. 7
( 10)


Objections to this argument may seem pressing, and indeed it must
be re¬ned in certain ways.5 First objection: Perhaps certain unconstituted
normative elements plus other non-normative elements together constitute
some sort of objective value in a world. Indeed, it may seem that this is

5 One objection is this: Perhaps the phrase “value-bearing elements” is ambiguous in a way
that makes the simple argument for Restriction A seem more plausible than it is. If a whole
has some sort of value, then that value can be ascribed in some sense to its elements, but that
doesn™t imply that the value accrues to the elements outside of that context. Broome (1991)
develops a way to bundle value into elements that implies standard utilitarian summation
procedures and yet can mimic a wide variety of apparently competing normative conceptions,
though this procedure doesn™t imply that the relevant sort of value accrues to the elements
outside of their context. But I mean “value-bearing” in the second sense suggested by
this objection, which presumes that the value accrues to the elements in themselves and
independent of their context.

just what this chapter suggests, when it deploys principles of construction
to help determine the value of worlds.
Reply: Our construction doesn™t deploy any other elements of feasible
worlds to constitute the value of wholes. The principles of construction
aren™t literally elements in the worlds, contingent bits that make them up,
in the sense that the hedonic values of ¬‚ecks of experience are elements
of such worlds. And to the degree that some sort of fact is constituted by
elements that are literally in worlds beyond the basic normative elements,
those additional non-normative bits of that fact remain non-normative.
Everything basic and normative about that fact is captured by its basic
normative constituents.
Objection Two: We are trying to legitimate constraints that ¬x the
value of a whole given the value of its parts, and it may intuitively seem
that such constraints could deploy extra information about the world,
beyond that expressing its basic normative elements, and suffer from no
obvious incoherence in doing so. Consider three intuitive instances. First,
the way in which ¬‚ecks of experience are arranged into lives may well be
thought intuitively relevant to any sort of appropriate distributive concerns
that play into determining the proper overall evaluation of feasible worlds,
distributive concerns that our Weak Equity restriction may seem to re¬‚ect
in only an unintuitive form. Second, some favor principles of organic
unity for determining the value of wholes, and they may believe that
some sort of overall pattern or arrangement of basic value elements, which
cannot be captured under the strictures of Restriction A, is relevant to
determining the value of a whole. Third, many believe, Kant perhaps most
notoriously, that happiness “ or, more to the immediate point, positive
hedonic tone “ does not always provide impartial rational spectators with
grounds for positive normative approbation, that it is good if the guilty
get what they deserve, which is not to be happy but to suffer, and bad if
someone receives pleasure from doing evil.6 They believe that the positive
hedonic tone of the evil is not good without quali¬cation. While desert
may well seem intuitively relevant to the value of wholes, Restriction A
screens out facts relevant to determining desert. In at least these three
ways, Restriction A may seem to rule out intuitive normative alternatives
without any adequate legitimation.
Let me reply by saying something general, illustrate it by application
to the organic unity case, and then go on to the other two cases. There

6 See the opening paragraph of Section I of Kant (1996a).

are two general points. The ¬rst is that we are not immediately con-
cerned with normative intuitions, though intuitions about the maximin
structure of HMP are our focus in the next chapter, and we have already
discussed intuitions regarding guilty pleasures. The second point, however,
admits a quali¬cation or limitation of the positive argument I have just
Our world is one in which there is only one sort of unconstituted nor-
mative value, indeed only one sort of unconstituted normative property at
all. And that property has a particular form that is immediately signi¬cant.
The nature of the basic normative phenomena is what determines ulti-
mately how they are relevant to the value of a whole containing them. If
instances of phenomenal hedonic value were such as to present themselves
as relevant to the value of a whole only in a certain kind of context, for
instance, that might help to legitimate other sorts of normative principles
than my own, and to undercut Restriction A. It is crucial that physical
pleasures involve positive hedonic value that is just that, which presents
itself as good or bad to a certain degree, and not as good-if-felt-by-the-
innocent-or-in-certain-lives to a certain degree. The latter is much too
complex a property to be plausibly present in phenomenal experience of
the concrete sort we actually have. Like it or not, hedonic value comes
unquali¬ed and simple. But some intuitive forms of resistance to Restric-
tion A must deny that.
There are other ways in which the exact nature of hedonic value serves
to buttress Restriction A. For instance, the classic organic unity view holds
that some organically uni¬ed arrangements of natural but non-normative
entities somehow possess as wholes some sort of normative status. But,
after the last part, we know that the normative cannot be constituted out
of the non-normative, and that any probably inconceivable and certainly
ghostly and implausible nonconstituted normative property of a whole,
in effect a kind of non-natural normative property, would not plausibly
supervene on its natural properties in the way classic organic unity views
demand. It is our world that rules against such accounts, which deploy
a kind of value element not found in feasible worlds. No organic unity
account with which I am familiar really violates one general principle
that underlies Restriction A, and that indeed implies it in our presumed
situation, in which the simple ordinal value of moments of experience is
the only unconstituted normative element in relevant worlds. That general
principle is that the normative status of a whole is dependent on the
basic normative properties that it instances, and whatever they invoke as
relevant, and nothing else.

This general principle may be accepted by forms of the other two con-
trary views that we need to discuss, as indeed by certain forms of organic
unity account. But that is only when the basic normative properties
deployed to provide the requisite direct vindication of such accounts
involve metaphysical complexities that are not found in the basic con-
crete properties of feasible worlds.
Turn, now for the second time, to the case of guilty pleasures. There are
two sorts of metaphysical complications in basic normative properties that
might legitimate our discounting such pleasures. First, Kant notoriously
held that good will is the only thing that is good without quali¬cation,
and indeed his equally notorious claim that the happiness of the evil is not
good is deployed as an intuitive argument for just that claim. Kant, with
his fondness for transcendental arguments of his individual sort, probably
did not think that there are objective normative properties of the kind that
we have seen to be crucial to legitimate normative practice, but if he had,
they would have to be nonconcrete and non-natural normative properties,
somewhat analogous to those underwriting familiar forms of organic unity
in the manner suggested earlier, which are forbidden in feasible worlds.
Likewise, a conception that value accrues somehow to lives as a whole in
the ¬rst instance, and not merely to their individual ¬‚ecks of experience,
might be underwritten by such an alternative metaphysics of value.
A second sort of metaphysical complication in basic normative prop-
erties might also deliver what is required, if basic hedonic value presented
itself as merely good-when-caused-by-innocent-action, or good-when-
in-a-certain-life. Then the basic normative properties themselves would
specify that certain non-normative information about a world is relevant
to valuation.
But these two metaphysical complications are ruled out by the nature of
feasible worlds. The basic normative properties in feasible worlds have the
simple concrete and nonrelational form that we discovered in Part Two.
Hence no principle for the ordering of worlds that violates Restriction A
can be asymmetrically vindicated in the appropriate way versus possi-
ble competitive violating principles, which, for instance, admit different
conditions as relevant to the contributory value of guilty pleasures.
Quite generally, the value of a whole is captured by the instances of basic
normative property that it contains in conjunction with the conditions, if
any, that those properties specify as relevant to that value. Otherwise, the
requirements of direct vindication are violated. But this implies Restric-
tion A, given the nature of feasible worlds and the very simple value that
they incorporate.

All this should not be taken to imply, of course, that information rele-
vant to determining desert and distribution over lives is not relevant in any
way to recognizably normative evaluation “ for instance, to determining
right action. It is merely that it is irrelevant in our circumstances to the
basic normative ordering of worlds from worst to best. That is a cost of
the kind of objective value that there is in fact, like it or not. Whatever our
normative intuitions, the simple nature of hedonic value and the nature
of direct vindication have tied our hands. Restriction A (Abstraction)
governs the proper ordering of worlds.
We next will consider restrictions B, C, D, E, and F. We can do so all
at once. But ¬rst let me remind you of these constraints.
Restriction B (Null Addition): Adding to or deleting from a world a ¬‚eck
of experience with null hedonic value yields a new world equal in value to the
Restriction C (Generality): The proper principle for ordering worlds must
be insensitive to the particular numbers of ¬‚ecks of experience they contain.
Restriction D (Value Responsiveness): If one world is better than a second,
then that is because some ¬‚eck of experience in the ¬rst is of greater hedonic value
than some ¬‚eck (or some ¬‚ecks) in the second.
Restriction E (Weak Pareto): Making every ¬‚eck of experience better off in
regard to the hedonic value it presents would yield a better world.
Restriction F (Separability): Adding to a pair of worlds (or deleting from
them) ¬‚ecks of phenomenal experience with equal hedonic values doesn™t affect the
relative value of the resulting wholes.
Recall that the hedonic value of ¬‚ecks of experience is the only basic
value “ that instances of such value are the only basic value-bearing ele-
ments “ of feasible worlds. Recall also, as we recently reviewed, that
this basic value is simple. It presents itself as value simpliciter, and not
for instance as value-in-a-certain-context or value-when-caused-in-an-
innocent-way. Those facts bridge these restrictions and more general con-
straints. Just substitute “basic value-bearing element” for “¬‚eck of experi-
ence”, and “simple value” for “hedonic value”. Now ask what legitimates
these more general restrictions.
Principles like many of these were held to be self-evident by, for
instance, some Cambridge Platonists. But various things have appeared
self-evident to various people that haven™t turned out to be true, and in
any case we presume a metaphysical framework that is not hospitable to
the synthetic a priori. Generalizations of Restrictions B through F are, I
think, arguably analytically rooted in our notion of the value of a whole.
But then the question becomes why we should have a notion of the value

