2. WHY IDEAL-ADVISOR ACCOUNTS?

I will use the term ‘cognitivism’ as a shorthand for the family of metaethical views that combine a propositional semantics for normative statements, with a non-error-theoretic view of normative facts (Smith Reference Smith, Jackson and Smith2005; Schroeder Reference Schroeder2010; Miller Reference Miller2013). According to ‘cognitivists’, (1) a normative statement has the (sole) semantic content of asserting that some normative fact obtains – that some object, e.g. an action, outcome or person, has a normative property; and (2) indeed some facts of this sort do obtain, so that normative statements can be true. Cognitivism is to be contrasted with views according to which normative statements have partly or whollyFootnote ⁸ non-assertoric content (expressing the speaker's emotions, commitments or plans); and with sceptical views that see normative statements as asserting the existence of facts that never obtain, so that normative statements are always false.

Ideal-advisor (‘IA’) views are a subfamily within cognitivist accounts. IA views analyse normative facts in terms of the preferences of some (single- or multimembered) community of advisors, preferences that are idealised in some way by imposing conditions of good information, rationality, etc. on the advisors. By ‘normative facts’, I mean facts that involve normative or value properties, such as moral goodness or rightness, well-being, being a reason for, etc.

Such views have figured prominently in contemporary metaethics. Here are perhaps the most famous examples.

(1) Firth. Firth proposes that the statement ‘x is morally right’ be understood to mean ‘any ideal observer would approve x’, where an ideal observer is an otherwise normal person who is omniscient with respect to non-moral facts; has unlimited powers of imagination; and is disinterested, dispassionate and consistent (Firth Reference Firth1952).

(2) Railton. Railton in a series of writings has advanced two distinct IA views, one for well-being, the second for moral good. (a) A given person's well-being (‘non-moral good’) is determined by what she (if idealized) would want herself to do or want in her actual, non-ideal circumstances.

(b) Railton suggests that ‘X is morally wrong’ be understood to mean:

(3) Smith. Smith offers a general account of ‘normative reasons’ in terms of the preferences of fully rational agents.

Moral reasons, for Smith, are in turn normative reasons with the additional special features (whatever exactly they may be) that are picked out by our platitudes about the domain of the moral (for example, that moral considerations involve important interests of persons other than the actor – thus that I have moral and normative reason to refrain from killing, but a non-moral normative reason to relax after a hard day at work) (Smith Reference Smith1994: 183–4).

(4) Brandt. Brandt, like Smith, offers a very general IA account. For Smith, the analysandum is the property of being a ‘normative reason’; for Brandt, it is the property of being ‘rational’. Some individual's action is ‘rational’, according to Brandt, if the action is optimal in light of her underlying desires and those desires themselves are ‘rational’ in the sense of surviving ‘cognitive psychotherapy’: a ‘process of confronting desires with relevant information, by repeatedly representing [that information], in an ideally vivid way’ (Brandt Reference Brandt1979: 113). Brandt then uses his conception of ‘rational’, together with the concept of a ‘moral code’ (roughly, norms regulating feelings of guilt), to define ‘morally wrong’. He sets forth two possibilities, here:

Metaethics is a field of controversy, with every account hotly disputed; but IA accounts, clearly, are prima facie appealing and have been embraced by some very sophisticated metaethicists. Why? Like all cognitivist accounts – and by contrast with views that see normative statements as doing something other than asserting facts – IA approaches are not troubled by the ‘Frege-Geach’ problem (Schroeder Reference Schroeder2010; Miller Reference Miller2013). Like other non-error-theoretic approaches, they do not see ordinary normative discourse as radically misguided – as making statements that are never true. By contrast with non-naturalist cognitivism – positing the existence of normative facts that are qualitatively distinct from the facts that figure within physical, psychological and social science – IA views are ‘naturalist’ in reducing normativity to a certain kind of psychological fact, namely facts about what an observer or observers in a certain informational and emotional state would desire.

Finally, facts about ideal advisors conform to two truisms about normative facts (or at least are well suited to conform to these truisms, given an appropriate specification of the community of advisors and the idealizing conditions). On the one hand, individuals are not infallible about normative facts (if such exist). On the other hand, normative facts, somehow, are tied to motivation: If I genuinely judge that x is morally good (for example), then I am motivated to pursue x. It is initially difficult to see how any fact could have both these features, but indeed facts about the preferences of ideal advisors could. Since a given person's preferences need not be ideal, she is not infallible about what ideal advisors would want. However, the belief that someone with preferences like my own, thinking calmly and with good information, would want me to x, will tend to motivate me towards x, notwithstanding that I lack good information, and even if my current deliberational state is less than fully ideal – just as my belief that someone with excellent information and cognitive capacities would believe p will tend to cause me (imperfectly informed as I may be) to believe p.

IA accounts (to be plausible) should not be understood as giving the meaning of the concept or term ‘moral’ or other normative or value concepts or terms. The statement ‘x is morally good’ does not have the same semantic content as ‘x would be approved by a community of ideal advisors’. Rather (to be plausible) such accounts should be understood as identifying the natural properties or property clusters referred to by such terms. For naturalist cognitivists, discovering such properties is quasi-scientific – a matter both of understanding what we mean by our normative concepts, the ‘truisms’ or ‘platitudes’ constitutive of them, and of establishing which physical, psychological or social properties are suitable to be the naturalistic basis for the normative concepts (given how such properties function in light of physical, psychological or social laws). Such discovery is at least roughly analogous to the discovery that the physical substance referred to by the term ‘water’ is the molecule H₂O – a discovery that combines conceptual analysis (the truism that ‘water’, as understood by anyone who grasps the concept, is a liquid, if fresh will quench thirst, is found in lakes, rivers and oceans, etc.) and empirical investigation (Jackson Reference Jackson1998).Footnote ⁹

Let me now suggest a differentiation between two types of IA accounts: ‘singleton’ accounts, where the community of advisors whose preferences give rise to normative/value facts is guaranteed to have a single member; and ‘multimember’ accounts, where this is not the case (i.e. the community can have multiple members).

