by Gerald Gaus
However, this revolution was not simply rearranging worlds with a fixed set of justice-relevant properties and social realizations: it was coming to revise some judgments about the ways social worlds work (for example, social worlds that insist on uniform religious practice were not more harmonious and stable, as was traditionally thought), as well as coming to appreciate new evaluative standards, such as personal dignity. That is, the change did not just occur within a stable ΣV perspective: it revised some of the core normative elements of the perspective itself—the evaluative standards, the world features, and the mapping relation. This example raises an important question: how radically can the similarity ordering of domain {X} be rearranged without also revising the perspective’s evaluative core (ES, WF, and MP)?
2.4 The Interdependence of the Elements of a Perspective on the Ideal
We have defined the ΣV perspectives as agreeing on the standards of evaluation (ES), the properties of the social world (WF), and the mapping function (MP). These perspectives secure agreement on the overall evaluation of the justice of all social worlds in the domain. The core results we have been examining derive from allowing the similarity ordering (SO) and the distance metric (DM) to freely vary while holding the other elements constant. It is important to stress that a great deal of variation in the similarity ordering is required to yield strong conclusions that we are very likely to find utopia, or that the ideal can be “brought” within our neighborhood.
Hong and Page’s results manifestly presuppose that the similarity ordering can be varied freely without affecting the evaluative core of a perspective, including its overall justice judgments of a social world. This is the main lesson of our example of the search for the best rights-protecting states. The GDP, economic liberty, and political functioning perspectives radically rearranged the similarity ordering, but they had the same set of evaluations over the same set of options. However, this sort of complete independence of the similarity orderings from the evaluative core cannot occur on the model I have been developing, for the similarity orderings are based on the perspective’s nonholistic evaluations of the justice-relevant features of social worlds.
To see why the model developed here is inconsistent with the assumption of complete independence of the similarity orderings from the evaluative core, suppose for the moment we accept the assumption. Assume further that we have an admissible perspective on the ideal, ΣV. Such a perspective, it will be recalled, does not engage in holistic evaluation, as this would result in a high-dimensional, essentially random perspective on justice (§II.2.2). Admissible ideal justice landscapes are moderately rugged; very similar neighbors have correlated justice scores (§II.2.4). Take, then, three worlds from the domain {X}, a, b, k. Assume that on Alf’s version of ΣV b is a world with almost exactly the same world features as a, with only the slightest recognizable difference. Now because of interdependencies between the justice-relevant features of institutions and background facts, worlds that are structurally extremely similar may be significantly more divergent in their overall justice. Nevertheless, on Alf’s version of the perspective two adjacent social worlds, a and b, have very similar justice-relevant features, and because the evaluation of a’s and b’s justice is based on nonholistic evaluations of these justice-relevant features, a and b must have correlated justice scores. Now take some randomly selected world k, and assume some version of the ΣV perspective, Betty’s, that adopts a similarity ordering such that k is between a and b. Our initial assumption (complete independence of the similarity orderings from the evaluative core) says that this is consistent with keeping the evaluative core of this perspective. But note that, because it is randomly selected, k can have any justice score in the entire range allowed by the ΣV perspective. So on Betty’s version of the ΣV perspective, it would follow that even though worlds a and k are adjacent they need not have correlated justice scores. Even though world a is, on Betty’s version of ΣV, very similar to k, knowing the justice of world a tells Betty nothing about the justice of k. The evaluation of any social world is based on its features, but here we see almost identical features result in uncorrelated justice scores. By iteration we could ensure this is true of all pairs in the domain {X} on Betty’s version of the perspective. This would produce a maximally high-dimensional landscape, where there is no correlation between any adjacent elements, and so no neighborhoods (§II.2.2). Such a perspective can result only if (i) the evaluation of the justice of social worlds was not a function of their features (WF)31 or (ii) the evaluation of those features was maximally holistic (any change in features produces entirely uncorrelated judgments). But our model of an admissible perspective on justice precludes both. It denies (i), since justice is indeed the result of the evaluation of world features, and our limitation on admissible perspectives on ideal justice prohibits (ii). Thus we have arrived at a contradiction: we assumed that that ΣV was an admissible perspective, but Betty’s version of it is not. Admissible perspectives cannot allow complete independence of the similarity orderings from the evaluative core.