of a whole like our own rather than a different one. I will instead legiti-
mate our restrictions in two other ways, which I take to be two different
ways of making the same point.
First of all, the nature of simple value, such as that found in feasible
worlds, requires these constraints. What is it to be null simple value, for
instance, but to be a property of something that when added to or deleted
from a whole makes no difference, and hence no difference to the value
of a whole? Hence Restriction B (Null Addition). This may seem too
quick. If something is null value, that may imply it has no value on its
own, but leave open whether it might contribute value to a larger whole.
But remember that hedonic value is not relational in that way. It is null
simple value, in the way we just noted.
What is it to be a positive element of simple value except to make
a positive contribution, and what is it to be a greater positive simple
value than to make a greater positive contribution? Hence Restrictions
D (Value Responsiveness) and E (Weak Pareto). What is it to be of the
same simple value as another element except to underwrite Restriction F
(Separability)? And Restriction C (Generality) seems trivially true of any
sort of unitary ordering procedure rooted in simple value.
One caveat is in order. There is a dif¬culty that has been created by
my formulation of Restriction D. One might reasonably worry about
this vindication of Restriction D because classical utilitarians have denied
it while deploying more or less simple value. Those who hold that the
utility of a whole is a sum of the values of basic value-bearing elements
may hold that replacing one value-bearing element by two of lesser value
may improve the value of a whole. And indeed, many may think that
there are situations in which one ends up with a better world if certain
value-bearing elements cease to exist and are replaced by others. But
recall the context provided by Restriction A, which rules out information
about the individual identity of ¬‚ecks of experience across worlds, among
other things, and also recall the gloss and explanation that was given
for Restriction D when it was introduced, and that is re¬‚ected in the
semiformal expression of D that will play a role in our later argument.
Let me repeat this with italics in order to make the relevant point clear: A
positive difference in the value of two whole worlds must be a function
of a positive difference in the hedonic value that is contained in them. If
one world A is better than another B that contains the same number of ¬‚ecks
of experience, then there is some pairing of the ¬‚ecks of experience in A to
the ¬‚ecks in B that meets two conditions: (i) In it, A contributes the better
member of one or more pairs, and (ii) A is better because it contributes

the better member or members of that pair or those pairs. I glossed (ii) as
follows: “A is better because it contributes the better members of those
pairs” means that if A had contributed the worse members of those pairs
while B and everything else about A were unchanged, then A would have
been worse than B. The italicized phrase undercuts the objection.
Still, someone might continue to object, there might be simple ordinal
value elements, relevant to the choice among those elements, and yet
which would not make a contribution to the value of a whole of the
sort that Restrictions B through F imply. The normative positivity of
value might not be a positive contribution to the value of a whole. But
emphasizing a second aspect of the considerations that we™ve just observed,
looking at the same considerations from another direction, can help to
show why this is a mistake.
Choice of something is always implicitly choice of something that is
part of the whole containing it, and ultimately of the way the world is. Any
practice of reason giving answering the question that is our concern in this
part that violated constraints such as these would in fact be incoherent.
It would not in fact be a coherent practice of all-told evaluation rooted
in justi¬catory reason giving. If the positive value of an element is to
be a positive reason, then it must be a positive reason for choice, and
choice is always implicitly of wholes. To recognize the positive value of
an element that does not make a positive contribution to a whole would
be to recognize it as a reason for doing something “locally” that was
inconsistent with what it required “globally”, but the local and the global
cannot come apart in a coherent practice of overall valuation of worlds in
this way. This is suf¬cient legitimation for our purposes.
Such an argument may seem too strong, for it may seem that there have
been obviously coherent views that have denied precisely such constraints.
Perhaps the most pressing historical example of such a denial is once again
the principle of organic unities. According to this principle, wholes have
a value that is not the kind of function of the individual value of their
parts that our principles of construction require. Another example is Kant™s
insistence that sometimes it is a better world if the guilty suffer, that not all
additional good things that can happen to individuals increase the overall
value of the world.7
But, I reply, it is important to consider once again the simple nature of
the objective normative value we have uncovered, and the very different

7 For another set of relevant considerations, see Temkin (1993b).

nature of basic value according to traditional principles of organic unity
or analogous Kantian conceptions, in which either only wholes or good
wills have basic value, or alternatively in which the value of ¬‚ecks of
experience is not simple but rather relativized to contexts or sources.
These normative alternatives are coherent, but only because they deploy
a kind of basic value that is other than the simple value presumed by
our constraints and delivered by the facts. Given that there is only simple
ordinal hedonic value found in feasible worlds, Restrictions B through F
must govern any evaluative practice that is justi¬catory reason giving at
all worthy the name and that answers the question before us. They must
govern any such practice that is at all recognizably similar to our own and
ful¬lls its own central requirements.
We turn now to Restriction G (Strong Ordinality): A complete represen-
tation of hedonic value must respect merely the three-part organization provided by
positive, negative, and null value, and its merely ordinal nature. The legitimation
of this constraint rests straightforwardly on the nature of ordinal hedonic
value, which it expresses.
Hedonic value is merely ordinal (beyond the three-part structure pro-
vided by positive, negative, and null value). So any representation that
captures that ordinal structure is as good as any other. No principle for
ordering worlds that depends on privileging one such representation over
another is legitimate; the proper ordering principle must not be sensitive
to differences in representations that are, given the ordinality of hedonic
value, arbitrary. For instance, cardinal comparisons of value levels are ruled
out by the very nature of the basic value found in feasible worlds.
But consider an objection. Strong Ordinality might be thought too
strong to capture the kind of ordinality that basic value exhibits. Strong
Ordinality assures that classical total utilitarianism is incorrect. But it may
seem that the ordinal nature of basic value doesn™t forbid such a classical
ordering, even if the classical ordering involves cardinality. It may seem
that it merely implies that such an ordering cannot be legitimated relative
to alternatives.
The nature of ordinal basic value does in fact suf¬ce against this objec-
tion. Hedonic value is ordinal and not cardinal, and that ordinality is
expressed by Restriction G. But a further reply is also possible: There is no
nonarbitrary way to justify any particular one of the alternative orderings
of the sort invoked by the objection that do not meet the Strong Ordinal-
ity constraint. So to propose such an ordering is to fall afoul of the demand
for asymmetrical legitimation that must be capable of being met by any
sort of evaluation that is properly rooted in justi¬catory reason giving.

The orderings that meet Strong Ordinality do have the kind of objective
asymmetry required relative to possible competitors that do not meet it.
Still, someone might say, the point of this objection is not to attempt
to privilege a single alternative, but rather to argue that there is merely a
partial ordering of worlds.
But, I reply, our constraints do go all the way to a single ordering. And
so there is this counterargument: Remember Restriction 0 (Complete-
ness). Now add an abstract principle of legitimation, a kind of Principle
of Suf¬cient Reason. Contrary to Leibniz™s suggestion, there are probably
things that happen in the world without a reason. But at least within the
sphere of a coherent practice of evaluation rooted in justi¬catory rea-
son giving, there must be a reason to properly prefer one evaluation over
another and competing one. Now put our two abstract principles together,
Restriction 0 and this Principle of Suf¬cient Reason. There is a single
correct ordering of worlds, we presume, and yet we cannot legitimate any
of the alternative orderings proposed by the objection under discussion,
relative to one another. So, by our two abstract principles together, none
of them is correct. Consider orderings that meet all our other restrictions
but G. Many remain. But it is not possible to pick out any orderings but
those that meet Restriction G in other than an arbitrary way, given the
nature of hedonic value that is found in feasible worlds.
We have only one more constraint to vindicate. But that will take a
while. Restriction H (Weak Equity) concerns pairs of worlds that cannot
be ordered by our previous constraints alone. The most relevant such pairs
are “questionable cases”. These are such pairs that contain the same num-
ber of ¬‚ecks of experience. We know that each world can be represented
by the levels of value of its ¬‚ecks ordered from worst to best. The ranks
of these two representations allow pairwise comparison of the values of
paired ¬‚ecks in the different worlds if the worlds contain the same number
of ¬‚ecks. In questionable cases, one world is better in one rank and the
other world is better in another. That is what leaves them unordered by
the other constraints alone. Restriction H is this: For at least one such pair
of worlds that contain only ¬‚ecks of experience with negative hedonic value, and for
at least one such pair of worlds that contain only ¬‚ecks of experience with positive
hedonic value, and for at least one such pair of worlds each of which contains some
¬‚ecks with negative value and some with positive value, the better world of the pair
is the world whose worse ¬‚eck is better than the worse ¬‚eck in the other.8

