VALUE NEUTRALITY AND THE RANKING OF OPPORTUNITY SETS MICHAEL GARNETT I defend the idea that a liberal commitment to value neutrality is best honoured by maintaining a pure cardinality component in our rankings of opportunity or liberty sets. I consider two challenges to this idea. The first holds that cardinality rankings are unnecessary for neutrality, because what is valuable about a set of liberties from a liberal point of view is not its size but rather its variety. The second holds that pure cardinality metrics are insufficient for neutrality, because liberties cannot be individuated into countable entities without presupposing some relevantly partisan evaluative perspective. I argue that a clear understanding of the liberal basis for valuing liberty shows the way to satisfying responses to both challenges. 1. INTRODUCTION Liberals typically believe that states ought to prefer policies that do not worsen the positions of their citizens with respect to liberty, absent reasons to the contrary.1 Many liberals also believe that states ought to maintain at least some degree of first-level neutrality with respect to evaluative disputes amongst their citizens.2 Insofar as these beliefs are correct, states need a neutral way of assessing what counts as a worsening of one's position with respect to liberty; that is, they need a neutral ranking of liberty or opportunity sets.3 What would such a neutral ranking consist in? Following Ian Carter (1999: 3167), philosophers and economists standardly distinguish between the specific value of liberty, i.e. its value qua liberty to do some particular thing (like practicing a religion or crossing the street), and its non-specific value, i.e. its value simply qua liberty. A natural thought may be that a value-neutral ranking of liberty sets is one that avoids contentious claims about the relative value of different specific liberties, focusing instead just on 1 Gaus (1996: 165) calls this presumption in favour of liberty the 'Fundamental Liberal Principle'. See also Feinberg (1984: 9), Benn (1988: 87-90), Rawls (2013: 292) and Gaus and Courtland (2011). 2 'First-level' neutrality is here contrasted with 'second-level' neutrality, i.e. neutrality with respect to the justification of neutrality itself. As we shall see below, commitment to (some degree of) first-level neutrality is simply a commitment to (some degree of) liberal toleration. C.f. Colburn 2010. 3 Though there may be a useful distinction to be drawn between liberty and opportunity, none of the arguments advanced or discussed in this paper turn on it. 2 liberty's non-specific value and ranking sets only in terms of the sheer quantity of liberty they represent.4 As we shall see, however, such an approach would be unduly restrictive, since not all claims about liberty's specific value need violate the requirements of liberal neutrality. Nevertheless, one might still expect that a neutral ranking of liberty sets would at least incorporate some pure cardinality metric as one of its component parts. Yet even this restricted position is open to serious challenge. First, it can be objected that a pure cardinality component is unnecessary for a neutral ranking, on the grounds that the non-specific value of a liberty set is correlated not with the amount of liberty it provides but rather with the range or variety of liberty it provides. Alternatively, it can be objected that a pure cardinality component is insufficient for a neutral ranking, since (as Robert Sugden (2003) has argued) any measure of liberty- even a purely quantitative one-necessarily presupposes some particular evaluative perspective. The aim of this paper is to defend the importance of a pure cardinality component in the ranking of liberty sets from these two objections. As we shall see, doing so requires paying careful attention to the nature of the liberal's underlying reasons for valuing liberty and neutrality in the first place. Section 2 reviews our initial reasons for desiring a neutral liberty metric. Section 3 relates these reasons to the familiar distinction between liberty's specific and nonspecific value. Sections 4 and 5 consider and respond to the objection that a pure cardinality component is unnecessary for neutrality, and Section 6 considers and responds to the objection that it is insufficient. Section 7 ties up some loose ends. 2. WHY A NEUTRAL METRIC? Adapting Gerald Gaus's (2009b: 82) formulation, let us say that some state action φ is neutral in relation to the members of some set of citizens C concerning some set of disputes D iff φ does not treat members of C differentially on the basis of D. It will not be relevant to the ensuing argument just what is to count as a state 'action', nor exactly which citizens are deemed deserving of neutral treatment, nor what precisely qualifies as 'treatment' (whether, for instance, neutrality is taken to apply to the state action's effects, to its aims, or to its justification); I therefore take no stand on these questions.5 What does matter here is the exact range of disputes (D) with respect to which the state ought to be neutral: as we shall see, some important disagreements about the relative adequacy of different liberty metrics are rooted in disagreements about just how broadly neutral states ought to be. 4 Examples of such rankings would include the 'naïve' cardinality ranking discussed (and criticised) by Pattanaik and Xu (1990), as well as the quantitative metric advanced by Carter (1999). 5 For a useful list of views on these issues, see Gaus 2009b, especially the long list of works referred to at pp. 81-2. 3 Let us say that a state action is extent-of-liberty-implicating iff its relevant effects are to be assessed, or its aim or justification stated, with at least partial reference to the relative or absolute position of at least some individuals with respect to liberty. If the state recognises a general presumption in favour of liberty, as most liberals believe that it should, then every state action is extent-of-liberty-implicating, since the impact on liberty of every state action is a necessary object of concern. Moreover, even in the absence of such a general presumption it is likely that a great many state actions are extent-of-liberty-implicating in this sense. Now consider the following liberal doctrine: Moderate First-Level State Neutrality. At least some extent-of-liberty-implicating state actions ought to be neutral with respect to at least some substantial range of evaluative disputes. This is purposely stated so as to be acceptable to many contemporary liberals. If we accept it, then we require a way of ranking liberty sets that is neutral with respect to some substantial range of evaluative disputes; that is, we need a (more or less) neutral liberty metric. The question is what reason there is to accept this doctrine. There are a number of familiar reasons for accepting it, notwithstanding disagreement between liberals over the relative merits of the different reasons. Let us call such reasons neutrality reasons. They include the following:6 1. Fallibility: The state's evaluative judgements may turn out to be mistaken (c.f. Mill 1999: 60-2; Carter 1999: 45). 