A cross-cutting distinction is between relativist and non-relativist (absolutist) IA accounts (Firth Reference Firth1952; Smith Reference Smith1994, Reference Smith2004: ch. 10). Relativists with respect to some type of normative/value property posit that statements regarding the property can hold true relative to one speaker or group, but false relative to another. This is a familiar idea from the literature on moral relativism (Harman and Thomson Reference Harman and Thomson1996). Extrapolating from this literature, one can imagine a type of IA account whereby the truth of the assertion of a particular normative/value fact is relativized to one or another community of advisors. By contrast, an absolutist IA account posits a single community of advisors: A particular normative/value fact either obtains or not, in virtue of the preferences of this single community, and an assertion of this normative/value fact is either true absolutely or not.

Note now that both absolutist and relativist IA views can assume either the singleton or multimember form. An absolutist IA account might analyse a particular kind of normative/value fact in terms of all persons’ idealized preferences (multimember); in terms of God's preferences (singleton); or, perhaps, in terms of the preferences of a particular person (singleton), if the fact concerns the actions or well-being of that particular person. For example, the fact that a particular action of Jane's would be morally wrong could be reduced to Jane's preferences. A relativist IA view might posit that assertions of normative/value fact are true relative to communities which can have multiple members (this counts as a multimember IA account on the definition offered above). For example, moral facts might be relativized to one or another community consisting of individuals in the same society. Alternatively, a relativist view could stipulate that the communities relative to which normative/value statements are true must be singleton.

That IA accounts can assume either the singleton or multimember form is evident even from my brief descriptions of Railton's, Brandt's, Smith's and Firth's views. Railton offers a singleton account of well-being, but not of moral rightness. Whether x is good for Sue's well-being depends upon what Sue (if idealized) would want; whether x is morally right depends upon what some plural ‘we’ would want.Footnote ¹⁰ Brandt, quite visibly, oscillates between a singleton and multimember account of moral rightness. Brandt's singleton proposal is: x is morally right relative to a given individual iff she would rationally want a moral code that approves x. Brandt's multimember proposal is: x is absolutely (non-relatively) morally right iff all of us would rationally want a moral code that approves x.

Smith offers a thunderous argument for an absolutist and multimember conception of normative reasons. Facts about normative reasons are made true by the convergent, fully rational desires of all persons.

In short: ‘Acts are right or wrong depending on whether, notwithstanding any contingent and rationally optional culturally induced differences in our actual desires, we would all desire or be averse to the performance of such acts if we had a set of desires that was maximally informed, coherent, and unified’ (Smith Reference Smith2004: 205). Firth's view is also explicitly ‘absolutist’ (Firth Reference Firth1952: 320) and multimember: it construes ethical statements as ‘assertions about the dispositions of all [hypothetical] beings of a certain kind’, namely all ideal observers (1952: 320).

It is well beyond the scope of this article to address the pros and cons of singleton versus multimember IA accounts with respect to moral goodness or rightness, well-being, or other normative/value properties. Rather, the remainder of the article will train its attention on the non-trivial problem of preference aggregation that a multimember IA account faces. The account either needs to show that the community or communities of advisors will be such that members will have identical preferences; or, alternatively, to explain what the normative facts will be when community members have non-identical preferences.

Let us now analyse this problem in detail – focusing specifically, as promised, on moral properties. How do moral facts arise from a multimember community of advisors?

3. AGGREGATING MORAL PREFERENCES: A QUASI-ARROVIAN FRAMEWORK

What follows is one cluster of concepts and axioms that might be used to model the problem of aggregating moral preferences. This set-up is similar, in formal structure, to that introduced by Arrow (Reference Arrow1951, Reference Arrow1963) in Social Choice and Individual Values – but not identical, and so I call it ‘quasi-Arrovian’.Footnote ¹¹

(1) We are given some set of items S = {x, y, z . . .}. The members of any such set (of an appropriate kind) have moral goodness or rightness properties. I focus on moral betterness (comparative goodness), and leave aside absolute goodness and moral rightness.Footnote ¹²

S, then, is any set of things each pair of which are appropriate for assessment as comparatively morally better or worseFootnote ¹³ – for example, different token actions that a particular agent might undertake at a particular moment in time, or different possible worlds, or different institutions or practices that might exist in a society. The totality of facts about the comparative goodness of the items in S can be summarized (I assume) by a moral quasiordering ≽^{M −S} of S. I will call S a ‘situation’, and will refer to the items in S as ‘alternatives’.

Let #S denote the cardinality of S. Unless otherwise stipulated, #S can take any value: S can have any finite number of elements, or be countably or uncountably infinite. One part of the analysis below does assume that #S > 2, and that will be stated explicitly.

(2) I assume a finite multimember set N of advisors. N = {1, . . . k, . . . N}, with k used below to denote a particular advisor, and N > 1. Which persons and, thus, advisors will exist is, of course, not independent of what we now do – which in turn may depend upon the goodness of actions and outcomes, the very thing that the community of advisors’ views is meant to be determining – but to simplify I ignore the possibility of a ‘variable population’ of advisors. Moreover, I assume that each advisor is an actual person, who exists in the actual world. The actual facts of comparative moral goodness concerning a given situation are, plausibly, fixed by the preferences of actual, not counterfactual advisors. Below, we will consider the kind of counterfactual moral goodness that arises from the non-actual preferences of the actual advisors; but the doubly counterfactual moral goodness arising from the non-actual preferences of non-actual advisors is beyond the scope of the model.

The membership of N depends on the particular IA view being modelled. It is appealing to think that moral facts are true absolutely, and true in virtue of what all persons (under idealized conditions) would prefer. This is indeed the position of Smith, Firth and Railton. On this view, N consists of all existing persons. Alternatively, N might be a proper subset of existing persons – for example, all existing human persons, or (on a relativist view) all persons within a given society. Except at one juncture, noted below, these differences in the specification of N will not matter to my analysis.

(3) I assume that advisors’ preferences are the grounding for moral goodness just in case they meet the following conditions: the preferences must be ‘rational’, ‘well-informed’ and ‘impartial’. (As a shorthand, I will refer to these conditions, collectively, as the ‘idealizing’ conditions, and preferences meeting them as ‘idealized’.) The conditions are deliberately stated at a high level of generality – so as both to capture the features of advisors’ preferences that are clearly demanded by our platitudes about morality, and yet to leave open for further debate and investigation the precise psychological content of ‘rational’, ‘well-informed’ and ‘impartial’.

