evaluative practice focuses on changes rather than resulting states does not settle any normative
issue about value. For it could be simply be a mistake to focus on changes rather than states of
affairs, perhaps an instrumentally valuable mistake -- a good heuristic -- but a mistake nonetheless.4
But we believe there is good reason to think that it is not a mistake -- that TA is a superior way to
evaluate consequences.5 The mission of this paper, then, is to introduce TA, to begin -- but only
begin -- to develop it, and to argue that it is superior not only to SA but also has advantages over
more sophisticated approaches to computing the values of consequences that have arisen from
2Kahneman, Daniel and Amos Tversky. (1979) “Prospect Theory: An Analysis of Decision Under Risk,”
Econometrica 47: 263-92. Also see Haidt, Jonathan. (2006) The Happiness Hypothesis, New York, Basic Books, pp.
8-31, who defends the “negativity thesis,” according to which losses are treated as more significant than equivalent
gains. What is important for us about these psychological findings is not so much this negativity thesis, but that
decision-making is based on the perceived value of changes instead of the resulting states. It is the latter that is in
harmony with TA.
3Haidt, pp. 85-6.
4Indeed, this is how most economists have responded to Kahneman and Tversky’s reflection effect and the other
empirical departures from the theory of expected utility maximization they document.
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doubts about the adequacy of SA. Perhaps most importantly, we explain that when TA is applied to
Derek Parfit’s famous Mere Addition Paradox (hereafter “MAP”) it is uniquely able to preserve the
highly plausible substantive judgments that generate the paradox without either falling into his
infamous Repugnant Conclusion or denying the transitivity of the better than relation.
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According to SA, the only non-normative knowledge required to rank prospective acts’
consequences is information about the available acts and the states of affairs that will
result. However, it often seems that evaluating the consequences of prospective actions requires
more; in particular, it often seems to also require considering the prevailing state of affairs. To put
it more colloquially, it often requires considering “where you’re coming from.” SA, therefore,
seems to overlook crucial evaluative features. To illustrate, consider states of affairs A and B
represented in Figure 1, in which the width of each column represents the size of the population and
the height represents the level of well-being of the people in that state of affairs:
Figure 1 (A and B)
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Assume that A contains a population that is very well off, while B contains all the same people as in A
(hereafter the “A-people”) as well as an equal number of additional people who are not as well off as
the A-people but nonetheless enjoy lives well worth living. Suppose an act a would bring about A and
an action b would bring about B—which act would have the best consequences? Given SA, the
answer will depend on the relative intrinsic values of A and B. But which has greater intrinsic value?
While some have intuitions about this, it seems clear that whether one should bring about A or B
depends on the actual state of the world at the time of choice. For if the actual world at the time of
choice is A, then a, which preserves the current state of affairs, seems better than b, which changes
things from state of affairs A to state of affairs B. After all, remaining in A rather than moving to B
spares the current population from a loss of aggregate and average well-being. On the other hand, if B
is the actual world instead, it is hard to deny that it would be positively tragic to move to A because a
large portion of the population is annihilated in the move.6 Thus, whether it is better to bring about A
or B seems to crucially depend on the prevailing state of affairs – it depends on where you’re coming
from.7 Whether one should choose the action (or non-action) that brings about A or the action (or
non-action) that brings about B depends on the current state of things, and not just the intrinsic
6 This assumes that the transition occurs immediately, rather than by a process of attrition (by the population
reduction occurring by natural deaths). However, this only bolsters the case, for it brings out in another way that
evaluation requires examining not just a (static) state of affairs but how a given state of affairs comes about.
7 How, then, do we account for the fact that some people claim to have intuitions about the relative intrinsic value
of A and B (independent of considerations about “where you’re coming from)? The explanation, we believe, is
that these intuitions are mis-identified: rather than being about the value of a given state, they are intuitions about
the value of a transition to that state from an ex nihilo state.
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features of A and B.8 In this case, SA seems inadequate, as it apparently cannot accommodate crucial
evaluative features of the situation.
Consider another example from population ethics. Just about everyone agrees that it would
be better for the current population to be made blissfully happy than it would be to replace (and
thereby annihilate) the current population with a same-sized (or bigger) blissful population. As Jan
Narveson famously wrote, it is better to “make people happy than to make happy people.”9 But, of
course, whether an increase in well-being is the product of replacement or improving the condition
of an existing population depends entirely on which states precede the increase. SA therefore
cannot account for the crucial evaluative difference between improvement and replacement.
More generally, many so called “person-affecting principles” (hereafter “PAP”), evaluate
gains and losses differentially depending on whether the gain or loss effects those that already exist.
Such principles can accounts for the intuition that if the existing state of affairs is A from Figure 1
that it would be bad to move to B, for no existing person is made better off and some (the A-
people) are made worse off. The same in the case of replacement: no existing person is made
better off, and some -- those who are annihilated -- are made worse off. Although there are doubts
about person-affecting principles, and how to best formulate them, most agree that person-
8 Notice that these judgments do not rest on an implicit appeal to deontological considerations: it’s not merely that
there may be something wrong with bringing about B when you begin in A (and vice-versa). Rather things go
worse when everyone fares worse when additional people are added or when half the population is annihilated.
These are bad occurrences, regardless of whether the forces that lie behind them are agents or not.
9Narveson, Jan. (1976) “Moral Problems of Population,” in Bayles, M. D., ed., Ethics and Population, Cambridge,
MA, Schenkman Publishing Company, pp. 59-80. It is thinking along these lines that suggests that even hedonic
value is not amenable to SA.
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affecting considerations are frequently evaluatively significant.10 The relevance of such person-
affecting considerations cannot be captured by SA.
The inadequacy of SA is not limited to population cases and some person-affecting
considerations. Consider, for example, Figure 2 below that represents two worlds that contain equal
numbers of virtuous and vicious people:
Figure 2 : (Sinners and Saints)
In the first world, the virtuous people enjoy a high level of well-being while the vicious suffer a very
low level. In the second, things are exactly reversed, such that in these two worlds both total and
average well-being are the same. However, most people believe that the first world is better than
10 For doubts about the universality of PAP, see Parfit, Derek. (1986) Reasons and Persons, Oxford, Oxford
University Press, Chap. 16, on the Non-Identity Problem, and Temkin, Larry. (1993) Inequality, Oxford, Oxford
University Press, (1993) “Harmful Goods, Harmless Bads,” in Value, Welfare, and Morality, Frey, R. G. and C.
Morris, eds., Cambridge, Cambridge University Press, pp. 290-324, and (1999) “Intransitivity and the Person-
Affecting Principle: A Response,” Philosophy and Phenomenological Research 59: 777-784.
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the second.11 To accommodate this, Fred Feldman has defended what he calls “Desert Adjusted
Hedonism,” according to which the value of a state of pleasure depends not only on the level of
pleasure individuals enjoy but also by the recipients’ levels of desert.12 But what someone deserves,
at least on the most plausible accounts of desert, depends on what a person has previously done.