2. Knowledge: Even our true value judgements cannot constitute knowledge unless they are challengeable, in practice as well as in theory (c.f. Mill 1999: 62-79; Kukathas 2003: 126-30). 3. Progress: We all stand to benefit from innovations and discoveries made possible when individuals are permitted to engage in evaluative experiments (c.f. Mill 1999: 101-21; Hobhouse 1994: 56-66; Hayek 2006: 21-35). 4. Autonomy: The freedom to act on one's own value judgements is an essential element of a flourishing human life (c.f. von Humboldt 2008; Mill 1999: 101-21; Raz 1986: 369-430). 5. Reciprocity: It is illegitimate to demand of others what one does not demand of oneself, namely, that they submit to coercive force for reasons that they reasonably reject (c.f. Larmore 1990; Rawls 2013). 6 The following list is adapted from Carter 1999 and Gaus 2009a. 4 Note that one or more of these reasons may themselves qualify as neutral with respect to some relevant range of disputes. Where this is the case, we have an instance of second-level neutrality, what Charles Larmore calls 'a neutral justification of neutrality' (1987: 53). The possibility and desirability of such second-level state neutrality is the central issue disputed by 'comprehensive' and 'political' liberals (see, for example, Larmore 1987, 1990; Hampton 1989; Raz 1990; Rawls 2013; Wall 1998). I here take no stand on this disagreement, focusing only on first-level neutrality of the kind already introduced. This form of neutrality is typically endorsed by liberals of both stripes. So liberals need a neutral liberty metric insofar as they endorse Moderate FirstLevel State Neutrality, and they typically endorse this doctrine on the basis of one or more of the neutrality reasons just mentioned. Moreover, the degree of neutrality required (the set of disputes D that demand neutrality) is a function of the nature and strength of these reasons. 3. NEUTRALITY AND SPECIFIC VALUE What would constitute a neutral liberty metric? An initially tempting thought may be that a neutral ranking of liberty sets must concern itself just with their non-specific value, on the grounds that judgements about their relative specific value cannot fail to take sides on relevant evaluative disputes. Yet this is not the case for, as we have seen, Moderate First-Level Neutrality requires neutrality with respect to some substantial range of evaluative disputes (as specified by our neutrality reasons) and not, as this thought suggests, neutrality with respect to all evaluative disputes. So at least some judgements concerning the specific value of liberty are likely to be consistent with neutrality, and therefore properly incorporated into a neutral metric. Moreover, it is also well known that at least some sensitivity to the specific value of liberty is essential if a metric is to avoid counterintuitive results (Taylor 1979; Crocker 1980; Sen 1990, 1991; Kramer 2003). By way of illustration, it may be helpful to imagine a character-call her the extreme first-level anti-perfectionist-who sees no place whatever for judgements of specific value in a neutral liberty metric. Such a person treats our neutrality reasons as absolutely decisive considerations in favour of recusing ourselves from judgements about the relative value of specific liberties, arguing that an overall measure of the value of a liberty set should therefore reflect only its non-specific value (and thus should measure only the sheer range of liberties offered, with no value weightings). Moreover, we might also imagine, by way of contrast, an extreme first-level perfectionist who takes the opposite line, arguing that since some specific liberties are valuable and others are not, and since an overall measure of the value of a liberty set should measure just what is actually valuable about that set, such a measure should count only the specifically valuable liberties (in proportion to their value) and disregard the rest. Hence whereas the extreme anti-perfectionist denies that our neutrality reasons can ever be defeated by 5 competing considerations, the extreme perfectionist denies that we have any neutrality reasons at all. In contrast, many liberals adopt an intermediate position, which is to say that they recognise at least some neutrality reasons but do not treat them as always absolutely decisive. According to this familiar, moderate position, our neutrality reasons only take us so far. Thus there may be cases in which our initial reasons for valuing certain specific liberties are not fully defeated by our reasons for maintaining neutrality in these cases. For instance, Matthew Kramer, in discussing the significance of the neutrality reason that I have labelled fallibility, writes: Although we should surely accept that freedom is endowed with contentindependent valuableness partly because of the proneness of human beings to err when they esteem or depreciate certain particular freedoms, we should hardly conclude therefrom that no judgements about the significance of particular freedoms can reasonably be made and confirmed. People sometimes go astray when reaching such judgements-a point whose importance should be neither underestimated nor overestimated-but very often their judgements prove to be correct. (2003: 434) So fallibility is an important consideration, but not an overriding one; it gives us some reason to be neutral with respect to some range of disputes, but by no means decisive reason to be neutral with respect to all disputes. (Similar points may be made with respect to the other neutrality reasons listed above.) It is this moderate position that underlies the familiar idea that a neutral liberty