It does not follow that a stable evaluative core cannot allow any differences in the similarity orderings on our model: differences within the same neighborhood are certainly allowed (§II.4.3). Consider the five economic systems sketched by Rawls, and much discussed in the current literature: “(a) laissez-faire capitalism [the classical system];32 (b) welfare-state capitalism; (c) state socialism with a command economy;33 (d) property-owning democracy; (e) liberal (democratic) [market] socialism.”34 Consider three different similarity orderings of these systems:
Alf: a–b–d–e–c
Betty: a–d–b–e–c
Charlie: e–a–d–c–b
I assume we are at world b (noted in bold above), a capitalist welfare state. Alf’s ordering is an intuitive continuum of economic structures.35 At one end is the classical system of economic freedom (a), embracing a strong system of private property and markets. Next to the classical system is the welfare state (b), keeping both these institutions and leaving property largely unregulated, with the proviso for state provision of basic welfare; property-owning democracy (d) might be seen as a development of welfare state egalitarian capitalism; market socialism (e) a step further away, as it gets rid of private property, while state socialism (c) continues on in this direction, rejecting both markets and property. Now we can imagine that Betty sees, and evaluates, the worlds in the exact same way, but has a somewhat different ordering. As in Alf’s, property-owning democracy is next to our current world, but Betty’s perspective emphasizes its deep reliance on markets and property and thus sees it as neighboring a, the classical world. Moving to market socialism (e) would thus be moving away from private property, thus going in the opposite direction. While the differing orderings of Alf’s and Betty’s perspectives can, I think, be plausibly construed as seeing economic systems in the same way, but with some slight difference in which features are emphasized in making similarity judgments, Charlie’s ordering seems to be picking up on very different features. As Charlie sees it, our welfare state is next to state socialism, which, in turn, is next to property-owning democracy. To explain this, it seems plausible to conjecture that Charlie’s similarity ordering is so different because he fundamentally differs in the features of the economic systems he is picking out. But this means that this difference in similarity must be linked to differences in the evaluative core of the perspective (relevant world features, WF). But if the features to be evaluated differ, then we must suppose that the overall evaluation will as well. Again, the assumption of the independence of the ordering from the core of the evaluative features is most dubious.
Because of its importance and power, it is useful to reflect on what changes in our model would accommodate Page’s understanding of perspectives. If those accommodations are plausible, then perhaps we should alter our initial model (§II.1) rather than dismissing the relevance of the Hong-Page theorem to ideal theory. To clear the way for application of the t
heorem it is necessary to, as it were, cut loose the similarity ordering from the core evaluative elements. Recall again our initial example of searching for the best rights-protecting state (§III.1.2). The states were ordered along a dimension that did not identify properties that were directly evaluated by the evaluative standards, but by some additional property that the perspectives hypothesized is correlated with a state’s overall justice. Thus one perspective identifies GDP, another economic liberty, and the third political functioning as the basis of similarity judgments, but none apply the evaluative standards to these features: the perspectives all evaluate the same justice-relevant features of states directly relating to personal autonomy and individual rights.36 So, in terms of our model, they do agree on the evaluative standards, mapping functions, and relevant features, but they do not rely on these relevant features when deriving similarity, employing instead some entirely different feature that, they suppose, is correlated with the overall judgments of justice.37 It is in this way that the similarity ordering floats free from the judgments of the evaluative core.
This is a puzzlingly roundabout way of orienting the quest for justice, the distinctive feature of ideal theory. If a perspective has identified the features of a social world that are relevant to evaluating its justice, the best way to orient the quest for justice surely is by focusing directly on these relevant features, rather than selecting some proxy dimension that is not itself to be evaluated for its justice, but is supposed to be correlated with justice. Page’s conception of a perspective makes sense when we are confronted by a different sort of problem: when we have a reliable way of evaluating the overall score of an option, but are uncertain of the features that give rise to the score. Suppose, for example, we are constructing a component for a computer system, and we know that the best product will be one that optimally combines modularity with other components, reliability, and low cost, but we are not certain what underlying features will result in high scores on these dimensions.38 Here a perspective would plausibly postulate some dimension that, it believes, tracks increasingly better solutions, but this would not be a direct function of the underlying features.