Critics of an IA account of moral facts might argue that these idealizing conditions are themselves, to some extent, normative – and that this undercuts the naturalist ambition of the approach, namely to reduce moral facts to ordinary, non-normative facts. But the proponent of the account has an answer. She can concede that ‘impartial’, ‘well-informed’ and/or ‘rational’ are normative – concepts that we use in deliberating about what ought to be done – but say that these concepts, like the concept of moral goodness itself, refer to non-normative properties. Identifying the psychological attributes corresponding to ‘impartial’, ‘well-informed’ and ‘rational’ involves the very same mixture of conceptual analysis and empirical investigation by which we establish the natural basis for moral goodness. The proponent can say: there is a fact of the matter regarding what psychological state someone is in when he is ‘impartial’, ‘well-informed’ and ‘rational’ – given the nature of various psychological states, as per the laws of psychology, plus the platitudes about ‘impartiality’, etc., that anyone using these normative concepts grasps. In turn, the idealized advisors are individuals in that psychological state; and moral goodness depends upon what such advisors prefer.

(4) I assume that the idealized preferences of each given advisor, k, over S take the form of a quasiordering ≽^{k- S}. Thus I allow for an advisor's moral preferences to be incomplete, but not for intransitivities. This is, in effect, a further specification of the term ‘rational’. I assert that rationality requires, at least, formal coherence in the sense of having a transitive, although perhaps incomplete, ranking. On the one hand, powerful arguments have been mounted to show that rational moral agents are permitted to rank some alternatives as noncomparable: x neither morally better than y, nor morally worse, nor equally good (Adler Reference Adler2012: 43–4). The rational permissibility of intransitive preferences is on much shakier ground (Voorhoeve Reference Voorhoeve2013).

The relations of strict preference, weak preference, indifference and noncomparability corresponding to ≽^{k- S} are denoted, respectively, as P^{k −S}, R^{k− S}, I^{k− S} and NC^{k −S}.

(5) Let P^S denote a profile of moral preferences (≽^1-S, . . ., ≽^{N- S}). A given P^S is ‘admissible’ if it is possible (in the relevant sense) for advisors to meet the idealizing conditions and have this profile of preferences. Let Φ^S denote the set of admissible profiles. A moral aggregation function or rule M ^S maps each admissible P^S onto a moral goodness quasiordering ≽^{M- S} of S, with P^{M- S}, R^{M- S}, I^{M- S} and NC^{M- S} now denoting the relations of strict and weak preference, indifference and noncomparability corresponding to ≽^{M- S}. Because ≽^{M- S} is a moral goodness quasiordering, we can equally well say that these denote, respectively, the relations of moral betterness, being at least as good as,Footnote ¹⁴ equal goodness, and moral noncomparability corresponding to ≽^{M- S}.

To avoid clutter, I will sometimes drop the ‘S’ superscript on ≽^{k- S}, ≽^{M -S}, P^S, Φ^S, M ^S and the R, I¸ P, and NC relations associated with ≽^{k- S} and ≽^{M -S}. However, where I do so, the reader should keep in mind that this superscript is implicit. Moral preferences and profiles thereof are rankings of a particular set S of items, and the associated set of possible profiles is also indexed to S.

I will use ≽^M _P to denote M ^S(P^S) – the moral goodness ranking onto which profile P^S (for short, P) is mapped by function M ^S (for short, M). And I will use ≽^k _P to denote the kth element of a given profile P. Again so as to simplify notation, I drop the P subscripts on ≽^k _P and ≽^M _P where it is clear from context which profile is intended.

(6) What does ‘possible’ mean, here?

The content of the set of possible preference profiles (here, Φ^S, the set of profiles for situation S) is a topic of great importance to social choice theory, typically referred to as the question of ‘domain’ definition. (Note that Φ^S is the domain for the function M ^S, hence the term.) Aggregation functions that are ruled out when combining certain axioms with a universal domain of preferences may no longer be precluded if the domain is restricted. Standard surveys of the field shine a spotlight on the question of domain definition (Sen Reference Sen, Arrow and Intriligator1986; Campbell and Kelly Reference Campbell, Kelly, Arrow, Sen and Suzumura2002; Gaertner Reference Gaertner, Arrow, Sen and Suzumura2002). However, there appears to have been little systematic discussion by social choice theorists of the more philosophical topic: what is the appropriate sense of the term ‘possible’ used to specify the domain of preferences?

Philosophers of modality distinguish between different kinds of possibility: for example, logical, conceptual, epistemic and metaphysical (Divers Reference Divers2002: ch. 1; Gendler and Hawthorne Reference Gendler and Hawthorne2002; Huemer Reference Huemer2007; Egan and Weatherson Reference Egan and Weatherson2011; Kment Reference Kment and Zalta2012). These distinctions are themselves contested, and it is well beyond the scope of this article to address them in detail. It will suffice to say this: a state of affairs is metaphysically possible just in case there is some possible world in which the state of affairs obtains. Metaphysical possibility is fixed by the modal facts – specifically, which worlds are genuinely members of the total collection of possible worlds – just as ordinary facts are fixed by what is true about the particular possible world that is the actual world. Metaphysical possibility is to be contrasted with what we believe to be true in some possible world, what our concepts seem to us to allow or preclude, and what logic allows or precludes. Logical impossibility is fixed by the logical connectives, and implies but is not implied by metaphysical impossibility: it is logically possible that a three-sided figure has four angles, but metaphysically impossible. Goldbach's conjecture, that all even numbers can be expressed as the sum of two primes, has never been proven or disproven. It seems conceivable that either the conjecture or its negation is true, and it is reasonable to believe either. But mathematical truths are true in all possible worlds, and so either the conjecture is metaphysically necessary and the negation impossible, or vice versa.