metric should be two-dimensional, taking into account both the specific and the nonspecific value of liberty (Taylor 1979; Crocker 1980; Arneson 1985; Sen 1991; Kramer 2003). Two particular points about the reasoning leading up to this conclusion will prove important later, and so are worth emphasising now. The first is that this twodimensional approach is the result of a balancing of, on the one hand, our reasons for according different liberties different degrees of specific value and, on the other hand, our neutrality reasons. The second is that exactly how much extra weight is to be assigned to the specifically valuable liberties in the calculus is determined by exactly how strong we take our neutrality reasons to be (and in relation to precisely which ranges of evaluative disputes). Thus the weights are not simply 'arbitrary' or 'subjective' (Carter 1999: 137-9): although this is a matter on which liberals typically disagree, it is one that can, in principle, be resolved by substantive philosophical debate concerning the merits of those reasons. So a neutral ranking of liberty sets need not restrict itself to relative assessments of the non-specific value of those sets. Nevertheless, it ought at least to incorporate some relative assessments of non-specific value (insofar as at least one neutrality reason has at least some application). Moreover, it is natural to connect the non-specific value of a liberty set to its size. In this way, we seem to arrive easily at the main claim to be 6 defended in this paper, that a neutral ranking of liberty sets must at least include some pure cardinality metric. Unfortunately, however, the path to this conclusion is not quite so easy. I turn now to the first of two possible objections. 4. PURE CARDINALITY AND THE PROBLEM OF DIVERSITY According to Carter, the non-specific value of a liberty set supervenes on its size (Carter and Kramer 2008: 93-4). Yet there are, as we shall now see, good reasons for thinking that this is incorrect. It has been widely observed that the diversity of one's liberties must be relevant to assessments of liberty (Crocker 1980: 54-7; Pattanaik and Xu 1990: 389-90; Klemisch-Ahlert 1993; Sugden 1998: 318; Rosenbaum 2000; Bavetta and Del Seta 2001; Bossert et al. 2003; Kramer 2003: 463-71). I now argue that such diversity considerations are best treated as relating to liberty's non-specific value. Thus there is good reason for thinking that the non-specific value of liberty supervenes not on the quantity of liberty afforded by an opportunity set but on the range or diversity of liberties it affords. This suggests that pure cardinality metrics are after all unnecessary for neutral rankings of liberty sets. The basic case for the relevance of diversity to assessments of liberty is clear. Lawrence Crocker puts it well: 'other things being equal, we add more to an individual's freedom when we open up a very different new alternative than when we open up a new alternative similar to alternatives the individual already has. If I am free to be a pitcher or a poet, I am freer than if my options are being a pitcher or a shortstop' (1980: 55). In a similar vein, Prasanta Pattanaik and Yongsheng Xu note that the opportunity set {blue car, train} seems to offer more freedom of choice than the set {blue car, red car}, despite each being of equal size (1990: 389-90). The important question in the current context, however, concerns how to relate the issue of variety to the distinction between the specific and the non-specific value of liberty. If the importance of variety relates only to liberty's specific value, then it provides no reason to doubt the relevance of pure quantity to measures of non-specific value. But if the variety afforded by a set of liberties relates to liberty's non-specific value-and, in particular, if it turns out to constitute that value entirely-then pure quantity may drop out of the picture all together. In this section I suggest that there is indeed a strong prima facie case for the latter view. To see this we first need to see what is wrong with attempts to subsume the issue of variety just within the category of specific value. Such a move might be motivated by the following considerations. The values assigned to specific liberties must be contextdependent; that is, it will not do to try to assign a value to some specific liberty, such as the liberty to eat beans, in an entirely general or abstract way. Instead, we must assess the value of this liberty to some particular person in some particular situation. Accordingly, we will recognise that the liberty to eat beans is normally less valuable to someone who has eaten nothing but beans for the past month than for someone on a more varied diet. Indeed, we may reasonably come to think that, in general, a liberty will always have more specific value when it serves significantly to increase the 7 diversity of options available to a person than when it fails to do so. So we may think that the category of specific value already adequately recognises the importance of variety. This line of thought should be resisted for two reasons. First, it is not always true that diverse liberties carry a premium of context-dependent value: think, for instance, of the increasing value that very similar liberties have for collectors. Second, and more importantly, this line fails properly to understand the distinct bases of our reasons for valuing specifically valuable liberties, on the one hand, and diverse liberties irrespective of specific value, on the other. This was the dialectic sketched in Section 3, where we began with our judgements that some liberties have more (context-dependent) value than others, and then saw that we have various neutrality reasons for partially recusing ourselves from such judgements-thus giving us reason for also valuing possession of a wide range of liberties irrespective of what we currently take to be their (contextdependent) specific value. The important result is that regardless of the view we take concerning the relevance of variety to the specific value of one's liberties, our neutrality reasons constitute further reasons for valuing the variety of our liberties in general, i.e. for treating variety as part of the non-specific value of liberty. So even if variety plays a role in the determination of liberty's specific value, this does not exhaust its importance to the value of liberty, since it is