Some explanatory comments about these elements of an evaluative perspective are in order. Consider first the world features (WF). I suppose that in perspective Σ, no two social worlds share the exact same justice-relevant features. Social world a may have justice-relevant features {f, g, h}, while b has some, but not all of these features (e.g., f and g, but not h), and c, a still different set of features (e.g., f and h, but not g). Social worlds are thus individuated by their justice-relevant features. Note that condition WF refers only to the justice-relevant features of a social world and their realization, since only these are strictly necessary to generate the evaluations required by ideal theory.7 We should not think, though, that our model implies that an ideal theorist starts out by knowing which features of the world are relevant to justice. In the development of its perspective, Σ would no doubt start by identifying a large set of features, and then, given its evaluative standards (ES), would determine which are relevant to justice. Indeed, later on (§§III.2.4–5), I shall stress how the evaluative standards and world features are interconnected within a perspective—a perspective’s evaluative standards affects its view of what features of the world are relevant to evaluation and vice versa. Certainly no assumption is made here that these features of a perspective are independent of each other—indeed we shall see quite the opposite obtains. All the model requires is that before a final judgment of the justice of any social world i can be generated, perspective Σ must have settled on the criteria of evaluation (ES) and the features to be evaluated (WF).
To begin to clarify the crucial, but typically overlooked, mapping relation (MP) between the evaluative standards and the justice-relevant features of the social worlds, consider three different procedures that might be employed. The first we might call “categorical” and is probably the most common type of evaluation in philosophy. Categorical judgments are concerned with whether or not a social world is just; employing this procedure would yield a series of yes/no judgments.8 Whatever their attractions in other contexts, such judgments are of little use for an ideal theory that seeks to orient our quest for justice by guiding us to better (i.e., more just) worlds, short of the ideal. According to the Social Realizations Condition, we need an evaluative function capable of generating a range of justice judgments. John Broome contrasts the philosopher’s use of “categorical” judgments with the economist’s focus on “comparative” judgments. Whereas the philosopher asks “Is a just or unjust?” the economist asks “Is a more or less just than b?”9
The idea of a comparative judgment, however, is itself ambiguous between strictly comparative and scalar interpretations. On the strictly comparative interpretation one can form a judgment about a given social world, a, only by comparing it to another social world, b. On this reading, judgments of justice have the same logical structure as preferences: they are primitive binary relations. Although philosophers often conceive of preferences, at their most basic level, as unitary states such as desires, so that one can have simply “a preference for x,” in decision theory they are inherently binary: one can only have a preference for x over something else, say y. Thus in decision theory a preference for x over y is not a comparison of, say, the strength of one’s preference for x and of one’s preference for y (concepts that do not enter into decision theory); “x is preferred to y” is the most primitive preference judgment. Similarly, then, a comparative notion of justice might say that the most primitive justice judgment is binary: “a is more just than b.” Such a comparative judgment would be primitive as it is not a comparison of two judgments—of a’s and b’s justice. Furthermore, on this understanding of the comparative nature of justice, because all judgments of justice share this primitive binary comparative structure with preference, just as we could have intransitive preferences (x is preferred to y, y is preferred to z, yet z is preferred to x), we could also have intransitive judgments of justice (a is more just than b, b is more just than c, yet c is more just than a).10 As is well known, unless we impose some sort of transitivity axiom (as does Sen’s social choice theory approach; §I.1.3) pairwise judgments made on the basis of N-dimensional underlying considerations can lead to a host of such pathologies.11
Because of this, without modification (such as imposing consistency conditions) such a strictly comparative approach is inappropriate as a model of ideal theorizing: the Social Realizations Condition may well not be met. Very roughly, unless we impose some sort of transitivity on the set of binary judgments in {X} (thereby creating an ordering of {X}) we cannot be assured that there will be a best element in the set—an ideal. A set with cycles at the top of the ordering of {X} would leave us without an ideal, and cycles involving many elements in the middle could lead us around in circles in our quest for greater justice.12 To avoid these problems, I model the evaluation of the justice of social worlds as based on a scalar function jointly defined by the evaluative standards, the world features and the mapping function, which is not inherently comparative (though, importantly, neither is it categorical). On this model, an evaluative perspective S has a set of evaluative standards (ES) and a consistent way of applying them to social worlds (MP), which generate for any social world a score of its justice, which is about the justice of its world without comparison to others. Comparing the justice of two social worlds is thus not a primitive binary relation, but a comparison of two different justice evaluations. Some understanding of comparative justice along these lines is necessary if we are to model the Social Realizations Condition: our ideal theory requires an optimal element (the ideal) in domain {X}, as well as a consistent set of comparative rankings of less-than-optimal elements. And if we are to make sense of the metaphor of a mountain range with “high peaks” we would do best to suppose some sort of cardinal-like scale, if only to understand the pure logic of ideal theory.