It is metaphysical possibility, I suggest, that determines the content of Φ^S (for short, Φ). A given profile of moral preferences (≽¹, . . ., ≽^N) is a member of Φ just in case there is truly some possible world in which advisor 1 meets the idealizing conditions and has the preferences over S described by ≽¹and advisor 2 meets the idealizing conditions and has the preferences over S described by ≽²and . . . advisor N meets the idealizing conditions and has the preferences over S described by ≽^N. Why conceptualize Φ as the set of metaphysically possible profiles with respect to S, rather than the set of logically, conceptually or epistemically possible profiles? Recall the ambition of the IA account of normative properties: to show how these properties, such as moral goodness, reduce to natural facts, specifically facts about the (in some way) idealized preferences of advisors. The moral aggregation function M is a kind of law (or, even better, bridge principle) of nature, mapping certain naturally occurring features of the world (advisors’ preferences) onto the facts about moral goodness that these features determine. A putative M, to be a genuine bridge principle, must be capableFootnote ¹⁵ of mapping any P that might naturally occur, onto a goodness ranking ≽^M. But whether a given P could naturally occur is a question of metaphysical possibility: a question about which arrangements of advisors’ preferences are to be found somewhere in the total collection of possible worlds, given the nature of preferences and the nature of the idealizing conditions for the advisors.

To be more concrete: the advisors’ idealized preferences have certain properties. On the IA account of moral facts, these are the properties picked out by the totality of our truisms about normativity and morality and about motivation, preferences and other features of human psychology. These are the properties I am referring to with the terms ‘rational’, ‘well informed’ and ‘impartial’. Which properties these are is a matter for empirical investigation; that may not be clear to us ab initio. And it may turn out to be metaphysically impossible for a particular profile P* of rankings of some S to have all of these properties. In no possible world does a group of ‘well informed’, etc., advisors have that collection of rankings. If so, P* should not be in Φ. It is not the function of the natural bridge principle M to operate on arrangements of preferences that could never actually occur, just as it is not the function of an ordinary law of nature (a causal regularity) to determine what an impossible state of affairs or event would causally produce.

To be sure, IA theorists are not omniscient, and will therefore have different beliefs about what is metaphysically possible. The formal apparatus here is a partly specified model of the determination of moral facts. It will be useful only to those theorists who already have certain beliefs about such determinationFootnote ¹⁶; and, among those theorists, will be further specified depending on what further beliefs they hold. In particular, as we will see in section 4, differing beliefs among IA theorists about what is ‘rational’ will yield quite different beliefs about the metaphysical possibility of a community of advisors meeting the idealizing conditions yet diverging in their rankings of a set of alternatives. A theorist's beliefs inevitably shape her modelling of the phenomenon of interest (here, the determination of moral facts). But it hardly follows that beliefs, thoughts or concepts are the target of the model. A profile (≽¹, . . ., ≽^N) belongs in Φ, according to a given IA theorist, if she believes the profile to be metaphysically possible. This is certainly not the same as saying that Φ contains all profiles which are epistemically possible, or which it is reasonable to believe are metaphysically possible!

(7) In short: M maps each metaphysically possible (henceforth ‘possible’) profile P of moral preferences over the set S of items, onto a goodness quasiordering of those items. This ranking, denoted M(P) or ≽^M _P, specifies what the facts about moral goodness would be, were the advisors to have the moral preferences set forth in profile P.

But where are the actual facts of moral goodness in this picture? The answer is (relatively) straightforward. Let P* be the actual moral preferences of the advisors. More precisely, since we are imposing idealizing conditions on preferences that advisors might not actually meet, P* = (≽^1*, . . ., ≽^N*), where ≽^k* are the preferences of advisor k in the nearest possible world – nearest to the actual world – in which all the advisors meet the idealizing conditions. For short, I will refer to P* as the advisors’ ‘actual idealized’ preferences. Actual moral goodness is given by the ranking, M(P*) = ≽^M _P*, onto which this profile is mapped by the moral aggregation function M.Footnote ¹⁷

One question that can be raised at this point is why M should be expected to operate on metaphysically possible profiles of idealized preferences that are not the advisors’ actual idealized preferences. Why not see the moral aggregation function for a given situation as having a singleton domain, namely what advisors prefer in the nearest possible world in which they meet the idealizing conditions?Footnote ¹⁸

Suffice it to say that natural laws support counterfactuals (the chemical law that salt dissolves in water tells us what would happen if this packet of salt were dropped in that glass), and also that moral discourse intelligibly asks questions regarding counterfactual moral requirements or values, namely what would be morally right or morally better if certain facts were otherwise. Both points suggest that Φ should include counter-actual as well as actual idealized profiles, at least to some extent. M, if genuinely the natural law by which moral facts arise from advisors’ preferences, should not only tell us that the actual comparative moral goodness of the items in S is given by M(P*) – with P* the advisors’ actual idealized preferences – but also that the moral goodness of the items in S would be given by M(P), were P instead of P* to be the advisors’ preferences in the nearest possible world where the preferences meet the idealizing conditions. Moreover, by including P as well as P* in its domain, the natural law M serves to explain why actual moral goodness is given by M(P*) – namely, that actual idealized preferences are P*rather than P. Conversely, if M does not operate on counterfactual but metaphysically possible profile P, then it is indeterminate what the moral facts would be, were the advisors’ idealized preferences in the nearest possible world to be P. But what grounds does the IA theorist have to believe in such indeterminacy? Footnote ¹⁹

(8) What, now, are the constraints on M?

First, M must satisfy the axioms of Pareto indifference and weak Pareto with respect to all admissible profiles of advisors’ moral preferences. If all advisors are morally indifferent between two items, the two are equally morally good. If all advisors strictly prefer one item to a second, the first is morally better. That is: (a) If x I^k _Py for all k, then x I^M _Py. (b) If x P^k _Py for all k, then x P^M _Py.

A key feature of the IA account is that the preferences of the advisors in the stipulated community, under idealizing conditions, are constitutive of the moral facts. It is not possible for the advisors, under those conditions, to be collectively mistaken about the facts. This constitutive role of the advisors’ preferences is captured by the weak Pareto and Pareto indifference axioms. On other metaethical views, such axioms would be problematic: there may be no community of persons relative to which the moral goodness ranking needs to satisfy weak Pareto and Pareto indifference. For example, if moral facts are constituted by God's ranking (with God a superhuman being who is not a person), the unanimous preferences of any community of idealized persons might diverge from moral goodness. Similarly, if goodness is a natural property with a particular explanatory role, then (perhaps) any community of persons could be collectively mistaken about how that property behaves – just as we (perhaps) might all be mistaken about the laws of physics.