also relevant to liberty's non-specific value. Moreover, our reasons for valuing liberty non-specifically-our neutrality reasons-appear to be reasons for valuing liberty sets in point of their diversity and not in point of their size, as I now explain. Consider fallibility. Suppose that one is sure that one's most valuable transport option is 'blue car'. Of course, one might still turn out to be mistaken, and it is therefore valuable to have alternative options as a kind of insurance against this sort of error. The question is, which alternative provides the better insurance against evaluative mistakes concerning the superiority of 'blue car' as a mode of transport: 'red car' or 'train'? I take it that 'train', the more diverse option, provides the better cover (c.f. Nehring and Puppe 2003: 1168). To take a different example, suppose that a state permits only heterosexual marriage, but that it offers a large choice of slightly different fonts and layouts in the issuing of marriage licenses. We might say that, although the state affords its citizens a large number of marriage options, it affords them a very limited range. And despite the large number of alternatives, the lack of variety means that the state fails to allow for genuinely diverse forms of life. In terms of knowledge and progress, then, citizens are relatively unlikely to have their current evaluative judgements challenged, either unsuccessfully or successfully, by others living lives of which they disapprove; and in terms of autonomy, the state is failing to allow citizens to live worthwhile lives as judged from their own evaluative perspectives (c.f. Sugden 1998: 318). For liberals concerned 8 with maintaining a protected space in which individuals can live a wide variety of potential lives, therefore, it is surely variety that matters.7 So it is with the variety of one's liberties, and not with the mere number of one's liberties, that the non-specific value of liberty seems most plausibly associated. In fact, pure quantity may even seem to be of vanishing importance. Suppose that you can choose between (i) taking any item from a fridge containing fifty identical cans of Coke, or (ii) taking any item from a fridge containing five hundred identical cans of Coke. Although the latter option clearly represents the greater quantity of liberty, any preference for it is minimal at best. What is more, any tiny preference for (ii) may be explicable by the similarly tiny amount of extra variety it affords (that is, the greater variety of spatial locations of the cans), and not by its size at all. This is because the addition of even a very similar liberty to a set must increase the diversity of that set at least to some minimal degree, if it is to count as a genuine addition (since non-identical options cannot have exactly similar properties-an application of Leibniz's Law). So it is possible (though, as we shall see later, not in fact the case) that quantity, taken simply in itself, makes no contribution to the non-specific value of liberty at all. Carter (1999) attempts to rescue pure quantity from these kinds of considerations by arguing that it is in general an excellent approximation of diversity. On his view, the amount of liberty a person has is best measured in terms of the extent of the physical changes that she is able to make to her environment. A feature of this physical approach seems to be that the addition of a similar liberty to a liberty set will typically add less to the total amount of liberty represented by the set than the addition of a dissimilar liberty. Thus, in his example, the liberty to choose any one of twenty-one brands of washing powder need not represent three times the liberty one enjoys when choosing from amongst only seven brands, because: the acquisition of the freedom to use a second kind of washing powder adds much less to one's overall freedom than does the prior acquisition of the freedom to use a kind of washing powder. Most obviously (and not only), the new freedom to use the second kind of washing powder will not add to our option set the option of washing our clothes (with a certain degree of efficiency), in the way that the freedom to use the first kind of washing powder did. For this is an option that we already had when we were free only to use the first kind of washing powder. Indeed, if the two brands are identical in terms of what can be done with them, then the only additional action made available through the availability of the second brand (as an alternative to the first) will be that of taking it (rather than the first brand) off the supermarket shelf. (1999: 199-200) 7 Moreover, if fallibility, knowledge, progress and autonomy are reasons for valuing possession of a variety of liberties, then reciprocity likely is too, insofar as these other reasons serve to constitute the basis for an overlapping consensus in favour of the importance of variety. 9 However, even if we accept Carter's physical approach, there are two problems with this particular strategy. The first, noted by Kramer (2003: 466-71), is that it is inconsistent with a separate part of Carter's account, that being his claim that the proper objects of liberty aggregation are not individual liberties but rather combinations of conjunctively exercisable liberties. This means that, say, the liberty to wash one's clothes does indeed enter the calculus twice, once as part of a conjunctive liberty combination that includes the liberty to buy Persil, and once as part of a conjunctive liberty combination that includes the liberty to buy Daz. So Carter's calculus does not, in fact, have the advertised feature. Faced with having either to abandon his argument concerning diversity or to revise his liberty calculus, Carter opts for the latter: 'I would like to think that what is at fault here is my proposed formula for measuring overall freedom' (2004: 78). Yet, even were this formula suitably revised, note that Carter's strategy does not fully succeed in subsuming the issue of diversity within the realm of pure quantity. This is because not all qualitatively distinct liberties open up unique sets of further liberties. To see this, suppose that you visit a restaurant for lunch and are presented with a wine list containing fifty wines of different varieties. For dinner you visit a different restaurant and are presented with a wine list containing fifty wines, all merlot. (Assume, improbably, that