To properly evaluate a given distribution of well-being, then, requires information about preceding
states of affairs. Desert, then, a value important to many, is not amenable to SA because what each
person deserves is not an intrinsic feature of a state of affairs.13
Just as those friendly to the value of pleasure and well-being have felt compelled to
incorporate desert into their view, egalitarians have famously worked hard to take responsibility
11 W. D. Ross is credited with first introducing this now-familiar example.
12Feldman, Fred. (1997) Utilitarianism, Hedonism, and Desert: Essays in Moral Philosophy, Cambridge,
Cambridge University Press.
13 Some might disagree, claiming that desert levels are a feature of states of affairs. After all, the situation can be
represented by a “static” diagram as in Figure 2. However, appearances are deceiving: the diagram illicitly
contains information about previous states of affairs, for the virtuous and the vicious are distinguished by their
earlier behavior. Moreover, deep problems with attempts to smuggle such historical features into our state
descriptions or evaluations will be outlined in section III. But briefly, note here that if these were features of the
worlds/outcomes themselves it would then be impossible for two worlds (at a time) to be qualitatively identical but
have different histories. Indeed, it would be impossible for the prevailing states of affairs to have been produced by
distinct causes. Because these both seem possible, desert, as well as other concepts that involve historical features,
must not be included amongst the intrinsic features of a state of affairs.
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into account -- to make their views “responsibility-sensitive.”14 According to responsibility-sensitive
egalitarian views, how good a distribution is depends not just on the degree of equality, but also on
whether each person’s share is proportional to his level of responsibility (for his share being what it
is). Like desert, responsibility is backward-looking: a person’s degree of responsibility (for his share
being what it is) depends on facts about previous states of affairs. As such, responsibility, like
desert, is a value that seemingly cannot be captured by SA.
Another example comes from David Velleman and others who have emphasized that the
value of one’s life (as a whole) depends on narrative considerations, such that two lives with
identical components can have very different value depending on whether the life displays an
upward trend or a downward trend -- on whether the “story” of the life is one of improvement
versus deterioration.15 But improvement and deterioration are not (intrinsic) features of states of
affairs. Whether a given state is an improvement or an instance of deterioration depends on its
relation to previous states. The values associated with the narrative structure of one’s life, then, also
cannot be captured by SA. And many of our most deeply held values are in a broad sense narrative,
including achievement, personal development, learning, self-expression, emancipation, and
autonomy. SA, then, is blind to a whole swath of our mostly deeply held values.
Even values as simple and straight-forward as desire- or preference-satisfaction are an
uncomfortable fit with SA. For satisfying a desire or preference plausibly requires an antecedent
desire or preference. One might object that it is possible to have a satisfied desire at t, without
14 The locus classicus here is Dworkin, Ronald. (1981) “What is Equality: Part I, Equality of Welfare, Philosophy
and Public Affairs 10: 246-62, and (1981)“What is Equality: Part II, Equality of Resources,” Philosophy and
having this desire prior to t -- this occurs every time we come to desire what we already have. But
this objection ultimately does not help SA. For there is often an evaluative difference between
getting what you wanted and wanting what you’ve been given, for the latter can be a problematic adaptive
preference or desire.16 Once again, looking only at the intrinsic features of prospective states of
affairs blinds us to an apparently important difference.
Most of the values people hold dear, then, are such that they can be manifest only when
certain states are preceded by other specific states. These considerations favor TA over SA, as TA
evaluates transitions from one state to another. It is therefore able to capture and explain the
evaluations that cause trouble for SA. In the initial example displayed in Figure 1, for example, TA
quite naturally captures all the evaluative considerations. For if one is in state of affairs A and has
the choice between remaining in A or acting so as to bring about B, TA counsels one to evaluate
not B, but “B coming from A” [A»B]. Because this transition is bad (and, presumably, [A»A] is
neutral), TA suggests that one ought to remain in A.17 Similarly, if one is in state of affairs B and
has a choice between remaining in B and acting so as to bring about A, TA counsels one to
evaluate not A, but “A coming from B” [B»A]. Since this transition is presumably very, very bad,
(and [B»B] is presumably neutral), one ought to remain in B. TA similarly handles the suggestion
that a life with an upward trajectory is better than a life with identical components that has a
16Also, many people are inclined to think that the satisfaction of a long-held desire or preference is, ceterus
paribus, better than one that is shorter-lived. This is an historical difference, and, as such, not amenable to SA.
17 Of course TA itself entails nothing about which would be better. It, like SA, yields no verdicts until
supplemented with a substantive theory of the good. Our observation here is simply that TA (when supplemented
with any common sense theory of the good) aligns with our pre-theoretic views about such cases in a way that SA
cannot.
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downward trajectory, for an improvement in one’s condition is a change for the better while a
deterioration in one’s condition is a change for the worse. Brief reflection on both our behavioural
and theoretical evaluative practice, then, suggests that TA is superior to SA.
II
These kind of doubts about the adequacy of SA are not new with us. Others have
emphasized that evaluative considerations cannot be fully captured in terms of the value of the
intrinsic features of states of affairs. Larry Temkin, for instance, rejects what he calls the Intrinsic
Aspect View (IA), according to which “how good or bad a situation is . . . will be an intrinsic feature
of that situation”. He emphasizes that how good or bad a situation is depends on “how . . . [it]
comes about . . . who its members are” and what it is compared to.18 However, he does not
suggest TA to replace SA. He concludes, instead, that while states of affairs are the proper object of
evaluation, the value of any state of affairs may vary depending on what has come before, or what it
is compared to. He illustrates the view with MAP, represented in Figure 3 below, constructed from
states of affairs A and B from Figure 1, with the addition of state of affairs A+, which adds to A a
population worse off than the populations in both A and B but nonetheless enjoying lives worth
living.
18 Temkin. (1987) “Intransitivity and the Mere Addition Paradox,” Philosophy and Public Affairs 16: 158-9.
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Figure 3 : MAP
Unlike A and B, there is inequality in A+. Following Parfit, Temkin suggests that the import of the
inequality in A+ varies depending on whether the alternative, or where one is coming from, is A or
B. If the alternative is A, or one is coming from A, he argues that the inequality in A+ doesn’t
make it worse for person-affecting reasons, namely because no one is worse off in A+. The A-
people enjoy the same level of well-being in A+ that they enjoy in A. The additional people in A+,
though worse off than the A-people, are not worse-off than they are in A, as they do not exist in A,
and enjoy a life worth living in A+. They are the product of “mere addition,” in the sense that they
are an additional group of people the addition of which does not effect those already existing, or
those who would exist in all alternatives. In contrast, again following Parfit, Temkin suggests that
the inequality in A+ does make it worse when compared to B, because the inequality is the product
of some faring worse so that others can fare better.19 Thus Parfit and Temkin agree that whether
inequality makes an outcome worse depends on how it comes about. Parfit puts it this way:
19 Temkin and Parfit both emphasize that in comparison to A+, B is better both in terms of utility and equality.
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Whether inequality makes . . . [an] outcome worse depends on how it comes about.