I do not build in strong Pareto as a foundational axiom of the IA approach. Strong Pareto says: If x R^k _Py for all k, and x P^j _Py for some j, then x P^M _Py. While the moral weak Pareto and Pareto indifference axioms see the unanimous strict preference or indifference of the advisors as sufficient for, respectively, moral betterness or equal goodness, strong Pareto (to the extent it goes beyond weak Pareto) identifies a condition of disagreement among the advisors as nonetheless sufficient for moral betterness. It is not clear that the IA theorist should be committed to this from the start.

To be sure, it may emerge that a moral aggregation function entailed by other axioms ends up satisfying the strong Pareto axiom. Indeed, as we shall see, this is true of the Unanimity Rule. In other words, it may turn out to be the case that the IA theorist is logically required to endorse the strong Pareto axiom as the result of other principles that she finds immediately appealing. But because strong Pareto does not directly express a key commitment of the IA approach – in particular, that advisors’ preferences are constitutive of moral facts – I do not incorporate strong Pareto into the quasi-Arrovian setup itself.

By contrast, strong Pareto has direct appeal in the context of interest aggregation (Adler Reference Adler2012: ch. 5). And perhaps it also does for voting rules. The absence of a foundational commitment to strong Pareto is one important difference between the metaethical variant of preference aggregation and these other variants (cf. Rabinowicz Reference Rabinowcz, Kuzniar and Odrowaz-Sypniewska2015).

A fourth kind of Pareto principle should now be mentioned. So as to avoid terminological confusion, let's call this ‘intermediate Pareto’: If x R^k _Py for all k, then x R^M _Py.

Like weak Pareto and Pareto indifference, intermediate Pareto is intuitively attractive. Imagine that all advisors weakly prefer x to y. This means, first, that no advisor strictly prefers y to x. But then the moral aggregation function should surely not rank y as better than x. To do so would contradict the universal view of the advisors. Observe, second, that if all advisors weakly prefer x to y then no advisor counts the two as noncomparable. But then, surely, the moral aggregation function should not rank the two as noncomparable – again, this would be to contradict the universal view of the advisors.Footnote ²⁰

Note that intermediate Pareto implies Pareto indifference. I therefore describe the quasi-Arrovian setup as including the axioms of weak Pareto and intermediate Pareto rather than (redundantly) weak Pareto, intermediate Pareto and Pareto indifference.

(9) Second, M satisfies Anonymity. Each advisor has equal weight in determining moral facts – assuming her preferences meet the idealization screen. Formally, if the preferences in profile P* are a permutation of the preferences in profile P, M(P) = M(P*). Again, this flows from the view that the community's preferences are constitutive of moral facts. If these were, rather, merely evidence of moral facts grounded in some other way, some community members might have special expertise with respect to these facts, and Anonymity would be unwarranted.

(10) Third, M ^S must satisfy a requirement of Across-Situation Ranking Consistency (ASRC). Note that the S superscript has been made explicit; it will be significant in what follows.

ASRC expresses several ideas. First, it is advisors’ ordinal preferences that determine the moral goodness ranking of alternatives. To be sure, that idea also informs the structure of the moral aggregation function: the function for a given situation operates upon a profile of advisor ordinal rankings (quasiorderings) of that situation. However, there is nothing in the ordinality of the inputs to M ^S which requires M ^S, the moral aggregation function for situation S, to be similar in any further sense to M ^T, the moral aggregation function for a different situation T. The formal setup, thus far, allows the choice of moral aggregation function for a given situation to hinge upon the specific features of the alternatives being compared. For example, if S and T each have three elements, with the elements of S actions of a particular sort, and the elements of T actions of a different sort, the aggregation functions for S and T might be quite dissimilar.

The IA theorist would (I think) resist such differentiation – which is in tension with the core claim of IA theory, that advisors’ preferences are constitutive, and wholly so, of moral goodness. It is just the pattern of advisor preferences, not further facts about the alternatives, that fixes the goodness ranking; nor are these further facts ‘smuggled in’ by having them determine the specific form of the function from advisors’ preferences to the goodness ranking. This is the second idea expressed by ASRC – that if advisors have ‘the same’ preferences in two situations, the moral goodness ranking should be ‘the same’. We now go back to the first idea, ordinality: advisors’ preferences are ‘the same’ in two situations if their ordinal preferences are ‘the same’.

In short, ASRC says that if each advisor has ‘the same’ ordinal ranking of the items in S as in T, then the moral goodness ranking should be ‘the same’. Formally: Let #S = #T, and let π(·) be a bijection from situation S to situation T. Let P^S be a profile of preferences in Φ^S and Q^T a profile of preferences in Φ^T. Let M ^S be the moral aggregation function for S and M ^T for T, such that M ^S(P^S) is a quasiordering of S, and M ^T(Q^T) a quasiordering of T. Let R^M _P denote the morally-at-least-as-good relation corresponding to M ^S(P^S), and similarly R^M _Q that relation corresponding to M ^T(Q^T).

If for all x, y in S and for every advisor k, x R^k _Py iff π(x) R^k _Q π(y) and y R^k _Px iff π(y) R^k _Q π(x), then: for all x, y in S, x R^M _Py iff π(x) R^M _Q π(y) and y R^M _Px iff π(y) R^M _Q π(x).

(11) The final element of the quasi-Arrovian setup is Independence. It says, roughly, that the comparative moral goodness of two items depends just on advisors’ pairwise rankings of those items. Independence could be expressed in an inter-situational version – namely that if advisors all have the very same rankings of the x-y pair as the z-w pair, with x-y and z-w belonging to the same situation or two different situations, the moral goodness ranking of the two must be the same. However, since across-situational consistency is already brought into play by ASRC, and since it will be illuminating to highlight the axiomatic work done by this inter-situational requirement as contrasted with Independence in the less ambitious, intra-situational sense, I formalize Independence as an intra-situational axiom. For any given pair of items in some situation, if each advisor's ranking of the two items under profile P is the same as her ranking under profile Q, the moral aggregation function must map the two profiles onto the same comparative moral goodness ranking of the two items.

Formally: Let x and y be any two alternatives from S, P and Q any two profiles of preferences in Φ^S. If for all k, x R^k _Py iff x R^k _Qy and y R^k _Px iff y R^k _Qx, then: x R^M _Py iff x R^M _Qy and y R^M _Px iff y R^M _Qx.