A quintessential philosopher may insist that something is lost in this comparative (noncategorical) approach: we have only comparisons of degrees of justice rather than two categories, “just” and “unjust,” which call for very different responses. Thus the quintessential philosopher may wish to at least introduce a “positive” and “negative” range in the justice scores, identifying classes of “just” and “unjust” societies. Now while in some contexts a binary contrast between justice and injustice may be critical, in a theory of the ideal we are seeking to chart a course from where we are to increasingly just social states. Along the way, we wish to avoid getting much less just than we are presently, while finding a way to reach the heights of justice. To understand this quest for the ideal, a distinction between the areas of the unjust and of the just is not necessary. That said, within a strictly scalar approach (ranging, say, from 0 to 100), a theory of the ideal can have a mapping function such that, unless evaluative criteria are met to some threshold level very low overall scores of justice result, while above a certain threshold the scores become very high and perhaps compressed.13 Our conception of a perspective on ideal justice allows, but does not require, this type of evaluation.
The mapping function has a number of critical tasks. Supposing that there are multiple evaluative standards, the mapping function must specify some sort of weighting system; it takes these multiple criteria and employs them to evaluate a social world.14 In Rawls’s theory the mapping function can be understood as the original position.15 Recall that in chapter I (§§2.1–2) I was skeptical of principle-defined ideals: even Rawls, who was so devoted to his two principles of justice, thought that the General Conception was more appropriate in some social worlds. Suppose, then, that we wish to evaluate two social worlds: a, whose features and their realization include severe economic deprivation of the entire society and b, with far more affluence. Rawls suggests that the justice of a should be determined by the General Conception while b should be evaluated in terms of the Special Conception. As both are part of the same theory of justice, there must be a set of underlying values (liberty, equality, reciprocity, quality of life prospects) that regulates this choice;
the parties to the original position, in deciding that world a is to be evaluated by one principle and b another, are, in effect, applying different trade-off rates between liberty and income in the two worlds: in world b no inequality of liberty for the sake of greater resources is allowed, while in world a such trade-offs are allowed. The model device of the original position thus is part of what I have called the “mapping function,” taking a set of underlying values and applying them to the evaluation of different social worlds.
That said, the model to be developed here does not depend on taking the set of underlying values and ideals—part of what Hamlin and Stemplowska call a “theory of ideals”—as more basic than the principles of justice. A theory might take the opposite approach. Instead of seeing principles as ways of commensurating underlying values in different social worlds, a perspective could insist that “in political philosophy as much as in aesthetics, the comparison of certain objects regarding their value (such as societies or paintings) depends on certain principles.”16 Such a perspective could put principles of justice at the foundation of the set of evaluative standards. So long as the principles were specified in a way such that they apply to all social worlds in the domain {X} to be evaluated,17 and the mapping function could score social worlds on how well they satisfied these principles, a principle-based perspective can be modeled. What is required is that, in some way, the perspective seeks to optimize the satisfaction of the evaluative standards, with the global optimum (the best in {X}), identified as the ideal. The evaluative standards, as weighted by the mapping function, yield a justice score for social worlds and thus define the ideal (as the optimum), as well as allowing comparisons of less-the-ideal conditions.18 Something like optimization is required to meet the Social Realizations Condition.