8 My quasi-formal expression of this constraint will be, strictly speaking, for questionable cases
where n = 2. This implies the existence of particular sorts of questionable cases, but as far

Note that this is, in one sense, a very weak constraint. Because of the
cumulative force of the other constraints, as we will see in the next section,
all we will need to show is that what are called maximax principles, which
maximize the well-being of the best-off at the cost of the worst-off, are
incorrect, in just one example of each of the natural cases noted in the
constraint, to underwrite our general principle for ordering worlds. But
there is unfortunately that slight complexity. We need to underwrite a
maximin treatment for three separate cases, one for each of the three
natural classes distinguished by the constraint.
Maximin principles like HMP are, certainly in contrast to maximax
principles, egalitarian. One historically important class of arguments in
favor of egalitarian normative principles is what we might call the class of
“conceptual” arguments. These arguments, analogous to arguments from
analyticity that one might deploy in an attempt to legitimate constraints
like B through F, point to some concept of the moral as legitimating
Weak Equity or its analogs. For instance, one might invoke the inherent,
perhaps indeed the analytic, weak egalitarianism of “the moral point of
view”, which requires us to give everyone equal consideration. But of
course what is at issue here is the legitimation of such a particularly moral
point of view, why we need to have or use a concept like that one.
There is also a long tradition of holding various principles at least
analogous to our Weak Equity constraint to be self-evident deliverances
of “right reason”. Of all the Cambridge Platonists, Henry More seems
most detailed in his speci¬cation of such principles. And he held that there
were two “axioms or intellectual principles”, which were “immediately
and irresistibly true” in the manner of mathematical axioms, and which
seem relevant here. He noted one axiom of rational prudence, supposed
to govern an individual™s own life, which he called “Noema VII”. It says:
“ ™Tis more eligible to want a good, which for weight and duration is very
great, than to bear an evil of the same proportion. . . .”9 This implies a
kind of skewing of our interest toward the relief of evils in our own lives,
reminiscent of some implications of our maximin principle. And More
proposed another principle to govern our actions toward others that may
be even more directly relevant. His Noema XIX is this: “ ™Tis better
that one man be disabled from living voluptuously, than that another

as I can see there are no grounds for objecting to this if the arguments of this section are
9 More (1997: 23).

should live in want and calamity.”10 But, of course, our metaphysical
presumptions here are not hospitable to Platonic faculties of intellectual
intuition, and many people have had seemingly analogous intuitions of
the false.
Nevertheless, egalitarian forms of the traditions of right reason and the
moral point of view, as well as the long tradition of Golden Rule argu-
ments, re¬‚ect an important and relevant truth. Justi¬catory reason giving
requires that like be treated as like, that deviations from equal treatment
demand special justi¬cation. This truism underwrites the second of the
two arguments that in fact properly legitimate Weak Equity.
We might call the two arguments that properly support Weak Equity
the Argument from Value and the Argument from Equity. As will soon be
clear, I endorse the ¬rst argument only in a limited sense, as underwriting
only one clause of Weak Equity. But there are also further possibilities for
this form of argument that are at least worth discussing.
The Argument from Value appeals to the nature of basic hedonic value.
That argument is, schematically, that the nature of basic value requires
Weak Equity. Familiar egalitarian arguments of this general form are not
useful to us, because they require a conception of objective value consid-
erably different from our hedonistic conception. Brink and Cummiskey,
for instance, recognize two very distinct classes of goods, with universal
possession of certain basic goods alleged to take a kind of lexical priority
over the maximization of other sorts of less basic goods.11 Still, there are
analogous arguments that might underwrite Weak Equity by legitimating
the requisite treatment of at least one instance of each of the three types
of cases we face.
Let™s begin with the best case for this argument. Consider what I
have called a questionable pair of worlds, each incorporating both positive
and negative hedonic value. A questionable case like this one cannot be
ordered by our other constraints alone. I believe that the nature of hedonic
value supports the following claim about such a pair: Physical painfulness “
negative hedonic tone “ presents itself phenomenally as more important
to choice than positive hedonic tone, as more urgent. Or, at the very
least, some physical painfulness presents itself as more worthy of succor, as
more urgently needing decrease than some physical pleasantness requires
increase. This form of argument may have been what moved some to

10 Ibid., 26.
11 Brink (1989: 270“273); Cummiskey (1996).

adopt the negative utilitarianism of Popper, which is analogous in certain
ways to my normative principle.12
Can we plausibly extend this argument to our unmixed questionable
cases? It is at least arguable, on the basis of the nature of negative hedonic
tone, that greater painfulness in at least one case demands succor prior
to lesser. The case of unmixed pleasure seems somewhat more dif¬cult.
There is an asymmetry in our account of hedonic value that we shouldn™t
ignore, namely, that there is a ¬‚oor for positive hedonic tone while there
is a ceiling for negative hedonic tone. But it is also relevant that our very
weak Weak Equity requires only one case of each type. There is, if I am
lucky, at least one relevant case of even unmixed pleasures, which involves
some level of physical pleasure that is vast enough to present itself as less
important to be increased than is some lower.
But some care is in order here, even if my two questionably optimistic
claims about the nature of the phenomenal properties in question, which
can rest only on introspection, are correct. First of all, it is slightly mislead-
ing to speak of increasing the value of a particular ¬‚eck of experience or
succoring a pain at all, when what is really at issue is the dominant mem-
ber of a pair of ¬‚ecks in a rank in a value pro¬le of two feasible worlds.
More importantly, Strong Ordinality implies that there are no differences
among levels of hedonic disvalue, or among levels of hedonic value, other
than those captured by their ordering. It implies, for instance, that there
are no facts about the relative size of certain differences in value level,
and that there are no structurally privileged levels of positive or negative
value. So such arguments as I have just given cannot properly turn on
intuitions that a certain size decrease in a particular level of physical pain
is worth a certain size increase in another particular level, while another
size decrease in another level would not be.13 Or at least they cannot
properly turn on these intuitions unless we modify Strong Ordinality.
It is consistent with Strong Ordinality that pains in general domi-
nate pleasures, that elimination of a negative hedonic tone dominates an
increase in a positive hedonic tone. But that is in part because Strong
Ordinality allows an objective difference between positive and negative
hedonic tone that is beyond mere ordinality.14 An extension of this form of

12 Popper (1966: vol. 1, 235). But see also the objections in R. N. Smart (1958) and J. J. C.
Smart (1973: 28“30).
13 Except in certain very unusual cases where those facts can be captured by representations
consistent with Strong Ordinality, which are not the cases we need here.
14 Even in this case we need to be careful. It may be that the most intuitive form of the
Argument from Value for even our most promising case, a form that doesn™t treat all pains

argument to the two unmixed cases properly requires one of three things:
First, it might require that the differences between different unmixed
pairs is not relevant, that all the relevant cases of each of the two types
present themselves in a way that underwrites Weak Equity. I believe this an
implausibly strong claim. Second, somewhat more plausibly, Strong Ordi-
nality might be slightly relaxed, to allow the introduction of further struc-
ture into hedonic value in order to underwrite Weak Equity in unmixed
cases, without affecting the overall implications of our hence modi¬ed
constraints. I believe this to be possible, but I can™t prove it. Third, we
might deploy a two-step argument in which the second step is analogous
in certain ways to the Argument from Equity that we will shortly consider.
Perhaps after justifying the clause of Weak Equity relevant to mixed cases
by the nature of hedonic value and disvalue, we might go on to argue that
there is a certain kind of like treatment of unmixed pairs that is required
by coherent justi¬catory reason giving and that delivers the rest of Weak
I commend these alternatives to your attention. They may be viable.
However, I cautiously adopt a fourth and more conservative possibility,
that the Argument from Value can deliver only one of the three cases
we require, that it can underwrite only that part of Weak Equity dealing
with mixed cases. This rests on the relevant phenomenal claim about
which I have most con¬dence, and it is consistent with unmodi¬ed Strong
So we must turn now to the Argument from Equity. As I™ve suggested,
arguments of this general form are familiar, and may well underlie certain
traditional appeals to the moral point of view or right reason. Practice
rooted properly in justi¬catory reason giving treats like as like. And this is
a kind of equity. Justi¬catory reason giving directly requires a kind of equity,
not because of quite contingent aspects of our concept of reason giving,
but because justi¬catory reason giving is indeed justi¬catory reason giving.
Reason commands that we treat like as like, so to engage in a practice
of evaluation as justi¬catory reason giving is to engage in a practice that
requires like evaluation and treatment of like. In effect, there is no further

as more urgent than all pleasures, is not strictly consistent with Strong Ordinality. Perhaps it
is merely some differences in pain, either anchored at particular beginning or ending points
or involving particular intervals, that present themselves as more urgent, as relatively larger,
than some opposing differences in pleasure. It may be only intense pain seriously assuaged that
intuitively trumps some normal increases in pleasure, and it may be that intuition about
these matters is guided by the nature of value itself. Intense pleasures, or at least intuitively
huge increases in pleasure, may seem intuitively to trump mild relief of mild pain.