Independence is, of course, a key element of the original Arrow framework. It is also the most controversial. Why take it on board? Let me hold this question in abeyance until section 6. We proceed by, first, adopting the quasi-Arrovian setup, including Independence and seeing its implications for M; and, then, in section 6 considering the arguments for and against this axiom.Footnote ²¹

4. THE QUASI-ARROVIAN SETUP PLUS ORDERING CONVERGENCE

‘Ordering Convergence’ is a (highly restrictive) stipulation regarding the admissibility of preference profiles. It says that a profile is a member of Φ only if each component preference has the very same ranking of the set S of items. Let a statement of identity between moral preferences, ≽^k = ≽^l, mean that: for all x, y in S, x R^k y iff x R^l y. Ordering Convergence, thus, says: P is an element of Φ only if ≽¹_P = ≽²_P = ··· = ≽^N _P.

If Ordering Convergence is adopted, the problem of moral aggregation becomes trivial. By immediate upshot of Pareto indifference and weak Pareto, M(P) must be some extension of the common advisor ranking.Footnote ²² If advisors have complete moral preferences, M(P) must simply be the common ranking.Footnote ²³

Various IA theorists, most prominently Michael Smith,Footnote ²⁴ have argued for the convergence of advisors’ preferences. Do his arguments indeed make a persuasive case for Ordering Convergence?

Ordering Convergence should not be conflated with a particular aggregation rule M or family of such rules. In the next part of this article, I will discuss an aggregation rule, the Unanimity Rule, which is such that the weak convergence of advisors’ preferences in ranking any two items is a necessary condition for those items to be morally comparable (one better than the other or the two equally good, rather than noncomparable). But convergence, here, is a feature of the rule – not of Φ. As we shall see, the Unanimity Rule operates perfectly well on preference profiles that include non-identical rankings – indeed, even if Φ contains every logically possible profile of advisor preferences.Footnote ²⁵ The Unanimity Rule is a methodology for aggregating advisors’ preferences, perhaps non-identical – a methodology that has the feature of propagating non-comparability from preference divergence – while Ordering Convergence is the view that a profile with divergent preferences is just metaphysically impossible from the outset.

Smith writes: ‘the truth of a normative reason claim requires a convergence in the desires of fully rational agents’ (Smith Reference Smith1994: 173). This statement, standing alone, does not show that Smith endorses Ordering Convergence. Rather, it says that if there is to be genuine normative reason in favour of one option rather than a second, then fully rational agents must desire the first.

At other points, however, Smith tries to show that all idealized advisors must have the very same preferences. To argue thus is, clearly, to put forth the case for Ordering Convergence. Smith writes:

More specifically, we might understand Smith as leveraging the rationality component of idealization into an argument for Ordering Convergence.

Is the argument persuasive? Smith asserts that ‘rational’ desires/preferences have the following feature (call it SJ): ‘people who have such desires have a justification for them that other people also could see to be a justification’. Assume, now, that any two advisors k and l have the same full information, including knowledge about what each other's preferences are; moreover, each has SJ preferences; finally, the two have common knowledge of all this. Then if ≽^k ≠ ≽^l, k will reason: ‘I can't see my current preferences as justifiable to l, since l, with the very same information as me, and reasoning just as well, has different preferences’.

Note that this argument works only if ‘having a justification for my desires’ means ‘having a non-agent-centred justification’ – a justification that excludes indexicals. Consider a case in which k prefers Renaissance painting to modern painting, and l has the opposite preference. If k can provide a systematic justification for the preference by saying, ‘Renaissance painting better fits with my deepest aesthetic values, the ones that have been inculcated in me since childhood’, and l by saying ‘modern painting fits better with my deepest aesthetic values, the ones inculcated in me since childhood’, the two can have full and common knowledge of everything relevant, including the requirement of systematic justification, and still end up with different preferences.

So let us revise SJ to NACSJ (non-agent-centred, systematically justifiable). If ‘rationality’ requires NACSJ preferences, and if the idealizing conditions for moral facts require the advisors to have preferences that are NACSJ and sufficiently informed, we have a good argument for Ordering Convergence. On these suppositions, it is metaphysically impossible for rational and well informed advisors to have divergent moral preferences.

A difficulty here is that nothing in the concept of ‘rationality’ clearly entails the NACSJ feature. A long tradition in thinking about rationality, going back to Hume, and embodied in modern economics and decision theory, thinks of ‘rationality’ in purely formal terms (Hooker and Streumer Reference Hooker, Streumer, Mele and Rawling2004; Weirich Reference Weirich, Mele and Rawling2004). Such a view identifies conditions regarding the internal coherence of preferences, such as transitivity, reflexivity, consistency across choice situations, or the axioms of expected utility theory; and then says that satisfying such conditions is not only necessary, but sufficient, for someone's preferences to be rational. The view is ‘purely formal’ because these coherence conditions permit preferences that do not conform to any commonly shared standard of desirability. I can ‘rationally’ prefer something ‘just because I want it’. Indeed, the purely formal view says that ‘rational’ preferences may seem substantively crazy – such as a preference to eat a saucer of mud, or Hume's example of preferring the destruction of the world to scratching my finger.

Nor does introducing the further idealizing element of ‘impartiality’ (as a condition on moral preferences) transform this formal conception of rationality into one that incorporates NACSJ. There's no apparent incoherence in Sarah explaining her impartial preferences to herself in Sarah-centred terms: ‘Abstracting from my own position in society, I morally prefer much higher income-tax rates that would move us toward a much more equal distribution of well-being, even at substantial cost to overall well-being; and the reason I have this preference is because welfare egalitarianism fits my deepest values, the ones that my parents and I have always held.’

Smith might respond that the properties of preferences picked out by the concept of ‘rationality’ may not be obvious to those using that concept; and that, indeed, those properties include the NACSJ property, even though many who use that concept mistakenly think otherwise. (This would be like a mistaken belief that water is not H₂O.) To be sure, Smith himself is not omniscient; he cannot know for sure which properties our normative language refers to. But he can say that he reasonably believes ‘rational’ preferences to be NACSJ; and that if preferences do indeed have this feature, Ordering Convergence follows.

Several other arguments for Ordering Convergence should be mentioned. First, the relativistic IA theorist (who views moral statements as true or false relative to one or another community, and sees the preferences of idealized community members as the empirical basis for the truth-value of such statements) might restrict the set of eligible communities so that each satisfies Ordering Convergence. She might argue that a community's preferences can be the touchstone for a relativized moral statement only if the community genuinely shares a moral code – and indeed does so in the strong sense required by Ordering Convergence. Such an argument, of course, is not available to the non-relativistic (absolutist) IA theorist.