We should not think of this as a “mechanical” optimization according to some obvious formulae. The mapping function can include weights and lexical principles, can allow for a number of ties, and can be context sensitive.19 Different weights can be used in different circumstances (think again of Rawls’s General Conception).
Also critical to a mapping relation must be a predictive model or models (part [ii]), which yield an estimate of the social realization of the set of justice-relevant features in a social world. As we have seen (§I.3.1), every set of world features will be associated, within a given model or models, with a probability distribution of social realizations. It is simply implausible to suppose that our understanding of nonexistent social worlds is so refined that for each set of features (WF), there will be one and only one possible justice-relevant social realization.20 That is why we suppose that each well-developed perspective on ideal justice must include a model or models of the social realizations of a set of world features. Supposing this, the mapping function must take the range of possible social realizations for any given set of relevant features (WF), and generate some sort of expected justice score. We can imagine optimistic functions that identify the justice of a set of features (a social world) with the best social realizations that might arise from it,21 and pessimistic ones that focus on the nastiest ones.22 And of course some theories seek to weigh the risks.23
1.2 Meaningful Structures and the Orientation Condition
Recall the Orientation Condition:
T’s overall evaluation of nonideal members of {X} must necessarily refer to their “proximity” to the ideal social world, u, which is a member of {X}. This proximity measure cannot be simply reduced to an ordering of the members of {X} in terms of their inherent justice.
The Orientation Condition requires that a theory of the ideal must make sense of the idea of the “proximity” of social worlds a and b, and how far they are from the global optimum, u, and this proximity cannot simply express their overall inherent justice scores. As I have been stressing, unless the Orientation Condition is met, T could meet the Social Realizations Condition and yet be a simple “climbing theory” à la Sen’s (§I.1.3), generating an ordering of social states (and in this sense proximity judgments) purely in terms of their inherent justice; the world closest to a would be the world in the domain {X} with the closest justice score. The Orientation Condition requires that we make sense of proximity judgments of social worlds in a way that does not simply reflect their inherent justice.
I believe that by far the best way to think about the “distance” between two social worlds is in terms of how similar their underlying features are (see further §II.1.3). When I say that social world a is “very close” to social world b, I shall mean that it is very similar to it. This makes sense of the critical idea that the ideal orients our pursuit of justice by providing a direction of our endeavors. We move toward the ideal by making our world more like it, by changing our institutions and background facts so that they better align with the ideal world. The insight that the ideal is needed to give direction to our endeavors for reform cannot, as I have been arguing, simply be that we should reform so as to make our society more just; no doubt that is true, but, once again, Sen’s climbing model can perfectly accommodate that. To say that the ideal gives direction for reform is to say that we know the sort of society (its world features) that characterizes the ideal, and this knowledge should help us in reforming the characteristics of our society.
Consequently, we need to add a fourth element to a perspective on justice that underlies a theory in which the ideal is ineliminable: the perspective must be able to generate consistent judgments of the form, that, with respect to the justice-relevant features, “social world a is more similar to b than a is to c,” which I shall denote as [(a∼b)>(a∼c)].24 Given the underlying features (WF) of worlds a, b, and the ideal, u, an ineliminably ideal perspective must be able to judge whether a or b is more similar to u in its defining features. This seems intuitive. Those worlds that, according to the world feature (WF) element of perspective Σ, have nearly identical justice-relevant properties will be seen by Σ as very similar worlds; if the justice-relevant properties of a are almost identical to those of b, worlds a and b will be very close; if the justice-relevant properties of world a are very different from u, it will be very far from u. To say that utopia is far from our current world is to stress how different its features are from our own; if utopia (or dystopia) is close, only a few modifications of our present world would bring it about. This is intuitively obvious at the limit: a is maximally close to itself because it has the precise same justice-relevant features as itself. The world closest to a will be that member of the domain {X} the justice-relevant properties of which are most similar to a. It is essential to stress that these similarity judgments are internal to a perspective: one of the things that defines a perspective on justice is not only what features of worlds it identifies as relevant to justice (WF), but which worlds it sees as very similar to others.