need to justify equality of treatment or of evaluation. It is deviations from
equality that require special justi¬cation, that have a necessary burden of
But such generalities are not enough. We need a particular argument
with this general form. We need to bridge the general conception that like
should be treated as like and the particulars of our Weak Equity constraint.
Familiar forms of equity focus on intuitively equal treatment of people.
But our Weak Equity constraint has a rather odd and unfamiliar focus, on
the ordinal hedonic value of ¬‚ecks of experience, indeed on the pro¬les
of instances of such value present in feasible worlds.
As we will see in the next chapter, there is in fact a conceptual bridge
between, on one hand, abstract principles requiring equal respect for
proper moral patients that underlie traditional concerns with equal respect
for persons and, on the other hand, our particular Weak Equity constraint.
Despite the presumption of many contemporary philosophers that indi-
vidual lives are the appropriate focus of distributional concern, that lives
are the appropriate unit of concern and respect, this is a mistake. Indeed, it
is a mistake for two reasons. It is wrong in our world because of the actual
nature of basic value, and whether we like it or not. But it is also wrong on
grounds of properly re¬‚ective normative intuition, such as those invoked
in the next chapter.
But for now our argument must be direct, with no detour through the
notion of an intuitively proper moral patient. To accept reasons as govern-
ing proper evaluation, to accept that normative evaluation is justi¬catory
reason giving, is to accept that like cases be treated alike. In the case
of ordering feasible worlds including ¬‚ecks of experience with ordinal
hedonic value, and in the case of considering alternative such orderings,
relevant likeness is governed by Restriction A and our other previous
constraints. All we can properly do is compare worlds by reference to the
patterns of levels of hedonic value that they incorporate. Like treatment
involves, other things being equal, a preference for equal outcomes. And
in this context, this requires Weak Equity. But why?
Presume that we are faced with certain questionable cases of the three
sorts relevant to Weak Equity. In particular, consider three cases in which
the paired worlds differ in only two ranks. In each case, we have a choice
between a pair of worlds in which there is more, or alternatively less,
spread between the values of two paired ¬‚ecks of experience, holding

15 This abstract form of argument is developed in another context by Barry (1989:
Chapter VI).

everything else equal. We cannot order the pairs by reference to our
other constraints alone. Such identity of ¬‚ecks as we can trace between
the worlds is constituted by their place in the patterns of value repre-
senting the worlds. What could a preference for equal outcomes be in
such a situation, what could a concern with equity be, other than a pref-
erence for the world in which there is less spread between the relevant
In various questionable cases that we might consider, equal treatment
supports Weak Equity in somewhat various ways. First, Weak Equity
can be supported by a preference, if we choose our questionable cases
cleverly, for genuinely equal outcomes over unequal outcomes in which
some ¬‚ecks of experience are at higher levels and some at lower.16 But
this preference is constitutive of the equal treatment required by justi¬-
catory reason giving. Recall that we need only one case of each of our
three natural types to support Weak Equity, and this argument will deliver
them. Second, equal treatment in a greater selection of questionable cases
underwrites the truth of Weak Equity in another and more general way,
by favoring a diminished spread between extremes. That is a movement
in the direction of equity in one clear sense. Equal treatment requires in
questionable cases a decrease of the spread between the well-being of the
relatively well-off and badly-off. And recall again that we require only
three cases of this sort to underwrite Weak Equity, which this argument
can also deliver. Third, equal treatment also requires (and indeed perhaps
more importantly requires, since the “direction” of equity invoked by my
second point involves dragging down what™s above) going in a direction
that in the long run, after many transformations that would not necessar-
ily occur even in an in¬nity of actual transformations, pulls every ¬‚eck
up. Equal treatment requires that there be a limit to how far down other
¬‚ecks of value can be dragged by allegedly overall positive transforma-
tions of the world, a ¬‚oor beneath which no ¬‚eck falls on any bettering
transformation. This third argument supports the treatment that Weak
Equity requires of mixed and negative cases. Care is in order about this
third point. We aren™t in fact concerned here to legitimate principles for
just the transformation of the same ¬‚ecks of consciousness, let alone the
same persons, to better states, but rather to rank outcomes in which the
particular identity of persons or ¬‚ecks of consciousness is not normatively
relevant beyond whatever facts are ¬xed by the nature of the value pro¬les

16 This treatment of mixed cases presumes that the zero point counts as within both the painful
and pleasant ranges.

of the worlds. Still, Restriction A leaves us only information about their
place in patterns of hedonic value to constitute any relevant identity of
¬‚ecks across worlds, so concerns for equal treatment of this third sort can
be addressed only in this unusual way.
The orderings mandated by Weak Equity, at least in the context of
the other constraints, give every ¬‚eck of experience three kinds of equal
consideration, which re¬‚ect the three abstract differences between max-
imin and maximax principles that are available to us consistent with
Strong Ordinality: Maximin provides a ¬‚oor; it favors less spread between
extremes in “questionable cases”; and it re¬‚ects a preference for literally
equal worlds in some questionable cases. That is suf¬cient legitimation
for Weak Equity.
To put this the other way around: As we will see, the alternative to
Weak Equity is, given our other constraints, various maximax orderings “
always looking to better still further the better-off at whatever cost to the
worse-off, indeed to many worse-off elements. And that is contrary to
the equal treatment that reason demands.
It may seem that I am equivocating between formal and substan-
tive understandings of “equal treatment”. Justi¬catory reason giving will
involve general criteria, but general criteria are captured by even a maxi-
max principle, so general criteria, it may seem, can™t be enough to deliver
substantively equal treatment. But in fact I am claiming that a restriction
to relevant general criteria in our particular argumentative context does
imply a substantive result, that there is a burden of proof for any sub-
stantively unequal treatment that is to be suitably justi¬ed. Notice that
those who hold that substantively unequal treatment is justi¬ed custom-
arily attempt to discharge that burden of proof, though in ways that are
untenable in the world we actually inhabit.
The ideal form for our arguments in this section involves imagin-
ing practices of alleged justi¬catory reason giving that deploy or neglect
the relevant constraints, and then asking ourselves whether they are at
all recognizably justi¬catory reason giving. And certainly very inegali-
tarian forms of what is recognizably similar to justi¬catory reason giving
are possible. But the most familiar rest on false beliefs “ for instance,
about what might properly justify unequal treatment “ or they are sub-
tly incoherent “ in the manner of practices that violate the Principle
of Suf¬cient Reason previously discussed. Indeed, that principle itself
underwrites the basically egalitarian nature of justi¬catory reason giving.
The form of egalitarian concern that is relevant in our unfamiliar argu-
mentative context is unfamiliar. But egalitarian concern of the unfamiliar

form we have developed here is what falls out of a general concern with
equity under our unfamiliar argumentative circumstances. And equity
of that abstract sort is a commitment of coherent justi¬catory reason
You may wonder how the arguments I have given here ¬t into the
metaethical alternatives we discussed in the ¬rst section of the last chap-
ter. The answer is that I have augmented the nonconstitutive natural-
ism of the last chapter with various constraints that are supposed to
be analytically required by the notion of justi¬catory reason giving and
the question we face. These underwrite the construction principles that
link the basic natural normative properties to other normative proper-
ties. They do not link non-normative natural properties with norma-
tive properties in the manner of the traditional analytic naturalism that I