Second, the non-relativistic IA theorist might allow that fully informed and rational persons can have divergent moral preferences, but include only humans in the community of advisors, and seek to make the empirical showing that idealized humans (given their genetic makeup) converge in what they morally prefer.

Finally, consider the disjunctive claim: either Ordering Convergence is true, or there are no moral facts. At one point, Smith makes comments suggestive of this claim.

The disjunctive claim, plus the truism of ordinary moral discourse that there are moral facts, would imply Ordering Convergence.

However, absent independent reason to accept Ordering Convergence, there is no reason to believe the disjunctive claim. Why believe it? (1) The disjunctive claim might, conceivably, be a feature of moral goodness that we discover by investigating the structure of moral aggregation. But there is no such discovery to be had. There exist moral aggregation functions – in particular, the Unanimity Rule – that yield facts about comparative moral goodness even without Ordering Convergence. (2) The disjunctive claim might express a truism of ordinary moral thought that any metaethical view should try to respect. But does it? Who (except for a few IA theorists) finds it pretheoretically obvious that convergence of moral preferences is the only alternative to moral nihilism? Indeed, many of us find the negation of the disjunctive claim to be pretheoretically obvious – observing moral disagreement all around us, and yet finding ourselves asserting moral truths in the teeth of such disagreement.

To sum up: the non-relativistic IA theorist who includes all persons (not just humans) in the community of advisors has one reasonable basis for endorsing Ordering Convergence – for believing that only profiles with identical moral preferences are metaphysically possible. That basis is the reasonable belief that the property of preferences picked out by the concept of rationality forces convergence.

However, since it is also reasonable to deny that ‘rational’ persons need to see their choices as systematically justifiable, or reasonable to accept agent-centred rationales as one such justification, it is also reasonable to reject Ordering Convergence. What doing so means for moral aggregation is the question we now consider.

5. THE QUASI-ARROVIAN SETUP WITH DIVERGENT PREFERENCES

For a given situation S, let UD^S be the set of all N-fold concatenations of quasiorderings of S. Universal Domain holds true in a given situation S iff Φ^S = UD^S. Φ^S, the domain for the moral aggregation function, includes every combination of formally well-behaved rankings of the situation.

Whether the IA theorist believes that Universal Domain holds true in a given situation depends, of course, on her beliefs about the properties picked out by the terms ‘rational’, ‘well-informed’ and ‘impartial’. It also depends on the nature of the situation. For example, let S = {x, y, z} be such that the three options are identical except that x involves the torturing of no babies, y the torturing of 10 and z the torturing of 100,000. Then (absent a radical disjunction between the idealized advisors and what we observe among non-ideal moral thinkers) it is hard to believe that any advisor would prefer z to y to x, let alone that all the elements of UD^S are metaphysically possible. By contrast, consider T = {x*, y*, z*}, with the three options otherwise identical except that x* causes non-fatal physical harm to a group of persons, y* a substantial loss of liberty and z* pain and suffering. Then (since we do not observe non-ideal moral thinkers agreeing on a strict ranking of any two of these harms) it is easier to believe that all patterns of preference among x*, y* and z* are possible for the ideal advisors.

I first discuss the implications of Universal Domain. If Universal Domain holds true in a given situation S (and #S > 2), the moral aggregation function for that situation must be the Unanimity Rule.

Conversely, if Φ^S has a narrower domain, other moral aggregation functions – for example, majority vote – may be consistent with the intra-situational axioms of the quasi-Arrovian Setup (regardless of #S): weak Pareto, intermediate Pareto, Anonymity and Independence. However, by adding Across-Situation Ranking Consistency (ASRC), and an assumption that Universal Domain holds true in a sufficient number of situations, we force the moral aggregation function in every situation (with #S > 2) to be the Unanimity Rule.

The surprising result of this section is that the connection between moral goodness and convergent moral preferences emerges not from a demanding view of rationality (such as Michael Smith's), but from a very different direction. If rationality (and the other idealizing conditions) are loose enough that a very wide diversity of advisor preferences are metaphysically possible in a sufficient range of situations, the combination of the intra- and inter-situational axioms of the quasi-Arrovian setup makes convergence a necessary condition for moral comparability.

6. BEYOND THE QUASI-ARROVIAN SETUP

The analysis to this point has worked within the quasi-Arrovian setup. The setup might be revised in various ways, either by changing the requirement that advisors’ inputs and the moral output be quasiorderings, or by changing the axioms. I will here briefly discuss the latter type of revision – in particular dropping Independence or Across-Situation Ranking Consistency (ASRC). It is harder to see how the IA theorist could reject the Pareto axioms (which express the constitutive role of the community of idealized advisors in determining moral facts); or the Anonymity axiom (which expresses the equal role within that community of each advisor).

One possible revision to the quasi-Arrovian setup is to drop Independence but not ASRC. The setup, thus amended, retains the idea that advisors’ ordinal preferences determine the moral goodness ranking of a set of alternatives. But it does not require that such determination occur on a pairwise basis. The comparative moral goodness of two alternatives need not be fixed by the advisors’ ranking of those two, taken alone. Instead, it is the advisor-by-advisor ordinal preferences with respect to the entire set of alternatives that fix the moral goodness ranking of that entire set. The social choice literature describes aggregation functions that satisfy ASRC while violating Independence, the most famous being the Borda rule (Brams and Fishburn Reference Brams, Fishburn, Arrow, Sen and Suzumura2002; Pattanaik Reference Pattanaik, Arrow, Sen and Suzumura2002).

A second amendment is to drop both Independence and ASRC.Footnote ³¹ The idea, here, would be that moral goodness depends in part on non-ordinal features of advisors’ preferences – so that the pairwise ranking of two alternatives cannot be fixed by advisors’ ordinal rankings of the two (Independence) and indeed the ranking of a whole set of items cannot be fixed by advisors’ ordinal rankings of the whole set (ASRC).