It might be true either . . . that some existing people are worse off than others, or . .
. that there are extra people who, though there lives are worth living, are worse off
than some existing people. Only . . . [the former] makes the outcome worse.20
Temkin puts it in terms of the inadequacy of IA:
“. . . how bad the inequality of a situation is, is not an intrinsic feature of that situation -- that
is, it depends on factors that are not internal to the situation . . . How bad it is depends
upon the alternative compared to it. Compared to B, [the inequality in] A+ is bad;
compared to A, it isn’t.21
The value of A+ in the Mere Addition Paradox therefore varies. This is an instance of the general
view that the states of affairs can have variable value. Call this the “variable value view”, or VV.
VV seems just as well equipped as TA to handle the cases that are problematic for SA.
Temkin’s analysis of MAP shows that it can accommodate instances where person-affecting
considerations are relevant. It can also account for narrative values, by maintaining that the value
of some achievement can vary depending on whether it is greater or lesser than previous
achievements, or whether it is just another in a string of successes of growing significance or a
triumph after (and in some way dependent upon) repeated failure. TA and VV, then, both seem to
be viable alternatives to SA. Indeed, one might think that the difference between VV and TA is of
no consequence, or even just a notational variation: one evaluates transitions, while the other
evaluates states depending on whether they realize these transitions. We think, however, that there
20 Parfit, p. 425.
21 Temkin, “Intransitivity and the Mere Addition Paradox,” p.150.
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are significant reasons to prefer TA. VV has significant drawbacks that become clear with a close
examination of MAP. TA, in contrast, handles MAP without these drawbacks, or so we shall
argue.
III
As we have just seen, Parfit and Temkin agree that the value of A+ in MAP varies. It varies
because the inequality in A+ does not count against it when coming from, or compared to, A, but
does count against it when coming from, or compared to, B. Temkin has powerfully argued that
given this assumption of variable value in MAP, a radical, and to most unacceptable conclusion
follows, namely the relation better than is not transitive.22 According to Parfit’s analysis of MAP, the
following are all compelling:
i) A+ is not worse than A
ii) B is better than A+
iii) A is better than B
A central part of Parfit’s rationale for i) and ii) is the variable value of A+. If the inequality in A+
does not count against it when coming from, or compared to, A, he argues that it is hard to see
how A+ could be worse than A. After all, the additional people in A+ enjoy lives well worth living.
They don’t live as well as the A-people. But, in this case, the inequality that this produces does not
count against the value of A+.23 In contrast, according to Parfit, the inequality in A+ counts against 22 This is the central thesis of Temkin. (1987) “Intransitivity and the Mere Addition Paradox.”
23It might be argued that A+ is worse than A on other grounds. For instance, it is worse in terms of maximin: the
worse-off are, in absolute terms, worse off in A+ than in A. However, as Temkin argues, if it is plausible that the
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it when the alternative is B, and this, among other things, makes it worse than B.24 Finally, Parfit
thinks that A is better than B for the familiar reason that if B were better the Repugnant
Conclusion seems inevitable. But of course i), ii) and iii) together violate transitivity: if A+ is not
worse than (or, at least as good as) A, and B is better than A+, then transitivity requires that B is
better than A.25 VV, as Parfit applies it in the Mere Addition Paradox, seems to entail that the better
than relation is not transitive.26
inequality that results from mere addition does not make an outcome worse, then so too with maximin and many
other evaluative considerations.
24 Parfit notes that B is also better in utilitarian terms.
25Parfit’s attachment to transitivity leads him to conclude that there is a paradox here: the three relations are
compelling, but one of the three compelling claims must be given up because they are, in his terms, inconsistent.
See Parfit, Chap. 19. Of course, we should note that there is an enormous literature addressing the Repugnant
Conclusion (and MAP). The most popular families of response include “variable value” views that in one form or
other weight the well-being of actual, future, and prospective individuals differently. See, for example, Ng, Y. K.
(1989) “What Should We Do About Future Generations? Impossibility of Parfit’s Theory X,” Economics and
Philosophy 5: 135-253, and Sider, Ted. (1991) “Might Theory X be a Theory of Diminishing Marginal Value?”
Analysis 51: 265-71. Some try to address the problem by appealing to “critical levels,” roughly thresholds of well-
being (between the levels of A and Z) wherein well-being below this level is discounted or counted negatively.
See, for example, Blackorby, C., W. Bossert, and D. Davidson. (1995) “Intertemporal Population Ethics: Critical
Level Utilitarian Principles,” Econometrica 63: 1303-20, (1997) “Critical Level Utilitarianism and the Population-
ethics Dilemma,” Economics and Philosophy 13: 197-230, and (1997) “Birth-Rate Dependent Population Ethics:
Critical-Level Principles,” Journal of Economic Theory 77: 260-84. Finally, it is becoming more popular to simply
embrace the Repugnant Conclusion, or at least try to explain away its repugnance. See, for example Tannsjo,
Tjorborn. (2002) “Why We Ought to Accept the Repugnant Conclusion, Utilitas 14: 339-59, and Huemer, Michael.
(2008) “In Defense of Repugnance,” Mind 117: 899-933.
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While Temkin thinks we may need to embrace this result, most find it unacceptable. Most
think it is counter-intuitive, or at least more counter-intuitive than the premises necessary for the
argument. Some even claim, Quine notwithstanding, that the transitivity of the better than relation is
entailed by its very meaning. But, perhaps most importantly, denying the transitivity of the relation
better than undermines the practical import -- the normativity -- of our evaluative judgments. If the
better than relation is transitive, and one faces a choice between A, B, C and knows that A is better
than B and B is better than C, then one also knows that A is better than all other options.
Consequently, one has at least some reason to choose A. But when the better than relation is
intransitive among three options one will be entirely at sea, with no option better than the rest. An
intransitive better than relation, therefore, threatens the practical role value is supposed to play in the
typical case where there are more than two options. Because it seems that any plausible view of
practical reason must attach some significance to the relative value of the consequences of
alternative courses of action, the intransitivity of the better than relation threatens practical reason
itself.27
IV
It might be argued against this that there is no intransitivity in MAP if VV is applied in a
more thoroughgoing fashion. In Parfit’s analysis, it is only the value of A+ that varies. But the 26 There is in fact nothing unique about MAP that leads to intransitivity when the value of states of affairs varies.
For any time there is variable value there is the possibility of intransitivity, since a state A whose value varies can
occupy two distinct places in an ordering of states A, B and C.
27 As Rawls, John. (1971) A Theory of Justice, Cambridge, MA, Harvard University Press, p. 30, notes, “[all]
ethical doctrines worth our attention take consequences into account in judging rightness. One that did not would
simply be irrational, crazy.”