Our nine restrictions are now vindicated. But they imply the lexical max-
imin principle for ordering feasible worlds that I have promised, as this
section will explain. Here is that principle: Of two worlds that con-
tain the same (¬nite) number of ¬‚ecks of phenomenal experience, the
better world is the one that has the better (more physically pleasant or
less painful) worst (most painful or least pleasant) ¬‚eck of experience, or
in case of ties the better second-worst ¬‚eck, and so forth. Any world is
equal in value to another that has the same number of ¬‚ecks of experi-
ence as the ¬rst at each level of value and disvalue plus any number of
null-valenced ¬‚ecks. So, since we can order worlds containing the same
number of ¬‚ecks, we can also order those that do not.
As I™ve said, this implication isn™t a surprise. There is a developed lit-
erature in decision theory tracing the implications of various sorts of
ordinalism involving preferences, and analogous results in the formal lit-
erature on social choice rooted in Arrow™s famous work. Ordinality of the
sort that governs hedonic value is widely known to have something like
the implications I will exploit here. Still, there are a few trivial differences
between the case we face and more familiar ordinalisms. Since we are
discussing ordinal value in particular, this involves a somewhat different
series of constraints and a somewhat different sort of modeling of those
constraints than is required for analogous cases involving preferences or
votes. We face a difference between value, disvalue, and null value. And
we need to rank alternatives that consist of different numbers of ¬‚ecks

of experience. But those two differences cancel out. We can add null
¬‚ecks to worlds to get worlds equal in value to the originals, and hence
indirectly rank worlds containing different numbers of ¬‚ecks.
While what I say in this section is no real surprise, nevertheless here is
my argument that our restrictions require our ordering:
(1) By Restriction B (Null Addition), we can add zeros to (n-x)-tuples
to create n-tuples equal to their successors. We just add the number of
null elements we need or want. Hence we can order (n-x)-tuples relative
to n-tuples if we can order n-tuples. This is as our maximin principle
requires, and reduces our problem to showing that the restrictions require
that the orderings of n-tuples for each arbitrary value of n are as our
principle speci¬es.
(2) Restrictions E and F together imply something that in our context
can do the work of a strong Pareto principle. Call it P: For n-tuples A and
B of equal arbitrary n, A > B if for no i is the ith element of A < that of B,
and for some k the kth element of A > the kth element of B. And clearly
an n-tuple equals itself. All this too is as our principle demands. We need
then merely determine that our restrictions require that the proper order-
ings of pairs of n-tuples of equal arbitrary n that are (i) not identical and
(ii) such that one is not greater than the other according to this interme-
diate principle are as our maximin rule demands. The remainder of this
section argues that this is so.
(3) First, some terminology: An ordering of two n-tuples is “question-
able” iff it is of two n-tuples that are not identical and such that one is not
better by P than the other. Let the “rank-i” of n-tuples A and B be the
pair of elements consisting of the ith element of A and the ith element
of B for some speci¬c i. An ordering of A and B can be questionable iff
there is some rank such that its element from A is greater than its element
from B and another rank such that its element from B is greater than its
element from A.
There are three types of questionable orderings: Type I are those in
which the n-tuples consist wholly of rationals greater than or equal to
zero. Type II are those in which the n-tuples consist wholly of rationals
less than or equal to zero. And Type III are those that include among them
both positive and negative rationals. I will argue in the several steps of (4)
that the constraints require that Type I questionable cases be adjudicated
in accord with our normative principle, before generalizing to the other
types in (5).
(4) Step One: Questionable cases of Type I cannot be equalities. Here are
the questionable cases of Type I where n = 2: <x,y> and <z,w> where

0 ≥ x < z < w < y. If in some cases of this sort <x,y> = <z,w>, then by
Restriction G in all cases of this sort <x,y> = <z,w>. Hence <1,6> =
<3,4>, and <2,7> = <3,4>, and so <1,6> = <2,7>. But this violates
Restrictions E and F. By Restriction C, this generalizes to cases where n
does not equal two.
Some more terminology: Let a single rank or pair of elements from
n-tuples A and B be said to “dominate” the ordering of A and B iff A
is > B whenever its member of that pair or rank is greater. The greater
member of a dominating rank or pair “dominates” the lesser.
Step Two: If questionable cases of Type I are not equalities, then there is a
single dominating pair for each Type I case. If they are not equalities, then
in each case one n-tuple is greater than the other, by Restriction 0.
But then by Restriction D, there is either some single pair of elements
or some plural set of pairs that dominates the ordering of each case. In
general, if plural sets dominate orderings, then it is possible for some of
the dominating pairs to favor one n-tuple in a questionable case and some
the other, and if a plural set dominates it must do so in a manner that is
decisive under such conditions. There are only two sorts of procedures
of plural domination that are so decisive, summation procedures sensitive
to the size of the elements in the n-tuples, and majoritarian procedures
sensitive to the number of pairs favoring one n-tuple over the other. But
Restriction G rules out any summation procedure, and a majoritarian
procedure violates the transitivity of our ordering and Restriction 0. For
instance, a majoritarian procedure pairing by ranks, where the greater
n-tuple contributes the greater members of a majority of ranks, requires
that <3,6,9> > <2,5,11>, <2,5,11> > <1,7,10>, and <1,7,10> >
<3,6,9>. So there must be a single dominating pair.
Step Three: If there is a single dominating pair for Type I cases, then there is
a dominating rank in those cases. Consider B = <2,8> and A = <3,5>. If
A > B and there is a single dominating pair, then Restriction D requires
that either (i) 5 dominates 2 or (ii) 3 dominates 2. If B > A, then either
(iii) 8 dominates 5 or (iv) 8 dominates 3. Possibilities (ii) and (iii) are
rank dominations, in which the dominating pairs are members of the
same rank. Possibilities (i) and (iv) are “cross-dominations”, where the
dominating pairs are not members of the same rank. Possibilities (i) and
(iv) are inconsistent, and there is no principled way to favor one over
another that does not itself invoke rank domination. It will not always
be the case that the extreme and intermediate elements of n-tuples of a
questionable case will exhibit the order of this example, with both ele-
ments of one 2-tuple inside those of another, so a description of the

favored cross-domination making use of that order will not always be
available. Possibilities (i) and (iv) cannot generalize into distinct princi-
ples that can determine all questionable cases. So we are left with rank
Step Four: If a rank dominates in Type I cases, then Type I cases are adjudicated
by our normative principle. Consider the questionable cases of 2-tuples A =
<1,5> and B = <3,4>. (a) If a rank dominates the pair of A and B,
then either the rank consisting of (1,3) dominates or that consisting of
(5,4) does. (b) By Restrictions G and H, (5,4) does not, hence if a rank
dominates, (1,3) does. (c) But if (1,3) dominates, it does so under a charac-
terization equivalent to “¬rst rank from the left with unequal elements”:
(i) (1,3) in A and B is degenerately a rank that ¬ts such a characterization.
(ii) By Restriction F, we can add equal elements to A and B to yield
successor n-tuples preserving their predecessors™ order. When the added
elements are less than or equal to one or greater than or equal to three,
(1,3) will be in the successors the ¬rst rank with unequal elements. (iii)
The only way we can add equal elements and create successor n-tuples
both meeting Restriction F by preserving the order of their predeces-
sors and such that their ¬rst rank that does not consist of equal elements
does not consist of (1,3) is the following: The equal elements are less
than three and greater than one. For example, two would create the suc-
cessors <1,2,5> and <2,3,4>. But then the ¬rst unequal rank of the
successors preserves the relative domination of the ¬rst rank of the pre-
decessors, and domination by the ¬rst unequal rank would yield what
Restriction F demands. (iv) By Restriction C, any ordering principle
that applies to A and B must apply to their successors. Hence if (1,3)
is dominant for A and B, it is under some characterization of that rank
equivalent to “the ¬rst rank from the left with unequal elements”. But by
Restriction G, this generalizes to all Type I 2-tuples, and by Restriction
C to Type I n-tuples of arbitrary n. Hence if a rank dominates in Type I
cases, then the correct principle for Type I cases is our lexical maximin
(5) By the four steps of (4), we know that Type I questionable cases
are adjudicated by our principle. But the preceding argument generalizes
to cases of Type II and Type III as well, utilizing the other clauses of
Restriction H, and by (3) these are the only questionable cases. Hence
the restrictions require that all questionable cases, and hence by (1)
and (2) all orderings of worlds, be adjudicated by our lexical maximin