Imagine, specifically, that moral aggregation proceeds using an approach analogous to the social-welfare-function (SWF) framework – which, as mentioned earlier, is a standard tool developed by social choice theorists for the context of interest aggregation. A given alternative is mapped onto a vector of ‘utility’ numbers. With N individuals in the population whose well-being is of concern, a given alternative x is mapped onto the vector (list) of numbers (u ₁(x), . . ., u_N(x)), with u_i(x) the utility number representing the well-being of individual i given x. An SWF is a rule for ranking such vectors (Bossert and Weymark Reference Bossert, Weymark, Barberà, Hammond and Seidl2004; Adler Reference Adler2012; Weymark Reference Weymark, Adler and Fleurbaey2016).

By analogy, the IA theorist might think that advisors’ ordinal rankings of a given situation plus the relevant non-ordinal features of their preferences can be summarized in moral utility numbers. On this view, moral aggregation proceeds by translating a profile of advisor preferences over the alternatives into a vector of moral utility numbers, one for each alternative; and then by using some rule to rank these vectors. Because the moral utility numbers are capturing more than advisors’ ordinal rankings of the situation, neither Independence nor ASRC can be expected to hold.

Should we indeed drop Independence, or Independence and ASRC, from our model of moral aggregation? Or is the quasi-Arrovian framework correct to include both axioms? How the IA theorist should answer these questions depends upon what it is reasonable to believe concerning the grounding of moral facts. Any IA theorist believes certain metaethical propositions that are basic to the IA approach: for example, that moral statements can be true or false, that there are moral facts, that moral facts are grounded in natural (physical, psychological or social) facts, and more specifically are grounded in the preferences of a group of idealized advisors. The IA theorist believes all this in virtue of considerations mentioned earlier, and is reasonable to do so. Now we can ask: Would it be epistemically more reasonable to believe that preferences constitute moral facts in the specific manner set forth by Independence and ASRC, or instead to deny this?

The metaethical discussion required for a full treatment of this question is well beyond what can be accomplished here. Let me simply make some initial, suggestive remarks.

To begin, there is reason to doubt that there are non-ordinal features of the advisors’ preferences, relevant to the determination of moral goodness and mirrored in moral utility numbers. This challenge to ASRC and Independence seems weak. Moral goodness is (as a matter of ordinary moral discourse) a purely ordinal property: we think of actions, outcomes and other items subject to moral assessment as being better or worse than each other, not as possessing degrees of moral goodness. So why wouldn't the advisors themselves, thinking morally, also have preferences that are purely ordinal?

There is an important disanalogy, here, between interest aggregation and moral aggregation. Ordinary discourse about well-being supports comparisons of well-being differences. It would be unexceptionable to say something like: ‘Ron should spend that extra money on headache therapy, not the big screen TV, because getting rid of his chronic headaches will make a much bigger difference to his life than a larger TV.’ Moreover, ordinary discourse about well-being does not share the scepticism about interpersonal comparisons that some economists espouse. No one (except an economist) would rebel at the statement that Stanley, who has a decent job, good mental and physical health, and a loving spouse and family, is better off than Xavier, who is unemployed, poor, depressed and alone.

The well-being utility functions that serve as the input to SWFs contain information about well-being differences and interpersonal comparisons, as well as tracking preferences: u_i(x) ≥ u_i(y) iff i has an appropriately laundered weak preferenceFootnote ³² for x over y. u_i(x) – u_i(y) ≥ u_i(z) – u_i(w) iff the difference in i’s well-being between x and y is at least as large as the difference in i’s well-being between z and w. u_i(x) ≥ u_j(y) iff i in x is at least as well off as j in y. To be sure, constructing well-being utility functions that reflect all this information is not a trivial matter (Adler Reference Adler, Adler and Fleurbaey2016); but the supposition that there are genuine facts about well-being differences and interpersonal level comparisons, to be measured by well-being utility numbers, is not problematic.Footnote ³³

By contrast, it is hard to see what the underlying facts are which are supposed to be mirrored in moral utility numbers. What would be the counterpart of well-being differences, or of interpersonal comparisons of well-being levels – differences in moral satisfaction, or comparisons of levels of moral satisfaction? Talk of moral satisfaction is no part of ordinary moral discourse. It would be weird to say ‘Ron should give his cash to Oxfam, not Greenpeace, because helping to prevent hunger makes a bigger difference to his moral satisfaction than helping to save the planet’; or to say ‘Phyllis is a big believer in animal rights, while Francine is a sceptic, and so if government were to regulate treatment of animals that occurs in factory farms Phyllis would be morally better off – more satisfied, morally – than Francine’. Whether a putative metaethical fact is genuine – specifically, here, whether advisors’ moral preferences have a non-ordinal aspect, in turn determinative of moral goodness – depends, in some more or less complicated way, on both the truisms constitutive of our moral concepts (as evidenced by what is said or not said in moral discourse) and on physical, psychological and social features of the world. On the first score, at least, the case for such non-ordinal information is weak.

Turning now to Independence: this axiom, too, seems warranted by ordinary moral discourse. Here, it should be stressed that our topic has been moral betterness (comparative moral goodness), rather than moral rightness or absolute moral goodness. Whether one or another alternative is right depends upon the totality of alternatives available. And of course the best alternative in a given situation depends upon the comparative moral goodness of all the pairs. But it seems to be a truism of ordinary moral talk that the comparative goodness of two alternatives depends just upon the characteristics of the two. For example, if government is choosing between a policy x that increases a population's happiness but limits individuals’ choices, and a policy y that increases individual liberties at the expense of happiness, it would be odd to think that the truth of the proposition ‘x is better than y’ might depend upon whether government was also considering a policy z targeted at population health.

Still, a plausible indirect argument can be mounted for rejecting Independence. Assume that we reject the supposition that non-ordinal features of advisor preferences help determine moral goodness. We thus accept ASRC. ASRC, plus the other elements of the quasi-Arrovian setup, plus the supposition that Universal Domain holds true in a sufficient number of situations, entails that the moral aggregation function for every situation with cardinality greater than two must be the Unanimity Rule. That was the upshot of section 5. And – it might be argued – the Unanimity Rule is too ready to propagate moral noncomparability from the heterogeneity of moral preferences that we observe around us and might imagine to characterize even idealized advisors. Via a process of reflective equilibrium – used here not in refining our substantive moral views, but in refining our metaethical understandings – we might end up rejecting Independence, despite its intuitive appeal, once we see what it yields when combined with other axioms that we find even more appealing.