Understanding “distance” as an indication of likeness on pairwise comparisons conforms to the general literature on measuring “distance” between different systems. As Martin L. Weitzman stresses, “Distance is such an absolutely fundamental concept in the measurement of dissimilarity that it must play an essential role in any meaningful theory of diversity or classification. Therefore, it seems to me, the focus of theoretical discussion must be about whether or not a particular set of distances is appropriate for the measurement of pairwise dissimilarity in a particular context, not about whether or not such distances exist in the first place.”25 I assume that pairwise similarity is the basic relation, on which more complex measures of distance build. For simplicity’s sake, I shall suppose that a theory of the ideal can array the domain of social worlds to be evaluated, {X}, as a consistent similarity ordering where the end points are most dissimilar from each other. (There are several ways in which such an ordering could be generated, and each has its distinct formal characteristics. For those who are interested in these matters, appendix A explores different approaches and some problems that arise.) I shall call this the Similarity Ordering (SO) of a perspective on ideal justice, Σ.
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br /> It might seem that this idea of an ordering of social worlds in terms of their overall similarity is artificial, and simply a result of accepting the Orientation Condition. Not so. In addition to identifying the relevant features of a social world and evaluating them (the tasks of evaluative standards, world features, and the mapping function of a perspective), a perspective on any optimization problem over a domain is useful only if it creates what Scott Page calls a “meaningful structure” or “meaningful relatedness” for that domain.26 A perspective on a problem like seeking justice does not simply see the option space as a random collection of social worlds with diverse justice-relevant features, but rather as a set of options differentiated by systematic variations in their underlying properties. The organization of the option space in terms of systematic variation in underlying structures is how a perspective makes sense of the domain; given that certain properties are relevant to justice (WF), Σ then arranges the options in terms of their variations of these fundamental properties. And so it makes sense of the optimization problem confronting the theory. It is thus part and parcel of this view of the meaningful structure of the domain {X} that Σ be able to make the sort of similarity judgments that the Orientation Condition requires.
The Orientation Condition refers to “proximity” to the ideal social world, u. An overall similarity ordering is a rough notion of “distance,” but only very rough. If we have a set of five ordered social worlds {a, b, c, d, u} in one sense we can say that b and u are far from each other, yet it may also be the case that the relations in figure 2-1 obtain. I thus suppose that a sophisticated perspective on ideal justice enriches its similarity ordering (SO) over the domain {X} by applying a distance metric. Recall Weitzman’s observation that “distance is such an absolutely fundamental concept in the measurement of dissimilarity that it must play an essential role in any meaningful theory of diversity or classification.”27 As he remarks, the real dispute between theories that seek to model similarity is not whether a distance metric will be used, but which one it will be. Different perspectives will, Weitzman suggests, arrive at different distance metrics; thus I do not suppose any specific metric for a perspective. However, to help fix the general idea of a distance metric, we can give a formal characterization. Let us say that Σ defines a metric space—an ordered pair (X, d), where {X} is the domain of social worlds and d is a function on {X} that defines the distance between all points in {X}. For now, at least, we assume that the distance metric (DM) is constrained by the prior complete similarity ordering (SO) of {X}. Again following Weitzman, we can say that such distances (X, d) must satisfy three core conditions. ∀i, j ∈ {X}: (1) d(i, j)28 ≥ 0; (2) d(i, i) = 0; (3) d(i, j) = d(j, i). To which we add (4) ∀i, j, k ∈ {X}: [(i∼j) >
The Tyranny of the Ideal Page 8