all wines across both lists are in standard bottles, have the same alcohol content, and are at the same price.) Clearly, your lunchtime set of wine-related liberties was more diverse than your dinnertime set. However, it does not seem that any liberties are causally generated by, say, the liberty to drink a bottle of chianti that are not also generated by the liberty to drink a bottle of merlot. In particular, the further physical effects of each can be expected to be more or less indistinguishable. Nevertheless, these sets of liberties differ greatly in point of diversity, just not in ways that have any knockon effect on one's possession of other liberties (see also van Hees 2000: 130-1).8 Of course, Carter's claim was just that quantitative measures approximate diversity-based measures (at least on a physical approach), not that they perfectly coincide with them. Yet if it is diversity that grounds the non-specific value of liberty, then it is diversity that should figure in our method for ranking liberty sets in terms of their overall value. Insofar as considerations of quantity and diversity diverge, we want our metric to track the former. So it does indeed look like quantity drops out of the liberty metric altogether: that a pure cardinality component is, after all, unnecessary for a neutral ranking of liberty sets. 8 What about, say, the liberty to savour a chianti's distinctive bouquet? Since this is not causally generated by the liberty to drink a bottle of chianti, but is instead simply a possible redescription of it, it is not properly included in Carter's calculus (1999: 175-83). (If it is nevertheless still suspected that the more diverse wine menu might work to open up a greater number of liberties for the agent down the line, imagine instead that the two menus are being presented to inmates from which to choose a final drink prior to execution.) 10 5. THE NECESSITY OF A CARDINALITY COMPONENT However, this conclusion is too hasty. As I shall now argue, liberals who wish to maintain a substantial commitment to first-level neutrality do in fact have continuing reason to preserve a pure cardinality component in their liberty metrics. This is because judgements of variety and diversity are inherently value-laden. This point has been widely noted (Sugden 1998: 329, 2003: 800-2; Bavetta and Del Seta 2001: 221; Nehring and Puppe 2002). The basic issue is that claims about similarity and dissimilarity-and therefore claims about degrees of diversity-are true or false only relative to particular ways of dividing up the world and, at least in the domain of human action, there is no way of dividing up the world that is not relative to some particular set of practical interests.9 For instance, it is presumably because we divide the world up into poets and baseball players, and not, say, into professions the names of which begin with different letters (poets and pitchers on one side, shortstops on the other), that we share Crocker's intuitions about the relative diversity of his pairs of career options. Moreover, the reason that we divide the world up in this particular way is to do with the fact that we share various obvious practical interests. So any judgement about the range of liberties possessed by a person can be true only relative to a particular taxonomy of act-descriptions, which is in turn merely an expression of certain fundamental values and interests. This means that judgements about the variety of liberties open to a person-and therefore, if the reasoning of the previous section was correct, judgements about the nonspecific value of those liberties-are inherently value-laden in a relevant sense. But the whole point of according liberty non-specific value was to maintain a degree of firstlevel neutrality by avoiding begging questions about the relative value of different forms of life. So whereas before it looked as if the non-specific value of liberty simply needed to be traded off against its specific value in an overall ranking, it now looks as though the entire project of trying to recognise a relevantly value-neutral dimension of liberty assessment may be fundamentally misconceived. All this poses a prima facie problem for the liberal neutralist, who now seems to have good reason for accepting each of a potentially inconsistent trio: (1) there are good neutrality reasons for valuing liberty non-specifically; (2) the non-specific value of a liberty set supervenes upon its diversity; (3) judgements of diversity are inherently valueladen. If the liberal is to have a coherent position, something will have to give. Fortunately, there are a number of routes through the thicket. The first is to hold that the neutrality reasons featured in (1) are sufficiently weak as to render the value-ladeness of (3) consistent with neutrality. This amounts to a kind of moderate first-level perfectionism, in which it is conceded that we have reason to recuse ourselves from (some of) our judgements about the relative specific value of liberties, but not to recuse 9 Matters may be different in domains where we do have objective reasons for preferring one taxonomical system to another, such as biology: see Weitzman 1992 and 1998, as well as Nehring and Puppe 2003. 11 ourselves from our judgements about which general evaluative position is the correct one for making assessments of diversity. This is by no means an unreasonable position, and worth dwelling on briefly. For it is important to keep in mind just how far working to provide diverse liberties can take us in furthering liberal aims. To illustrate, imagine a society in which, at one time, people are permitted only those specific liberties deemed valuable by a dictator; but in which, at a later time, the dictator decides also to provide a wide range of diverse liberties irrespective of their specific value. Notwithstanding the fact that the later settlement includes only what counts from the dictator's perspective as a wide range of liberties, it almost certainly represents an important improvement from the point of view of liberal neutrality. Indeed, the sense in which specific value judgements are value-laden likely differs significantly from that in which diversity judgements are value-laden (Dowding and van Hees 2007: 146-7). For whereas the former are value-laden in the focused sense of proceeding from particular, contested moral views, the latter are value-laden only in the