We have come through a rather dense thicket, but we know now which
feasible worlds are better than which others. Still, we don™t yet have
the answer that this chapter ultimately seeks. We don™t yet know which
chances or risks of which worlds, which lotteries over worlds, are better
than which others, except of course in the degenerate case of lotteries
that have only one possible outcome each. And to assess actions in our
chancy world, it seems, we must assess lotteries. This section will close
that gap.
Consider lotteries over feasible worlds. For a lottery over some set of
feasible worlds to be the case is for there to be some nonzero probability
that each member of the set is the case and a probability of one that
some member of the set is the case. It is for there to be some chance
that each of those worlds is actual and no chance that none of them are.
A general theory of value should tell us, it seems, which lotteries over
worlds are better than which others, and we will know this when we have
an ordering of lotteries from worst to best, allowing of course for ties.
What is the proper ordering of lotteries over feasible worlds, given the
ordering of worlds (and hence of degenerate lotteries having only one
possible outcome each) that we discovered in the preceding sections of
this chapter? We can answer this question by a construction reminiscent
of our former construction of an ordering of worlds from their ordinal
hedonic value. The questions are quite analogous.
I will assume that the relative value of lotteries is a function of the rela-
tive value of their outcomes. This is the intuitive view. Consider lotteries
A and B. Assume that they have an equal number of equally probable
outcomes such that all of the outcomes of A are better than any of the
outcomes of B. Will it not follow that A is the better lottery? I can imagine
someone who denied such a principle “ for instance, evaluating lotter-
ies by the relative equality of the probabilities of their outcomes. But no
one could conceive of lotteries in such a way that some property of the
lotteries legitimated this. How could an objective probability itself be a
normative value? We seek a kind of objective value of lotteries. For a
lottery to be the case is for its possible outcomes to be variously probably
the case, so it seems that the intrinsic value of lotteries over worlds must
be a function of the value of the worlds themselves. Such objective value
as is to be found in a lottery seems to be found in its outcomes.
How then can we use our ordering of worlds to determine an ordering
of lotteries over them? There are various ways to reduce the question

we face. Consider lotteries over outcomes with rational probabilities. A
lottery with a 60 percent chance of outcome A and a 40 percent chance
of outcome B is the same as a lottery with two 20 percent chances of
B and three 20 percent chances of A. We can always represent a lottery
over outcomes with rational probabilities in this way, as a lottery over
equally probable outcomes. Call a lottery over equally probable outcomes
an “equiprobable” lottery. If there is any reason to consider irrational
probabilities, which I doubt, then we can approximate a representation of
them in this way as closely as we want. We can order lotteries over worlds
if we can order equiprobable lotteries over worlds.
We will need to order equiprobable lotteries over different numbers
of outcomes. But consider a pair of equiprobable lotteries A and B, such
that the probability of each outcome of A is a and the probability of
each outcome of B is b. The number of possible outcomes of A will
be 1/a, that of B will be 1/b. We can form two new lotteries from our
original pair, replacing each outcome of A with 1/b similar outcomes of
a(b/1) probability, and each outcome of B with 1/a similar outcomes of
b(a/1) probability. These new lotteries are equivalent to their predeces-
sors. Hence we can order pairs of equiprobable lotteries if we can order
equiprobable lotteries with the same number of possible outcomes. Hence
our problem reduces to that of ordering equiprobable lotteries with the
same number of outcomes.
Several restrictions on such an ordering are evident. The ¬rst three
are beyond reasonable question, in the sense that any practice that vio-
lated those three would not recognizably be a practice of treatment of
risks rooted in justi¬catory reason giving. The fourth, given our previous
general principle that an objective ordering of lotteries over worlds must
re¬‚ect the value of the worlds, follows from the merely ordinal valuation
of worlds we have developed.

(i) If one of these lotteries is better than another, it is because there is some
outcome or are some outcomes of the ¬rst that is or are better than some
outcome or outcomes of the second.
(ii) If there is a one-to-one pairing of the outcomes of lottery A and lottery B
such that no outcome of A is worse than and at least one is better than that
of B with which it is paired, then A is better than B.
(iii) Consider lottery A, which is either better than, worse than, or equal in value
to lottery B. If we form a new equiprobable lottery from A and another
from B by eliminating (or adding) an equally valuable outcome from (or
to) each, we form two new lotteries that preserve the relative value of their

(iv) No ordering of lotteries that requires more than a merely ordinal valuation
of worlds is admissible.

These constraints generate a problem that will look familiar. The prob-
lem of constructing an ordering of lotteries from ordinally valued worlds
is quite similar to that of constructing an ordering of worlds from ordinally
valued moments of experience. Our current problem, ordering equiprob-
able lotteries with the same numbers of possible outcomes, is as our pre-
vious problem about ordering worlds would have been had there been
no zero point in value levels and had we needed only to order worlds
that contain the same number of ¬‚ecks of experience. Those differences
cancel out; the lack of a zero world for lotteries is unimportant given the
presence of the method already outlined for reducing the ordering of lot-
teries over different numbers of outcomes to the ordering of equiprobable
lotteries over the same number.
Given our four constraints, the correct ordering of equiprobable lot-
teries over the same numbers of outcomes would follow a maximin rule
or a maximax rule. That is because the second constraint reduces the
problem to that of ordering pairs of lotteries that are closely analogous
to the “questionable cases” of the previous section, in which appropriate
pairwise comparisons of the outcomes of the two lotteries do not all favor
one lottery. And the three other constraints require that we treat such cases
uniformly in the maximin or the maximax way, as the analogous con-
straints we discussed in the last section require rankings resting on maximin
or maximax. The maximin rule for risks holds that the better lottery is the
one with the better worst-possible outcome, or, in case of ties, the better
second-worst-possible outcome, and so on. The maximax rule holds that
the better lottery is the one with the better best-possible outcome, or, in
case of ties, the better second-best-possible outcome, and so on.
An additional restriction specifying a weak conservatism over risks
would ensure that the maximin ordering is correct. In light of the other
constraints governing an ordering of lotteries, it need only rule out the
very risky maximax ordering in one relevant case, an ordering that tells us
to order lotteries by their best possible outcomes no matter how improb-
able they are.
Why is this constraint legitimate? If someone takes a normative risk
with someone else™s fate, then intuitively a choice following the maximin
principle would make it much easier to justify an unlucky outcome to its
victim than would a choice following a maximax principle. Of course,
there might be a very good chance that a maximin choice would end

up with a worse outcome than some principle that worried a lot about
serious bad risks and not only about the very worst possible outcome.
But because of our other constraints, and particularly because we have
only an ordinal valuation of outcomes, such intuitive middle routes are
not available to us. All weak conservatism requires is that there be some
very risky shot that is ruled out. And very risky shots are intuitively very
dif¬cult to justify, especially if they go wrong. It is our other constraints,
and especially the ordinal valuation of feasible worlds, that yield a maximin
principle in particular in this context.
But, of course, intuition is not our current concern. So we need
another argument. There is an argument that justi¬es a maximin treatment
of risks “ or, more directly, weak conservatism about risks “ by appeal to
the nature of the objective value of lotteries and hence of worlds, which is
analogous to our earlier Argument from Value for Weak Equity. It might
seem that such an argument is more problematic in this instance, because
the kind of objective value that worlds possess is only the constructed sort
we developed earlier, and hence a bad world doesn™t seem plausibly to
incorporate some special urgency of the sort that the phenomenal dis-
value of ¬‚ecks of experience seems to possess. On the other hand, the
very same disvalue of ¬‚ecks of experience that makes up the disvalue of
worlds plausibly has, at least in the single instance we require to under-
write weak conservatism over risks, the necessary stringency. Painfulness,
or at the very least, painfulness of a certain level, demands not merely that
it be assuaged, but that it not be idly risked, I believe.
There are also analogues of our Argument from Equity that are avail-
able. Like a maximin principle for evaluating outcomes, a maximin prin-
ciple for risks is recognizably equitable “ in the way in which it treats
possible outcomes, in the way (if this is relevant) in which it treats pos-
sible or actual people in the situations that they would inhabit in each
possible outcome, and even in the way it treats possible or actual ¬‚ecks of
experience or levels of value. I believe that because reason requires like
treatment of like, a practice of evaluation rooted in justi¬catory reason
giving needs on pain of incoherence to accept a principle equivalent to
at least our very weak conservatism over risks. Perhaps it will be useful to
recall again that this merely requires that there be some very risky shot at
some good outcome that involves great risk of a very bad outcome that
is forbidden. Our other constraints take up the rest of the argumentative
slack and lead to an overall maximin treatment of risks.
So we have an ordering of lotteries over worlds that is analogous in
some ways to our ordering of feasible worlds. Just as in ordering worlds

we are to look to maximize the relative value of the worst-off ¬‚eck of
experience, so in ordering lotteries we are to look to maximize the value
of the worst possible outcome. As our principle for ordering worlds is
quite distribution-sensitive, so too our principle for ordering lotteries is
quite risk-sensitive.
My argument here may inspire objection that focuses on restriction
(iv). If worlds can be assigned only ordinal value, it might be claimed,
still that ordinality doesn™t rule out lottery orderings that adopt different
cardinal comparisons. It just prevents one ordering from being legitimated
by the value of the objects ordered. If this objection were correct, then
even given an ordering of worlds and all our other constraints, we would
have only a partial ordering of lotteries: Two equiprobable lotteries A
and B of the same number of outcomes are such that A is better than B iff
there is a pairing of outcomes of A and B in which all outcomes of A are
better than or as good as those of B to which they are paired, and at least
one is better. It might also be, however, that other reasonable constraints
on lotteries could provide still greater resolution. Alternatively, someone
may object to weak conservatism over risks. If weak conservatism alone
were relaxed, then both the maximin and maximax orderings of lotteries
previously suggested would slip by. But I believe that these objections fail
and my argument stands.
I have presumed that it is necessary for a basic normative principle to
order lotteries, and that is not undeniable. We seek here not so much a
decision procedure for actions as a factual criterion of rightness, which
may be very dif¬cult to apply in our epistemic ignorance. And so it may
seem that one way to avoid the rigid risk aversion of my principle is to insist
that one should always choose the lottery that will in fact have the best
outcome. I believe that such a treatment of risks would provide insuf¬cient
normative information for ethics, because the alternatives open to agents
will not characteristically involve this level of factual determinacy.17 But
that is a long story for another day. So while I will continue to pursue
the implications of my own risk-averse principle, I also commend such
an alternative treatment to your consideration.