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value of A and B might well vary too. Indeed, we’ve already seen reason for thinking this: in our
critique of SA it was emphasized that if you’re in A and the alternative is B, it is better to remain in
A, while if you’re in B, it is better to remain in B. Alastair Norcross has in fact argued along exactly
these lines, insisting that Temkin is not sufficiently thorough in the application of the idea that the
value of a state of affairs can vary depending on where you’re coming from (or what it is being
compared to).28 He starts by agreeing with the reasons we adduced for thinking that A is better
than B if you start in A, but worse when you start in B:
If we start at A, A is better than B. What happens if we start at B? The move from B to A
would involve the deaths of half the population, and a small improvement in the lives of
the other half. Could a large loss of utility for one half be made up by a small gain for the
other half? This hardly seems likely. So if we start at B, B is better than A.29
It would be contradictory to say that all-things-considered both A is better than B and B is better
than A. He insists, therefore, that A is better than B only “relative to starting at A,” which he
denotes by saying that A is “Abetter” than B. Similarly, B is (only) Bbetter than A. This
relativization, he then claims, does away with the apparent intransitivity in MAP. Assuming that
A+ is not worse than A whether one starts in A or A+, and that B is better than A+ whether one
starts in B or A+, we have the following relations:
a) A is Abetter than B
b) B is Bbetter than A
c) A+ is not Aworse than A 28Norcross, Alastair. (1999) “Intransitivity and the Person-Affecting Principle,” Philosophy and Phenomenological
Research 59: 769-76.
29 Norcross, p. 771.
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d) A+ is not A+worse than A
e) B is Bbetter than A+
f) B is A+better than A+
But there is no intransitivity here. A is Abetter than B, and B is Bbetter than A+. But nothing
follows from this about the relation between A and A+, since the relation between A and B (being
Abetter) is different from the relation between B and A+ (being Bbetter).30 A thoroughgoing
application of VV, then, avoids intransitivity, or so Norcross argues.
But even if Norcross is right, it is a pyrhhic victory because his view threatens to undermine
practical reason just as much as does the denial of transitivity.31 Where Temkin and others postulate
variable value, Norcross offers us a kind of ambiguity or multiplicity: the value or “betterness” of a
state does not change; instead, there is more than one better relation, indeed there are as many “better
relations” as there are possible states of affairs. That is, states can be Abetter, Bbetter . . . and XBetter.
But this multiplicity leads to a new and potentially worse concern, which we will call radical
incomparably: there is no way to combine the various better relations in order to actually reach a
practical verdict -- an all-things-considered verdict about which states to bring about.32 If A is
30 Norcross, p. 772, puts it this way: “ . . . A is Abetter than B, which is both Bbetter and A+better than A+, which
is neither A worse nor A+worse than A. But this doesn’t violate transitivity. For that we would need the claim that
B is Abetter than A+.”
31 Temkin. (1987) “Intransitivity and the Person-Affecting Principle: A Reply,” thinks that Norcross isn’t right --
that intransitivity isn’t avoided by the relativization of “better than.”. Since we think that Norcross faces an equally
big problem even if he is right, we will not enter into this debate.
32 The point here is similar to one Velleman. (1993) “The Story of Rational Action,” Philosophical Topics 21: 229-
54, makes against a similar contextualization strategy in rational choice theory.
19
Abetter than B, and B is Bbetter than A, which state is it better to bring about? This can’t be
answered without knowing how to compare “A-betterness” and “B-betterness.” Even if the
current state of affairs is A, whether it is better to remain in A or switch to B depends on the
relative significance of A-betterness and B-betterness. The action-guiding function of value, once
again, is apparently lost. The very thing that allows Norcross to avoid intransitivity -- the
multiplicity of better than relations -- prevents his view from grounding practical reason.
Avoiding radical incomparability requires a rule specifying which “better relation” is
practically most important in a given context. One suggestion that seems in the spirit of Norcross’
view and answers the question of what “better than” relation to privilege is the following: when you
are actually in X realize the available state that is Xbest. In other words, if you find yourself in A
choose whichever available state is A-best; if in B realize the available state that is B-best; and so on.
Though this approach can save the practical import of Norcross’ alternative, it would ultimately
lead right to the Repugnant Conclusion. For A+ is not Aworse than A, and B is A+better than
A+. Moving from A to B via A+, then, must be an improvement, as each step is either neutral or
an improvement. Moreover, if A+ is not Aworse than A, then there must be a state of affairs B+,
which differs from B in just the way A+ differs from A, that is not Bworse than B. Similarly, if B is
A+better than A+, then there must be a state of affairs C, which differs from B+ in just the way B
differs from A+, that is B+better than C. This can be carried out, of course, through C+, D, D+,
etc., to Z, with the result that it is an improvement to move from A to Z (because each step is
either neutral or an improvement). Of course, one could avoid this conclusion by denying
transitivity -- by denying that Z is better than A even if A+ is not Aworse than A, B is A+better
than A+, B+ is not Bworse than B, etc. But then it seems that we must either accept the
20
Repugnant Conclusion or deny the transitivity of the relation better than. Neither is particularly
appealing.
Indeed, that one must choose between the Repugnant Conclusion and denying the
transitivity of the relation better than is what many take to be the true challenge of the Mere Addition
Paradox.33 For the same progression from A to Z via A+, B, B+, C, C+, etc., can be generated
without the relativization of better than that Norcross recommends. For if A+ is not worse than A
and B is better than A+, then B+, which differs from B in just the way A+ differs from A, must
not be worse than B, and C, which differs from B+ in just the way B differs from A+, must be
better than B+ (See Figure 4).
Figure 4
Each step from A to Z, then, is either neutral or an improvement, which means that Z must be
better than A. Here too the progression from A to Z can be stopped by denying transitivity. For
33 See, for instance, Rachels, Stuart. (2004) “Repugnance or Intransitivity: A Repugnant But Forced Choice,” in
The Repugnant Conclusion: Essays on Population Ethics, Ryberg, Jesper and Torbjorn Tannsjo, eds., Dordrecht,
The Netherlands, Kluwer Academic Publishers, 2004, pp. 163-186.
21
without transitivity it does not follow that Z is better than A even if A+ is not worse than A, B is
better than A+, B+ is not worse than B, etc. The variable value view (including Norcross’ version
of it), is therefore stuck with accepting the Repugnant Conclusion or denying the transitivity of the
relation better than. One way or another, there is a heavy price to pay for VV.
There is another reason to be less than fully satisfied with VV. Just as instrumental goods
entail and are explained by the existence of non-instrumental goods, so too it seems that the
variable value of states should entail and be explained by the invariant or unconditional value of
something else. As such, VV does not seem to reach axiological bedrock. Indeed, brief reflection
on VV suggests that it is state transitions that are a better candidate for bedrock. Conditional
goods are items that are unconditionally good only when the relevant conditions are met: If A is
good conditionally only on its being accompanied by B, then it’s the conjunction of A and B that is
good. This is important because variable value theorists treat states and state-types as having a
value that behaves like a species of conditional good: they possess a certain value (or disvalue)
depending on the presence of particular antecedent states of affairs. Accordingly, the most natural
conclusion is that it is in fact these conjunctions of obtaining states and particular historical events
that are the object of value. But such conjunctions just are state transitions. TA, then, seems to
correctly identify what is evaluatively most fundamental. Moreover, this structure is embedded in
the way we think and talk about value. To illustrate, suppose that Dan weighs 180 pounds at t. On
its face there seems to be nothing immediately evaluatively relevant about such a state of affairs.34
34 Of course Dan’s weighing 180 pounds might be thought to be very good or bad. If he is quite short, then at 180
pounds he is likely overweight, possibly obese. If he’s average height or slightly more he is likely at a healthy
weight. But this misses the point. Being overweight or at a healthy weight is a distinct state from weighing 180
pounds. The point here is that the state of weighing 180 pounds (in and of itself) is neither good nor bad.