broad and diffuse sense of proceeding from general and widely-shared human interests and concerns. It is therefore possible, and indeed quite common, for people to divide the world up in the same basic way and yet to disagree fundamentally about the relative value of the elements of the world so divided (Rosenbaum 2000: 218-9). For example, two people may agree that the opportunity set {using a contraceptive from one packet, using a contraceptive from another packet} contains a narrower range of options than the set {using a contraceptive from one packet, aborting a pregnancy}, but disagree radically over which contains the more valuable opportunities. It is because diversity judgements often remain in this way independent of the specific value judgements we make about particular liberties that liberal aims may be met to a significant degree through the provision of wide ranges of options, despite the inherent value-ladeness of diversity judgements. This said, some liberals may nevertheless favour a more robust and wide-ranging value-neutrality than such a response permits. At the other extreme, then, an alternative response to the potential trilemma described above would be to insist that the valueladeness of diversity judgements precludes their playing any role whatever in a neutral liberty metric, thereby abandoning (2) in favour of the view that non-specific value must be taken to supervene on pure quantity after all. This is the hard line response that might be expected, for instance, from the extreme first-level anti-perfectionist of Section 3. These two possible responses are diametrically opposed: while the moderate perfectionist denies that we have any reasons for recusing ourselves from judgements about which general evaluative perspectives are the correct ones, the extreme antiperfectionist takes us to have absolutely decisive reasons for doing so. This suggests a third, intermediate position, according to which we have neutrality reasons that are not fully decisive. That is, our initial reasons for taking one particular general evaluative perspective to be the correct one are somewhat, but not entirely, defeated by our neutrality reasons. So in devising a neutral measure of the non-specific value of liberty 12 we must balance our reasons for favouring one particular evaluative perspective, on the one hand, with our neutrality reasons, on the other. This means adopting a twodimensional approach to the measurement of non-specific value: on this view, the nonspecific value of a liberty set is given by some metric that combines a measure of variety with one of pure quantity. Moreover, the relative weighting of variety as against quantity is determined by how strong we take the relevant neutrality reasons to be, where this is a matter resolvable only by substantive philosophical debate. If this sounds familiar, it is because it is a near-perfect recapitulation of the dialectic of Section 3. There we started with the idea that certain specific liberties-such as liberties of speech and religion-are of particular value, and then saw that we also have neutrality reasons for valuing possession of a wide range of liberties regardless of their specific value. That is, we saw the need to trade off between our conviction that certain specific liberties are the especially valuable ones and our desire not to prejudge certain questions of substantive value, a need which we saw could be met by adopting a two-dimensional method of overall liberty assessment that gives weight both to the quality and to the range of liberties a person enjoys. Now this move is simply repeated. This time we start with the idea that possession of a wide range of liberties is particularly valuable, but see that our need not to prejudge certain questions of substantive value gives us reason also to recognise the importance of having a large number of liberties regardless of their variety. There is therefore a need to trade off between (i) our conviction that one particular conceptual framework is the appropriate one for making meaningful judgements concerning the diversity of options and (ii) our liberal desire not to prejudge entirely which conceptual frameworks are appropriate. Note that this iteration of the previous dialectic is now located within the category of non-specific value itself. That is, what we value when we value liberty nonspecifically is best captured by a metric that incorporates both quantity and diversity. Moreover, the overall value of liberty incorporates both its specific and its non-specific value. So the overall value of liberty is therefore three-dimensional, incorporating (1) specific value, (2) variety, and (3) quantity, as represented in Figure 1. Value of Liberty Non-Specific Value (1) Specific Value (3) Quantity (2) Variety Figure 1 13 I therefore conclude that this first objection fails, and that there is no reason to doubt that some pure cardinality metric is after all a necessary component of a (substantially) neutral ranking of liberty sets. 6. THE SUFFICIENCY OF CARDINALITY FOR NEUTRALITY I turn now to the second objection. It has been an assumption of the discussion up to this point that, whereas measures of diversity (as well as, obviously, measures of specific value) are value-laden, measures of pure quantity can be relevantly value-free. However, this assumption has been challenged. In an influential paper, Robert Sugden (2003) argues that no method of individuating opportunities for the sake of measurement can avoid prejudging relevant evaluative questions. If this is correct, then a pure cardinality metric is in fact insufficient for neutrality (or, at least, for the sort of very substantial neutrality to which Sugden takes Millian liberals to be committed). Sugden writes: If we are to measure the extent of opportunity offered by different sets of options, we cannot avoid imposing some conceptual structure on the space of options, and if that structure is not to be arbitrary, it must rest on assumptions about what people might normally or reasonably wish to choose. Thus, no measure of opportunity can fully capture the scope that a person has to develop and express his or her individuality. (2003: 785) So 'necessarily, measures of opportunity are biased against individuality and originality' (2003: 808). Sugden's conclusion is therefore that, insofar as the importance of individuality and originality constitutes a reason for