We can now conclude the main argument of this chapter: A crucial fea-
ture of our evaluative practice is that it is rooted in justi¬catory reason

17 Mendola (1987) argues that our options are too indeterminate even to be captured by

giving. So any proper evaluation must be capable of being legitimated by
an appropriately objective and asymmetrical vindication. We have discov-
ered two elements that allow us to discharge that obligation in answering
the particular question we face. Those elements are the ordinal hedonic
value found in ¬‚ecks of experience and explored in Part Two, and the
construction principles whose legitimation we explored in this chapter.
But those elements together imply the Hedonic Maximin Principle, the
basic normative principle of my proposal. HMP is this:
First, of two lotteries over feasible worlds that consist of the same num-
ber of equally probable outcomes, the better lottery is the one that has
the better worst-possible outcome. If they have equally bad worst-possible
outcomes, then the better lottery is the one that has the better second-
worst-possible outcome, and so on. Given the method noted in the pre-
vious section for turning lotteries with different numbers of unequally
probable outcomes into equiprobable lotteries with the same numbers of
possible outcomes, this yields a complete ordering of lotteries over worlds,
which implies that of any two lotteries over worlds, the better lottery is
the one that has the better worst-possible outcome.
Second, of two feasible worlds that contain the same number of ¬‚ecks
of experience, the better world is the one that has the better worst ¬‚eck.
If they have equally bad worst ¬‚ecks, then the better world is the one that
has the better second-worst ¬‚eck, and so on. And any world is equivalent
in value to another that has the same number of ¬‚ecks of experience at
each level of positive or negative ordinal phenomenal value as the ¬rst
plus any number of ¬‚ecks of null value. So we have a complete ordering
of feasible worlds.
It hasn™t been pretty, but the battle is over. HMP is true, I have argued,
whether we like it or not and whatever our normative intuitions. But
Chapter 4 showed that its hedonism is properly intuitive. And the next
chapter will show that its maximin structure is also properly intuitive. You
may not think this can be done. Once I didn™t either. But I was wrong.
Part Four will further reveal that, in conjunction with MAC, HMP has
appropriately intuitive normative implications about cases.
The argument of this chapter has turned crucially on the ordinal nature
of hedonic value. Of course, I may be wrong about that. And, in the
last chapter, I promised to track some of the complications that ensue if
hedonic value is not as I have presumed it to be.
If there are various sorts of incomparable phenomenal ordinal value “
say, those associated with pushpin and poetry “ then each provides an
independent ordering of worlds. Consider a case in which there are two

sorts of incomparable value. Then the ordering by regard to one sort
of value might distinguish among ties within an ordering by regard to
the other, or vice versa. But we should not expect a single complete
ordering of worlds. If one sort of phenomenal value is lexically dominant
over a second, a complete ordering is possible in the obvious way. The
subordinate ordering would serve only to distinguish ties according to the
dominant ordering.
Restriction G (Strong Ordinality) captures the ordinality of intrinsic
value by ruling out any principle of construction that is sensitive to sup-
posed comparisons in value differences as well as levels. And there are
various ways to object to Restriction G.
One might think that the proper response to the ordinality of value is
not to rule out constructions that variously adopt different cardinal com-
parisons, but merely to realize that none can be asymmetrically justi¬ed
by the value of the objects ordered. Restriction H in such an eventuality
would have relatively trivial and implausibly isolated implications, which
it would hence perhaps be best to abandon. If we relax Restrictions G
and H, the other restrictions still rule out many candidate orderings.
Any ordering slips through that obeys Restriction B and a sort of Pareto
principle: If two worlds A and B contain an identical number of ¬‚ecks of
experience, and the ¬‚ecks of the two can be paired such that (i) for each
pair, the ¬‚eck in A is better than or equal in value to that in B and (ii) for
at least one pair, the ¬‚eck in A is better than that in B, then A is better
than B. In other words, this yields only a partial ordering of worlds.
But a more obvious and promising way that Restriction G might be
wrong is that hedonic value might come cardinally, with interpersonal
comparisons possible. Then various restrictions quite like those we have
deployed, minus Weak Equity and Strong Ordinality, would yield a stan-
dard classical total utilitarian evaluation of worlds. We would sum the values
in the world to get the overall value of the world. If hedonic value comes
cardinally, it is also clear that a more standard utilitarian attitude toward
risks “ namely, the maximization of expected utility “ would be justi¬ed
by the kind of construction that we have been pursuing here.
Something resembling Weak Equity might be rendered consistent with
such a largely classical utilitarian ordering of worlds by allowing that, in
case of ties under the standard total utilitarian evaluation, equity some-
times matters. Something like that was indeed proposed by Sidgwick.
But there are dif¬culties. Given that we seek a principle that has a direct
vindication, it is worrisome whether there could be an appropriately
privileged distributional locus on this conception, which would tell us to

attend speci¬cally to equal distributions among people, or moments of
their lives, or even ¬‚ecks. Perhaps any locus might be given appropriate
consideration, other things being equal, but there might be no privi-
leged way to adjudicate con¬‚icts among the demands of different sorts
of distributional loci. Or perhaps we are forced back to a concern, or at
least a ¬rst concern, with distribution among ¬‚ecks. Since, in any case,
these sorts of equity could matter only in cases of ties in total utility, they
probably wouldn™t practically matter very much anyway. For all practi-
cal purposes, we might as well just stick with simple total utilitarianism.
So I will not attempt to track the implications of this particular sort of
Another class of alternative conceptions of hedonic value deploys
various sorts of intermediate structure, somewhere between ordinality
and cardinality. One interesting case deploys ordinal comparisons of some
value differences. But this class implies a complex situation that I do not
There are indeed various classes of alternatives that are in some sense
between standard hedonic total utilitarianism and HMP. Some seem
attractive. For instance, I would have antecedently preferred a principle
whose locus of distributional concern wasn™t ¬‚ecks, but rather whole lives,
or at least whole brief periods of lives. And I would have antecedently
preferred a principle that was egalitarian, but not so ruthlessly egalitarian
as maximin. For that matter, I would have liked a principle that, while
somewhat risk-averse, was not so risk-averse as HMP. But it is hard to
see how speci¬c complicated structures of these sorts could be rooted in
a plausibly simple form of phenomenal value. And otherwise it is hard to
see rationales for particular such conceptions that are suf¬ciently robust
to constitute direct vindications. For that matter, such conceptions may
seem attractive only because they are vague and undeveloped. But still, it
may be that hedonic value has some structure between ordinality and car-
dinality that delivers something that is in some way intermediate between
HMP and total utilitarianism.
The price of ethics is direct vindication, the price of that is normative
realism, and the price of normative realism is that you may not be able
to get the ethical principles you like the best. I wouldn™t be delighted if
total utilitarianism were true, especially because it has no fully adequate
response to the objection from distribution with which this chapter began.
In fact, I would be appalled. But since in conjunction with MAC it delivers
adequately intuitive normative implications, as we will see, ethics would
not fail even if total utilitarianism were true. Or so I believe. One of the