22
Now further imagine that after years of struggling with his obesity, it is just now, at t, that Dan
finally reaches his long-sought target weight of 180 pounds. Many would be inclined to say this is
good. But are we thereby claiming the state or a sequence ending in this state is good? It is most
natural to say something like “although there’s nothing particularly good about one’s weighing 180
pounds, in virtue of reaching 180 pounds, Dan has improved his health, succeeded, or had his efforts
rewarded, and these things are valuable.” The variable value theorist cannot say this. Instead, he
would have to say something subtly different, but certainly more awkward: Dan’s weighing 180
pounds is, in fact, good; and it is good because it partially constitutes an improvement of health or
effort rewarded. On VV, it is not good that Dan’s health has improved, or that his efforts have
been rewarded -- as these are types of transitions -- and yet these are the very things we appear to
be endorsing. In this way, TA seems more faithful to our evaluative discourse.
V
Nevertheless, some may not be impressed. Certainly it is a risky to derive normative
conclusions directly off of ordinary talk, since the way we talk is structured and constrained by
factors other than philosophical accuracy. Further, some might argue, TA cannot be more
reflective of either the “axiological bedrock” or evaluative practice unless it yields different and
superior substantive results than versions of VV. But TA, one might suspect, cannot be superior in
terms of substantive results because the two approaches are too similar, perhaps merely “notional
variants” of each other, as suggested before. While it is true that TA and VV will employ essentially
the same substantive axiological principles, they do have different substantive implications. The
difference emerges upon looking at how TA would analyze MAP. The analysis suggested by VV,
recall, seems unable to avoid the unhappy dilemma -- a forced choice between the Repugnant
Conclusion and denying the transitivity of better than. This has led some to embrace the Repugnant
23
Conclusion, and others to accept intransitivity (and attempt to deal with its radical implications). If
TA can avoid this dilemma -- and we think it can -- it surely emerges as a promising approach
worthy of careful consideration.
According to TA, prospective consequences are evaluated not in terms of the value of the
resulting state of affairs but in terms of the value of the resulting state transitions. If TA is to
avoid the Repugnant Conclusion it must not be the case that in MAP the sum of the value of the
state transitions from A to Z via transitions to A+, B, B+, C, etc. is higher than the value of
remaining in A. Although it is perhaps impossible to establish that it is not without a complete
axiology for state transitions, an initial case can be made. Consider first the transition [A»A+]. Call
this “T1”. Intuitions about whether this is a good transition are mixed. Some claim the transition
is neutral, others claim it is slightly negative, and finally some that claim it is somewhat positive.
However, it doesn’t seem plausible to maintain (without ulterior motives) that T1 is either very
positive or very negative. Let us assume the worst-case scenario among those that are plausible for
avoiding the Repugnant Conclusion, namely that T1 is slightly positive. Now consider the transition
[A+»B], and call it “T2”. It is hard to deny that T2 is good: it constitutes an improvement in
equality and average well-being. Now it initially looks like we’ve run head-long (again) into a
version of the Repugnant Conclusion. If the move from A to B involves the two positive
transitions T1 and T2, then presumably things go best if we move to B, and then B+, C…and so
on down the line to Z. However, this is a mistake. According to TA, actions are evaluated
according to the sum of the value of the transitions that would be realized. And when we realize
T1 and T2, a consequence is realizing the further transition [A»B]. Analogously, suppose I start a
trip in San Francisco, stop in Chicago, and next travel on to Miami. By traveling from San
Francisco to Chicago, and then from Chicago to Miami, I make it the case that I traveled from San
24
Francisco to Miami. Our unmotivated intuitions in MAP about [A » B] are rather clear. With this
transition, which we’ll call “T3”, we make everyone worse-off for no one’s sake: peoples’ well-being
is sacrificed for mere addition. And, as we move along the alphabet, the transitions (from A to C,
A to D…A to Z) become increasingly bad, repugnant even. If that’s right, then we arrive at the
following results:
1. The transition T1 [A»A+] is at best slightly positive.
2. The transition T2 [A+»B] is positive.
3. The transition T3 [A»B] is negative.
4. The sequence [A»A+»B] realizes T1, T2 and T3.
5. If T3 is more negative than [T1 + T2] is positive, the consequences of initiating this sequence are
worse than that of staying at A.
Thus, any axiology that predicts that T3 is of greater disvalue than the sum of T1 and T2 is of
positive value avoids the conclusion that it would be better if we moved from A to B, even if via
A+. And, a fortiori, such an axiology would predict that it would be bad if we started in A and
moved to Z (either directly, or via A+ through Y+).
While it is not obvious that T3 is of greater disvalue than the sum of T1 and T2 is of positive
value, it is certainly plausible that it is. Therefore, there is a plausible axiology for state transitions
that avoids the Repugnant Conclusion. And, of course, the better than relation between these
transitions would be transitive: T1 is not as good as T2, and T3 is worse than both. We’d have the
following stable ordering: T2 is better than T1, and T1 is better than T3. According to a plausible
version of TA, then, the dilemma that confronts the defender of the view that the value of states of
25
affairs varies -- either reject transitivity or succumb to the Repugnant Conclusion -- can be
avoided35
VI
Even those sympathetic to TA might be suspicious of our approach to MAP. One might
ask why we sum the value of the longer transition from A to B, when we have already evaluated its
component transitions, namely [A»A+] and [A+»B]. Why sum the value of all the transitions
produced, rather than simply all the “consecutive” or “sequential” transitions? Longer length
transitions, it might be argued, should not be counted independently because their value is
accounted for in our evaluation of the shorter, component transitions. Call this suggestion
“TAsequential” or “TAS”. TAS is atomistic insofar as it counts only changes that are contiguous
and non-overlapping.36 To illustrate, if a sequence begins A at t1, transitions to B at t2, and then
finally moves to C at t3, TAS claims that the sequence should be evaluated by summing the value
of the transitions [A»B] and [B»C] (see Figure 5):
35 The reason this is possible on TA, which might seem only a notational variant of VV, is that once you make it
transitions that you are evaluating there become more items to sum, namely the transitions like [A»B] that are
realized in virtue of other component transitions.