neutrality, liberty cannot be measured; taking this neutrality reason seriously means rejecting any method for measuring liberty. Elaborating on this with respect to the physical approach to the measurement of liberty proposed by Carter, Sugden concedes that Carter's metric is ...a coherent measure of changes to the world, but of changes viewed in one particular perspective-a perspective in which the world changes to the extent that physical objects change their locations... But why privilege physics? What about a biologist's perspective?... Or an artist's perspective?... As far as I can see, there is no neutral perspective in terms of which we can measure pure quantities of action: any measure of change to the world is a measure of change viewed in a particular perspective. (2003: 802) So even the physical approach is insufficiently neutral, since it arbitrarily privileges one particular perspective over others in a way that risks loading the dice against certain unpredictable and original forms of individual human development. 14 In response, Carter (2015: note 12) accuses Sugden of confusing value-neutrality with (what Carter calls) value-independence. Carter concedes that his physical metric is not wholly value-independent in the sense of being justifiable entirely in non-evaluative terms. To the contrary, Carter argues that adoption of the physical metric is justified precisely from the familiar Millian perspective that values autonomy and progress. It is from this evaluative perspective that Millian liberals ought to assess the relative adequacy of rival metrics, and it is from this evaluative perspective that, according to Carter, the physical approach can be shown to be optimal. Yet none of this undermines Carter's claim that the physical approach is value-neutral, in the sense that it 'does not imply the superiority of any one of a set of contrasting substantive ethical points of view' (2015: sec. 1). (Indeed, it is because the physical approach is neutral in this sense that it is so appealing from the value-laden liberal perspective from which rival metrics are assessed.) In demanding value-independence, Carter argues, Sugden is holding him and others to an impossible standard; once we see that value-neutrality is in fact consistent with value-dependence, the objection evaporates. However, this reply perhaps misconstrues Sugden's argument. It is unlikely that Sugden, so alert to the normative reasons for valuing opportunity as a space for individuality in the first place, would demand a way of measuring opportunity that makes no reference to these reasons for valuing it. Instead, I take Sugden's claim to be that it is a special feature of the Millian evaluative perspective that it imposes neutrality requirements that are impossibly stringent. That is, measurement of the kinds of spaces for individuality that we deem valuable demands a liberty metric that is neutral with respect to all conceptually possible evaluative disputes; anything less will fail to manifest the relevant impartiality with respect to the full range of possible evaluative discoveries and innovations. Yet any system of measurement, simply by making decisions about what is and is not to be measured, inevitably tilts the field towards certain evaluative outlooks at the expense of others. Hence the spaces for individuality that we have good political reason to value must be conceived so neutrally as to render measurement impossible. Sugden is therefore not arguing against the strawman that our liberty metric must be wholly value-independent; he is arguing that our normative reasons push us towards a metric that turns out to be impossible. This is, for Sugden, 'the problem of originality'. Nevertheless, the general thrust of Carter's response is fundamentally sound. Sugden comments that 'if the perspective we use is not to be arbitrary, it must surely be one that is salient in relation to opportunity, rather than salient in relation to physics or biology or art' (2003: 802). Yet Carter's claim is that the perspective of physics best captures what we have in mind when we talk about the 'perspective of opportunity' in this context. Sugden may wish to block this move by insisting that the relevant 'perspective of opportunity' must be one that is neutral with respect to competing conceptions of opportunity itself, meaning that no conception of opportunity can solve the problem. But this must be mistaken. Our reasons for valuing opportunity-here, the Millian reasons that Sugden considers-are ipso facto reasons for valuing opportunity as 15 understood in some particular way, and disputes about how to understand opportunity can be resolved with reference back to these very reasons. Put differently, when we value 'spaces for individuality', we value something more or less determinate, and thinking carefully about what it is that we have reason to value here in the first place ought to point the way to the relevant notion of opportunity. Carter's claim is that the relevant notion is best captured by the physical approach. This is of course contestable;10 but the argument now is about which metric is best, not about whether a metric is possible in the first place. I therefore conclude that this second objection fails, and that it gives us no reason to doubt that inclusion of a pure cardinality metric in a ranking of liberty sets can be partially sufficient for neutrality. 7. LIBERTY IN THREE DIMENSIONS Liberal states have reason to prefer policies that do not worsen the position of their citizens with respect to liberty, other things equal. Moreover, liberal states have reason to maintain some degree of first-level neutrality with respect to some significant range of evaluative disputes. Therefore, liberal states need a way of assessing how well their citizens are doing with respect to liberty that is evaluatively neutral in relevant respects. I have argued that such a neutral assessment must be three-dimensional: that it must incorporate measures of the quantity, diversity and specific value of each citizen's liberty set. This is a familiar idea that I have here defended from a pair of objections. There are two final points to be made about this. The first concerns the phrase 'one's position with respect to liberty'. I have adopted this clumsy expression in order to avoid talking here about the extent of one's liberty. As I have argued, how much liberty one has is just one (perhaps