heads of one of our dragons would take a bite, but not a fatal bite. I will
give the total utilitarian alternative to HMP some attention in Part Four,
so that we can see that in conjunction with MAC it is, barely, enough.
But the most plausible alternative to ordinality is not cardinality. It is
rather something intermediate. Because I don™t understand these inter-
mediate structures and their implications, I will presume simply that an
intermediate structure would yield intermediate implications. I hope that
someone else can see more clearly, and ¬nd something better. But I will
presume here that by showing that the two extremes “ HMP and total
utilitarianism “ are intuitively adequately acceptable, I will have shown
that principles rooted in intermediate structure would be acceptable also.
In the end, it all turns on the nature of hedonic value. If there is none,
then ethics fails because there are no genuine practical reasons. Or so I
believe. If it is cardinal, then total utilitarianism is true. If it is ordinal,
then HMP is true. And if it is in between, then we are in between.
In Chapter 8, we will return to the detailed normative implications of
both HMP and total utilitarianism in conjunction with MAC, and see
that they are suitably intuitive. We probably know already that we can
live, grumbling, with the abstract structure of total utilitarianism, though
it isn™t completely adequate. And in the next chapter I will argue that
the abstract structure of HMP is suitably intuitive. As I™ve said, I think
these various tests by intuition are important. But the immediately crucial
point is that the true basic normative principle also turns crucially on the
normative facts.
They are mostly contingent normative facts. I have deployed some
analytic and necessary claims here. Consider, for instance, some of the
abstract claims that root the Argument from Equity. But since ethical
principles must have a direct vindication and hence depend on the world,
and since the world is concrete and its elements are contingent, ethics turns
on contingent normative facts. In particular, it turns on the contingent
nature of phenomenal value. Ethics is not a purely a priori discipline, and
yet it is a cognitive discipline. If the Hedonic Maximin Principle is false,
it isn™t because I™ve tried to square the circle, or because I™ve tried to drive
a cart with square wheels, but because I™ve claimed that there are corners
on the sun.

Maximin, Risks, and Flecks

The speci¬c maximin structure of the Hedonic Maximin Principle is
mandated by the direct argument of the last chapter. It may seem intu-
itively troubling in various respects. But this chapter argues that such a
structure is in fact in appropriate concord with commonsense normative
intuitions of the same level of generality and abstraction. You may be ini-
tially disinclined to believe this. So was I. But please bear with me, since
I hope to surprise you. In the next chapter, we will consider the detailed
normative implications of this structure in conjunction with hedonism
and Multiple-Act Consequentialism, and see that they are also properly
There are three controversial elements of this structure. First, it is a
maximin structure, which gives special preference to the maximization of
the well-being of the worst-off, regardless of the cost to others who will
remain nevertheless relatively better-off. Second, it considers distribution
not over individual lives but rather over individual moments of lives, and
indeed, to be precise, over individual bits of individual moments of lives,
over ¬‚ecks of experience. Third, it incorporates a maximin treatment of
risks, and hence is very risk-averse.
Sections I, II, and III concern the plausibility of ¬‚ecks of moments of
lives as the basic locus of moral concern. Section IV concerns maximin.
Section V concerns risk aversion. Section VI traces relevant interactions
of these three structural elements.
Entire lives are perhaps the customary basic locus of concern in moral
theory. Our contrary road to ¬‚ecks as the basic locus has two stages,
from lives to short periods of lives, and from short periods to ¬‚ecks. The
long ¬rst stage will occupy two sections. Please forget about ¬‚ecks for
the moment. First, I will try to convince you that distribution within

a life intuitively matters in only some of the ways that are ultimately


Prudence “ the maximization of one™s own welfare irrespective of tempo-
ral propinquity “ seems to many obviously rational. Special, controversial,
and often dif¬cult argument seems necessary to show that an equivalent
concern with the welfare of others is rational. But Henry Sidgwick asked
an important question about this distribution of the burden of proof:

I do not see why the axiom of Prudence should not be questioned, when it
con¬‚icts with present inclination, on a ground similar to that on which Egoists
refuse to admit the axiom of Rational Benevolence. If the Utilitarian has to answer
the question, ˜Why should I sacri¬ce my own happiness for the greater happiness
of another?™ it must surely be permissible to ask the Egoist, ˜Why should I sacri¬ce
a present pleasure for a greater one in the future? Why should I concern myself
about my own future feelings any more than about the feelings of other persons?™1

Thomas Nagel and Derek Par¬t have gone on to argue that the ratio-
nality of prudence may in fact require the rationality of the generalized
benevolence favored by Sidgwick and other utilitarians.2
Sidgwick, Nagel, and Par¬t are right to suggest that there is a close
symmetry between the proper distribution and summation of good or
well-being within individual lives and across distinct lives. But I think
they are wrong to conclude on this basis that we should in¬‚ate prudential
maximization within a life into utilitarian maximization that ignores the
differences between lives. We should, rather, argue in the other direction.
The kinds of distributional concerns that intuitively engage us when many
lives are in question should also play a similar role within lives. Periods
of individual lives “ indeed, short periods of lives “ should receive the
same sort of distributional concern that lives receive in recent discussions.
Temporal segments of all our lives are the central and proper focus of
moral and rational concern, or at least close to it.
One prominent complaint against utilitarianism is that it attempts to
extend principles of maximization of welfare traditionally thought appro-
priate within individual lives outward across people, and hence fails to

1 Sidgwick (1907: 418).
2 Nagel (1970); Par¬t (1984: 115“347).

properly respect the real distinctions between persons.3 But both tradi-
tional utilitarianism and its contemporary competitors often fail to prop-
erly respect the real differences between periods of people™s lives.
Egalitarian principles are thought by many to properly govern distribu-
tions among equal people. The welfare of each should be of real and equal
concern, it is generally thought, even if that will not in the end trans-
late into equal welfare for all. And this equal concern, it is also generally
thought, requires distributional sensitivity that is violated by maximizing
utilitarianism. But I claim that such principles must be extended inward,
to govern distribution within individual lives. We should extend to peri-
ods of lives the same rough kind of real and equal concern that general
consensus now holds must be extended to individual lives. Call this an
egalitarianism of periods.
An egalitarianism of periods may be the proper response to a variety
of normative questions, and there are complex and controversial relations
among those questions. There is a range of views about how the overall
goodness of the world should affect moral decision making. And there is
range of views about how the well-being of people, including malefactors,
is relevant to the overall value of the world. There is also a range of views
about the relation between the rational and the moral. But in the context
of the rest of this book, the currently relevant question is this: How is the
value of the whole world affected by the distribution of well-being within
the lives of individuals? Still, it may also be revealing that we can answer
another question at the same time. Presume a situation in which only one
person™s life is in question “ say, your own. Then ask how one should
rationally assess different distributions of well-being within that life. I will
argue in section II that an egalitarianism of periods is the proper response
to both these questions.
My argument there will traverse three steps. First, the temporal dis-
tribution of good or well-being within a life does matter in some ways
and to some degree, as a matter of well-founded intuition. Second, there
are various possible attempts to account for the normative importance
of such distributions in a nonegalitarian way, notably by reference to the
normative signi¬cance of temporal patterns of two sorts, objective and
perspectival. Third, neither objective nor perspectival temporal patterns
of these sorts are normatively signi¬cant, and hence neither can prop-
erly account for our well-founded intuitions about the signi¬cance of

3 Rawls (1971: 22“27).

the temporal distribution of good or well-being within lives. That will
leave only an egalitarianism of periods to properly underwrite the real
normative importance of distribution within a life.
But before we can take these three steps, some background will be
necessary. It is the focus of the rest of this section.
Traditional prudence is familiar, and hence may seem for that very
reason more antecedently plausible than an egalitarianism of periods. But
the ¬rst piece of necessary background for our argument is that com-
mon sense itself is not as determinate on these questions as our tradition
pretends. We can see this by considering ¬ve speci¬c points.
First point: Our normative intuitions re¬‚ect our common practice, and
our common practice is not necessarily in accord with traditional philoso-
phers™ conceptions of individual rationality. For instance, we don™t really
engage in much expected utility calculation about the satisfaction of our
own preferences, even in our sel¬sh evaluations of our own future lives.
Rather, we think imaginatively about various possible future outcomes
and give special attention to especially bad or painful or troubling out-
comes that we act to avoid, or to especially tempting positive outcomes
that we pursue. Damasio has argued that most of our practical reasoning
takes something like this form.4 And Fredrickson and Kahneman have
found that there is a general tendency to evaluate aversive experiences
by regard to their peaks and ends, and to relatively neglect the durations
of aversive experiences.5 It is also very clear that people do in fact at
least sometimes act so as to discount the future and favor their immediate
pleasures more than the traditional philosophers™ conception of rationality
allows. People certainly need to be trained into the kinds of long-term
thinking that the supposedly intuitive traditional prudential evaluation of
lives requires, and that training is far from completely successful despite
its venerable pedigree.
The second point is that it is far from clear that our normative intu-
itions, even when we can see that they do diverge from common practice,
support the sort of evaluation of lives that traditional prudence suggests.
People in old age sometimes seem remarkably distant from those same
people in youth, to the degree that intuitions that happiness at one age
can make up for unhappiness at another become unclear. And many


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