36 In this way, TAS is just a notational variant of VV.
26
Figure 5
TAS, however, is not plausible because it misses important evaluative considerations. TAS
counsels us not to count every change, but only those that are not composed of other changes. But
many evaluatively relevant transitions, e.g., falling in love, becoming ill, achieving a goal, and even,
arguably, dying, are composed of complex sets of shorter transitions. Summing only the value of
the shorter changes may not accurately capture the value of the transitions they compose.
Consider the case of falling in love. Typically, this is a gradual process -- love rarely strikes us in an
instant. Each day (or hour, or minute, or second) one’s affections are just a bit stronger than the
day (or hour, or minute, or second) before. From one day (hour, minute, or second) to the next,
the increase in the value of the relationship is minimal.37 But surely, critics can contend, this does
not force us to conclude that the sum of such increases is less than the value of the relationship
when love has bloomed. Indeed, isn’t it at least possible that this position is overly romantic, 37The thinking here is similar to a line Temkin. (1996) “A Continuum Argument for Intransitivity,” Philosophy and
Public Affairs 25, has pushed, namely that the two ends of a continuum can differ in kind even if no two
consecutive points along the continuum differ in kind.
27
introducing a degree of ineffability concerning (the value of) love better suited to poets than
philosophers?
We agree that nothing about the gradual nature of falling in love forces the conclusion that
the value of a relationship when love has bloomed is greater than the sum of the incremental steps
along the way. But the problem with TAS is not that it is blind to the irreducible value of falling in
love. Rather, the problem is that it does not allow any such (irreducible) value -- it is blind to the
possibility that a “composite” transition has a unique value worth counting in its own right. Thus,
TAS is a very restrictive view. Views that allow for such value in composite transitions are more
plausible because they are more ecumenical -- more generous concerning the kinds of values that
might exist. Barring powerful reasons for a restrictive view like TAS, a more ecumenical approach,
one that permits us to sum more than just the sequential transitions, seems preferable.
Moreover, a strict application of TAS shows it to be wildly implausible, possibly incoherent.
The transitions that compose one’s falling in love -- the incremental increases in affection and care
-- are also presumably themselves composed of still shorter transitions. TAS would thus tell us to
evaluate only those shorter transitions. Strict application of this reasoning requires evaluating the
very smallest or most basic units of change, e.g., sub-atomic changes. But, first, there may be no
such basic level; and second, if there is, it seems clear that transitions at this level would not
instantiate any evaluatively relevant property, much less all evaluatively relevant properties.
It seems, then, that our approach to MAP is superior to the approach recommended by
TAS, since capturing the full range of values seems to require evaluating and aggregating every
change, including the composite changes that occur at greater and smaller intervals of time. After
all, if its the various transitions that determine whether the world goes better or worse, we ought
not artificially restrict ourselves to counting only some small sub-class, because any transition is, in
28
principle, evaluatively relevant. Call the view that incorporates the evaluation of all changes or
transitions “TAUnrestricted” or “TAU”. According to TAU, a sequence that begins with state A at
t1, transitions to B at t2, and finally moves to C at t3, is evaluated by summing the value of the
transitions [A»B], [B»C] and [A»C], as in Figure 6:
Figure 6
Despite TAU’s promise, we will now explain why computing the value of prospective
consequences isn’t quite as simple as TAU would make it. However, we will try to show that in
each case where TAU is problematic, a similar problem holds for traditional outcome or state-
based theories, and as such, is not special grounds for rejecting a transitional-based approach. The
foremost among these concerns is that while TAS can underestimate total value, TAU can
overestimate. Consider again a sequence of states A (at t1), B (at t2), and C (at t3). A and B, and B
and C are temporally contiguous, but A and C are not. A to C is, therefore, a non-sequential
transition. TAU tells us to evaluate this sequence by summing the value of all the transitions it
instantiates. The problem is that counting the value of the final non-sequential transition can
29
involve an illicit doubling of the value of the contiguous transitions.38 For example, consider the
value of pleasure. Suppose at one moment you experience none, then you feel some, and then you
feel a bit more. Presumably, it’s plausible to count the first two transitions as improvements worthy
(respectively) of positive scores. What is not plausible is to further say that the value of this
sequence is doubled by the transition from none to even more. For this means, absurdly, that it is
twice as good to go from none to some to a bit more, than it would be to go directly from none to a bit
more. TAU, therefore, permits unacceptable double-counting.
To avoid double-counting without reverting to the problematic sequential approach, one
might advocate a “holistic” approach: rather than count the component transitions [A»B] and
[B»C], just count value of the transition of which they are parts, namely [A»C]. Again, returning to
our example, this version advises us to count neither [none » some] nor [some » a bit more]; it tells us to
merely count [none » a bit more]. Though the holistic approach handles this case fairly well, it is also
not plausible. In short, the problem is that the value of a sequence does not merely depend on how
it begins and how it ends. For example, if we were evaluating lives, the fact (were it one) that all
lives begin in the same state and end in annihilation would not entail all lives are of equal value --
what happens in between, and in what order, also matters. The same is true of worlds. If we
discovered that all metaphysically possible histories begin with a Big Bang and end in Heat Death, it
does not follow that none of these possible histories is better than any other. How you get from A
to B doesn’t always matter. But surely sometimes -- likely most of the time -- it does.
38 This is the same problem besetting SA, as noted at the very beginning of this discussion. Thus, as we note
below, this is not a special problem for TA (that might count against it compared to SA or other alternatives).
30
It appears, then, that the transitional approach faces a dilemma: it must either a) employ an
implausible sequential or holistic approach, or b) face an intractable double-counting objection. It
is important to note, first, that this is not a special set of problems for TA. Rather, it is an instance
of the long-standing problem of computing the value of parts and wholes. Analogous problems
plague SA, for as we pointed out earlier just as non-sequential or composite transitions are
composed of other transitions, states of affairs are likewise composed of other states. For example,
suppose the following states obtain at a particular time: John taking pleasure in X, John taking pleasure
in Y, and John taking pleasure in two things. Plenty of axiologies will treat all three states as good (or
better than if they did not obtain). However, it would involve an objectionable double-counting to
sum the value of all three. Thus, to avoid double counting one appears forced to count the two
“lower-level” states that make the third obtain or just the third “higher level” state by itself. But
both approaches fail. If you just count the “component” states, important evaluative information is
sometimes missed. For example, presumably my feeling at peace, or my accomplishing all my goals, are
states that obtain in virtue of other valuable states. One is at peace, we assume, in virtue of not
suffering in various ways and not being anxious or fearful in various way. And one accomplishes all
of one’s goals in virtue of accomplishing each of one’s goals. In these cases, if we just count the
value of the component states we fail to capture the special value of the whole. The solution also
won’t be to count only the higher-order or “holistic” values, because sometimes the components
make a difference. For example, it is true in both A and Z in MAP that everyone has a life that’s worth
living. This complex state of affairs may be independently valuable -- worth counting in it’s own
right -- and yet it is not present in individual states of affairs that compose A and Z. Thus,
counting only the highest-order or “holistic” values may not allow us to say A is better than Z.