relatively small) part of how well one is positioned with respect to liberty: doing well requires not only having a lot of liberties, but also having varied and specifically valuable liberties. Nevertheless there is a confusing tendency, both in ordinary language and in some of the literature, to describe a person's being well positioned with respect to liberty in this sense as that person's having more liberty. For instance, Sen (1990: 470) claims that 'we find it absurd to dissociate the extent of our freedom from our preferences over the alternatives', while Sugden (1998: 316) tells us that, on his account, 'information about preferences might be used in measuring the amount of opportunity offered by a set of options' (emphasis added in both; see also Pattanaik and Xu 1990: 390 and 2000, and Peragine and Romero-Medina 2006). This leads to the problematic thought that a more valuable (or more preferred) liberty set contains more liberty than a less valuable (or less preferred) liberty set; that, as Carter puts it, 'the degree of one's freedom is a function both of the degree of one's freedom 10 For criticism of this physical approach (adopted not only by Carter but also by Steiner (1994) and Kramer (2003)), see Rosenbaum 2000 and Garnett 2007. 16 and of the importance of that freedom in terms of other goods... that the measurement of these two variables in combination is identical to the measurement of one of them' (1999: 145).11 Suppose that we each have a bag of apples. There are various questions we can ask about our relative apple endowments, including: Who has more apples? Who has the greater variety of apples? Who has the more valuable apples? These are, of course, different questions-it will not do to say, for instance, that because you have better apples you therefore have more of them. Yet there is also a fourth, more general, question we can ask, something along the lines of: Who is in the better position with respect to apple possession? Doing well with respect to apples may simply be a matter of having a lot of them, or of having a wide range of different varieties, or of having some particularly high-quality specimens-or some function of the three. The answer depends on what our reasons are for valuing apples in the first place. In this paper I have argued that, in the case of liberty, a basic liberal perspective on its value leads us to a three-dimensional assessment of what it is to do well with respect to it. The second point concerns how we are to understand each of the three dimensions of overall liberty assessment. I have assumed that it is possible, at least in principle, to have three separate rankings of liberty sets: a ranking in terms of the amount of liberty each includes, a ranking in terms of the variety of liberty each inclues, and a ranking in terms of the specific value of the liberties each includes. While I have sought to defend the idea that an overall ranking must be some function of these three subrankings, I have said nothing about the three sub-rankings themselves (nor about how, formally, they are to be combined).12 Although it would be consistent with the claims of this paper for the three subrankings to be treated as analytically basic, this would be theoretically unsatisfying. Fortunately, much work has been done on trying to develop deeper understandings of them. As already discussed, Carter (building on prior work by Hillel Steiner (1994)) has developed a sophisticated analysis of what we might usefully mean when we talk about 'more' or 'less' freedom in terms of the degree of physical change we are able to make 11 Kramer contends that the notion of one's 'overall freedom' is in fact ambiguous between one's freedom as measured by a pure cardinality metric (which he calls Fr1) and as measured by a partially evaluative metric (Fr2), and hence that 'Carter has begged the question against [the latter] by assuming that its adherents must be seeking to ascertain the level of Fr1 rather than of Fr2. In his eyes, of course, only the former phenomenon should be labelled as 'freedom'. However, since his stance on that matter is a key point of contention between his opponents and himself, he cannot legitimately ascribe that same stance to his opponents when he states what they are endeavouring to ascertain' (2003: 447-8). Yet this response is too easy, since this particular dispute is not, as Kramer suggests, over the meaning of 'freedom', but rather over the meaning of 'an amount of freedom'. And there is nothing question-begging about supposing that a purely quantitative notion such as this demands a purely quantitative analysis. 12 More precisely, I have sought to defend this idea just from the two objections considered above; there may well be other objections, including objections rooted in technical problems of a kind not addressed in this paper, to which the idea remains vulnerable. 17 to the world, while both Rosenbaum (2000) and Garnett (2007) have suggested alternatives. As regards variety, although Martin van Hees (2004) has detailed a number of problems faced by attempts to analyse the diversity of an opportunity set in terms of the relations of similarity and dissimilarity of its members (as attempted, for instance, by Klemisch-Ahlert 1993, Rosenbaum 2000 and Pattanik and Xu 2000), some other recent work on the matter, such as that by Bossert et al. (2001) and by Nehring and Puppe (2002), offers to make more progress. Finally, there has been much debate on how to interpret the assignment of specific values to liberties: whether on the basis of the preferences of the agent whose liberty is being assessed (Sen 1990, 1991, 1993), the potential preferences of the agent being assessed (Arrow 1995; Crocker 1980), the preferences of a reasonable or typical agent (Pattanaik and Xu 1998; Sugden 1998), those values that can be endorsed by an overlapping consensus of reasonable comprehensive doctrines (Nussbaum 2011: 79), or the objectively correct values (Taylor 1979; Swanton 1992; Kramer 2003). In this paper I have attempted to shore up the general approach to the evaluation of liberty sets that takes these three elements as components. I have argued that a careful analysis of the liberal basis for valuing liberty, and in particular of the structure of liberal neutrality, is enough to show the way past two otherwise difficult challenges to this view. 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