31
So both TA and SA face a problem posed by counting states and/or transitions that are
constituted by other states and/or transitions. Sometimes it is appropriate to include the value of
the whole and sometimes it is not. But, crucially, there’s no real mystery about when, roughly, the
relevant whole should be independently evaluated and summed: it should be evaluated and
independently summed when the state or transition instantiates an evaluatively relevant property
(according to one’s favored axiology) that’s not instantiated by its constituent parts. Accordingly,
we should look towards a transitional view that allows us to add the value (or disvalue) of non-
sequential transitions only when these non-sequential transitions manifest a value that is
independent of the value of the sequential transitions that compose it. Moreover, we count the
non-sequential transition only to the extent that its value differs from the value of its constituent
transitions.
It turns out to be surprisingly difficult to find a formula that properly captures what we’re
looking for here. But this problem of how to aggregate in TA does not have be solved to see the
promise of the approach -- its ability in MAP to avoid both the Repugnant Conclusion and the
denial of the transitivity of the relation better than. Recall that in our initial application of TA to
MAP, we followed TAU -- we evaluated all transitions, and simply summed. The problem, we have
seen, is that this simple view often implicitly “double-counts” the value of the component
transitions. But in MAP both component transitions (A to A+, and A+ to B) are positive. So if
any double-counting has occurred, it would be objectionably biased towards the conclusion that it
would be better to go from A to B (through A+) than to simply remain in A -- towards the
Repugnant Conclusion. The flaw in the model, then, cannot have generated our favorable result.
Nevertheless, we acknowledge that we have yet to provide a fully satisfactory theory of
aggregation for TA. As we suggested at the outset, in this paper we can only begin to develop the
32
transitional approach. Surely there is more work, and more trouble, ahead if one wants to fully
develop and defend the view. However, even without solving the problem of including all relevant
evaluations without double-counting, it is more than plausible to say that the transitional approach
can avoid the Repugnant Conclusion without denying the transitivity of the relation better than. For
any adequate theory of aggregation for TA will have it that the unique values associated with non-
sequential transitions must be independently evaluated and summed, in which case in MAP if the
negative value of T3 [A»B] outweighs the sum of the positive value of T1 [A»A+] and T2 [A+»B],
then the value of the sequence as a whole will be negative, and therefore better to remain in A than
to move to B via A+.
VII
There are a few other concerns that we think need to be addressed to adequately establish
the promise of the transitional approach. It might be argued that the solution the transitional
approach offers in MAP is too thin: it rests on an assertion that it is plausible that the disvalue of
T3 is greater than the combined positive value of T1 and T2. Some defense of this assertion should
be given. It seems that we already know that T3 is really quite bad: the A-people suffer a loss while
no existing people are made better off, and if the transition is not bad, the Repugnant Conclusion
looms. However, it might be argued that this disvalue is associated with a direct transition from A to
B, while T3 is an indirect transition from A to B, via A+. And, further, it can’t be assumed that just
because the direct transition is bad that the indirect transition is bad. Consider again traveling from
San Francisco to Miami. Suppose that traveling direct from San Francisco to Miami is bad because
there is frequently severe turbulence on this route as one flies over parts of Texas and Oklahoma.
Now imagine, instead, that the flight has a stop-over in Chicago. In this case, one entirely bypasses
flying over Texas and Oklahoma, avoiding entirely that potential for that severe turbulence. So
33
what made the direct flight bad simply doesn’t apply to the indirect flight with a stop-over in
Chicago. The indirect route, we might say, does not necessarily inherit the disvalue (or the value)
of the direct flight. Analogously, the fact that a direct transition from A to B is very bad provides
no reason for thinking that the transition from A to B via A+ (T3) is bad, never mind that it is
sufficiently bad to outweigh the combined positive value of the transition from A to A+ (T1) and
A+ to B (T2). After all, a lot of what is bad about the direct transition, namely that some existing
people are made worse off while none are made better off, does not apply to either [A» A+] or
[A+» B]. For in the transition from A to A+, the A-people are not made worse-off, while in the
transition from A+ to B, though some existing people are made worse off, others are made better
off.
Though this objection is seductive, it does not threaten the transitional approach’s
appealing treatment of MAP. First of all, the travel example misleads. Experiencing turbulence, as
the example makes clear, is only contingently connected to flying from San Francisco to Miami.
Such contingent factors can surely affect the overall relative value of the direct versus the indirect
route. However, such contingent considerations have no bearing on the value (or disvalue) of
intrinsic features of the transition. If there is something intrinsically bad about one’s location
changing from San Francisco to Miami, then it is bad whether one traveled directly and experienced
turbulence or traveled indirectly and did not experience turbulence. Similarly, it would seem, if
there is something intrinsically bad about transitioning from A to B in MAP, then it is bad whether
one takes the direct route or the indirect route through A+. Thus, the travel example provides no
grounds for thinking that an indirect transition does not necessarily inherit the value (or disvalue) of
the equivalent direct transition. It may not inherit the value (or disvalue) of contingent features of
34
the direct route; however, no reason has been provided for thinking that the indirect transition
doesn’t inherit the value (or disvalue) of intrinsic features of the direct transition.
And, as we’ve seen, there is something intrinsically bad about the transition from A to B in
MAP: in the transition the A-people are made worse off, without any existing people being made
better off. This bad result is realized whether one gets from A to B via A+ or not, just as if there
were something intrinsically bad about one’s location changing from San Francisco to Miami, it
would be bad whether one travels through Chicago or not. It should be clear from this that the
objection under consideration here really amounts to nothing more than a re-packaged insistence
on the sequential approach (TAS). For the fundamental point of the objection is that because the
indirect route may not inherit the bad (or good) features of the direct route, the non-sequential
transition from A to B should be evaluated (only) in terms of its component parts. Given the
inadequacy of TAS, our favored version of the transitional approach’s appealing treatment of MAP
withstands the objection.
There might be a lingering sense that the objection has not been fully addressed. Aren’t
there cases in which an intrinsic feature of a transition is bad (or good) when the transition is direct
but not when it is indirect? The best candidates seem to come from population cases. For
instance, it would surely be a bad thing, as we’ve discussed previously, if the current population
were annihilated and replaced by an equivalent population at the same or higher level of well-being.
But of course the whole of human history, if looked at with a wide lens, is a history of replacement:
approximately every 100 years a new population has entirely replaced a previous population. Call
this evolutionary replacement, in contrast to instantaneous replacement. Instantaneous
replacement is direct, while evolutionary replacement is indirect, passing through intermediate
states where some of the old and some of the new population exists. Common sense seems to be
35
that while instantaneous replacement is surely terrible, the evolutionary kind is not. The suggestion
is that our view is blind to this difference.
The obvious response is that while replacement is a feature of both the direct and the
indirect transition, it is not the evaluatively relevant feature. Instead, what makes instantaneous
replacement bad is not that it is an instance of replacement; what makes it bad is that an entire
population is killed -- all its members suffer a premature and/or unnatural death. In evolutionary
replacement, this is simply not the case. So even in this example it is not the case that there is an
intrinsic feature of a transition that is bad (or good) when the transition is direct but is not when
the transition is indirect. This obvious reply may be fully adequate. However, those with a more
tragic frame of mind may hold that a more fine-grained axiology is unnecessary because it really is
bad (now and forever more) that those who once lived -- even long, long ago -- are now gone. For
the tragic-minded, even evolutionary replacement is bad. This view would assign some negative
value to any prospective change that does not include everyone who has ever existed. To some,
such a view will sound silly. But silly or not, it will not lead to counter-intuitive practical
conclusions, for all available transitions will share these negative features so long as resurrection
remains impossible. And pre-mature deaths will be, on this version, still be worse: your dying at T1
rather than T4 entails that the transitions realized between these times intervals will have a bad
making feature they would not have otherwise had. So, either way, the objection that indirect
transitions do not necessarily inherit the value (or disvalue) of equivalent direct transitions does not
ultimately have force against the transitional approach to MAP.
VIII
A big worry is about the transitional approach is that it too will suffer from some of the
very problems that motivate it. After all, if the trouble with SA is that it merely sums the value of
36
the states without any regard for the order in which the states obtain, why should we think the
transitional approach escapes the very same concerns? The transitional approach after all, merely
sums the value of all the transitions that occur, but with no regard for the order in which they
obtain. Even though transitions are by their very nature temporally ordered, why should we assume
that the value of more complex multi-part narratives can be adequately captured by summing the
value of the two-place changes that compose them? Perhaps the arguments we’ve provided are
even more powerful grounds for a theory that sums the values of ordered triples, quadruples, or
quintuples. Indeed, if we really take this thinking to its conclusion, why shouldn’t we arrive -- as
Velleman does regarding the prudential value of a life -- at the view that proper evaluation of a
sequence requires the independent and non-aggregative evaluation of the sequence as a whole?39
Let’s call such a view “rich holism” about value, following our suggestion in Section I that
consequentialists sometimes reject SA in favor of more holistic alternatives.40
We have no proof that value is not richly holistic. But from a practical perspective it
would be unfortunate if it were. First, it would be impossible to evaluate any sequence, or its parts,
until the sequence is complete. We would be unable to evaluate how well things went, or are going,
39 Velleman. (1991) “Well-Being and Time.”
40 Campbell Brown has recently suggested such a holistic view according to which an action is right if and only if
there is no alternative action that will result in a superior (complete) possible world. (2011) “Consequentialise
This,” Ethics 121: 749-771. A similar view, introduced (but not defended) in an early version of Derek Parfit’s On
What Matters—contends that the value of something’s consequences—the extraordinarily complex and perhaps
infinite history that would result from it—is wholly independent of the value of the parts (i.e. the ordered set of
states of affairs or worlds) that compose this history.
37
until the narrative ends. But at that point -- the end of the universe? -- no one will be around
anyway. Maybe that result is not all that surprising or unsettling. But the more important worry is
that on such a view we can make no evaluation of the parts without knowledge of the whole that
they will ultimately compose. Because we’re always going to be ignorant of how the complete
narrative turns out, we’re thereby unable to evaluate any of our available options at a time, and,
once again, value cannot play an action-guiding role.
Furthermore, there are many reasons to be confident that two-place changes, and not more
complex multi-part sequences, are the proper objects of evaluation and aggregation. First, as we
explained above, most of our axiological principles and practice are best seen as assessing
transitions rather than singular events. But no familiar principle seems to express an evaluation of
three or more step changes. And, of course, any such principles would soon become too complex
to be manageable. Most importantly, changes have a special status that makes them the most likely
suspect as our axiological “atoms”: they are the least complex unit that allows us to reconstruct
complete narratives. Knowing which states obtained during a period of time will not allow us to
determine the order in which they obtained. However, knowing which state-transitions obtained
will. All information about the nature of a many-part sequence can be inferred from mere
knowledge of the state-transitions of which it is composed. For example, imagine that one knows
the following six state transitions occurred:
([Z»B], [Y»A], [Z»Y], [Z»A], [B»A], and [B»Y])
With a little thought, it’s easy to see that there’s only one temporal ordering that’s compatible with
all and only these transitions: Z before B before Y before A. This result generalizes even when the
same state-type occurs more than once. For example, consider the case in which the following
three state transitions occurred:
38
([A»B], [B»A], [A»B])
One can infer that the whole sequence is [A then B then A] rather than [A then A then B] or [B
then A then A], which respectively decompose into different sets of three transitions.
Because we can reconstruct the full nature of more complex sequences (three parts or
more) merely by knowing the transitions of which they are composed, it seems like any more
complex axiology that assesses longer sequences would be otiose. No information is lost in merely
evaluating the transitions alone. Consequently, we have strong grounds for suspecting that this is at
least one case where the value of a whole is a simple function of the value of the parts.
IX
We admit that there’s an appealing simplicity in a purely forward-looking theory -- a theory
that never looks at the way the world is, or has been, but looks only at the intrinsic features of the
ways things will be as a result of various courses of action. But such views are a radical departure
from the way we actually think, as Kahneman and Tversky’s prospect theory has shown, and from
the way we theorize about value, as the considerations in Part II above make clear. Once we realize
that our evaluations are past- and present-sensitive, we face a choice: either i) claim that the
fundamental bearers of value remain states of affairs, but allow that their value is non-intrinsic and
varies depending on the history that precedes them, or ii) conclude that it is misleading to claim
that states have value independent of the value of the changes they would realize. The difference is
subtle -- a real philosophers’ distinction. But it is important -- indeed, we claim, monumentally
important. For the former approach forces us to give up something nearly sacred: either our
conviction that that world is not improved when a very large population, leading nearly ideal lives,
evolves into an enormous population living lives barely worth living, or the transitivity of the better
than relation (or, even worse, the very idea that there any facts about whether outcomes are better
39
or worse).41 We think it is time to try the second option. Since the 1984 publication of Reasons and
Persons, the hard lesson appears to be that something almost sacred must go. We agree. However, we
suggest an alternative that, as far as we know, has not been previously considered, namely that we
should replace the view that states of affairs are the bearers of value -- the theoretical apparatus
philosophers, economists and psychologists have typically used to express our substantive verdicts -
- with the view that it is changes, or state transitions, that are the bearers of value. Much more
needs to be done to fully develop and defend the transitional approach. It too is beset with many of
the obstacles that continue to confront the traditional approach, and it surely has unique problems
of its own. But even at this preliminary stage its potential is exciting. Shifting away from the old
approach, both in our axiological theories and the consequentialist views based on them, promises
to be a change for the better.
41 Arrhenius, Gustaf. (2011) “The Impossibility of a Satisfactory Population Ethics” in Colonius, H. and E.
Dzhafarov, eds., Descriptive and Normative Approaches to Human Behavior, World Scientific Publishing
Company, pp. 1-26, suggests our best option may be to simply give up cognitivism about such axiological claims.