Page’s model of a perspective then makes most sense when the investigators agree on how to score a solution, but not on the features on which the scores depend. Thus there is no need to include the relevant features in Page’s notion of a perspective, for, in a fundamental way, those are what we are uncertain of. The diverse perspectives can employ different understandings of the salient features of each member of the domain because they have, as it were, a common test for judging the overall value of each element. As Landemore and Page put it in a recent essay, it is as if all the perspectives assume that there is an oracle who gives the correct answer, which all accept. “A problem-solving task consists then of generating potential solutions and identifying the best from among them. In this pure problem-solving context, we implicitly assume the existence of an oracle, namely a machine, person, or internal intuition, that can reveal the correct ranking of any proposed solutions.”39 So perspectives endorse the same elements to be evaluated and the same oracle but can disagree about the relevant features that give rise to the oracle’s judgment.
Let us consider how the Utopia Is at Hand Theorem (§III.2.3) looks assuming Landemore and Page’s understanding of a perspective, but allowing our basic Neighborhood Constraint. Recall that the crux of the Utopia Is at Hand Theorem is that there is some utopian perspective according to which the ideal, which seems far away from our present world on our current perspective is, as it were, next door on the utopian version. Let us call the utopian version Ulysses’s perspective and the current version Betty’s. Figure 3-5 makes this concrete with an example of a six-world domain, with three-world neighborhoods. Notice first that Betty’s and Ulysses’s perspectives concur on the justice score of each world in the set (column 2), as accepting the same oracle requires. Betty identifies certain fundamental features {f g}, of a, our current social world, as critical; she then draws on some dimension that yields similarity judgments for other possible worlds (in this case b and c) that form her current neighborhood. Thus on Betty’s perspective, the local optimum is b, with a justice of 15. Ulysses sees things differently. He identifies a’s fundamental features as {m n}, and given his similarity judgments, the most similar worlds are e and u. And, of course, u is both the local and the global optimum. So on Ulysses’s perspective the ideal is within the current neighborhood.
But why would they think they are actually talking about the same social worlds, at least when they are not talking about the current one? Given that they do not ascribe the same features to the social worlds, it seems doubtful that they could even communicate to each other which worlds they are describing. Recall figure 3-5 and the world designated as “b.” If Betty’s perspective is analyzing a world composed of {f h} while Ulysses sees the structure as based on {n q}, in what sense are they talking about the same possible social world at all? In our earlier example of states protecting individual rights, we had independent identification of the elements of the domain (existing countries with names); in Landemore’s example there was also a domain (French cities) with names attached. As Page stresses, if there are artifacts that can be independently identified, then we can deeply disagree about their properties while agreeing what we are talking about.40 Although figure 3-5 designated this world as “b,” that begs the question in describing possible social worlds—we do not have names designating each world. A possible social world is designated by its features, and it is precisely about these that Betty and Ulysses disagree. Deep perspectival disagreement, in other words, will prevent them from characterizing certain social worlds in terms that others are capable of understanding as the same “thing.” Betty and Ulysses thus do not agree on the domain, {X}, to be evaluated.
Figure 3-5. Two perspectives that agree only about justice scores
Suppose that this problem could be overcome, and Ulysses and Betty could agree on a way to identify social worlds, say by their causal histories (such as “the world that would be produced by pulling the red lever.”) Nevertheless Betty would be perplexed by Ulysses’s claim to have identified the ideal. His perspective radically disagrees with hers about the relevant features of the social world yet somewhat miraculously concurs on their justice. Why should worlds of {i, l} and of {m, p} have the same justice score? There is no test through which they can run these worlds to determine their overall justice; all they can do is apply their predictive models to these features, and evaluate them according to their evaluative standards and mapping relations. If different features are being evaluated by the same evaluative criteria, then we would expect variance in their justice. Of course there may be cases where the justice of worlds with different features happen to be identical, but it seems a bit fantastical to expect (let alone assume) that this could be true for every social world. Surely Betty’s most reasonable conjectures are either that Ulysses’s perspective is simply erroneous, or that it he is using a different set of evaluative standards too, and, thus, Ulysses does not in fact share Betty’s evaluative standards or weighing system. If, however, Ulysses is confused, or has very different evaluative standards, it is not clear that Betty has much to learn from him. This is different from saying that Ulysses’s perspective does not make sense to Betty; but it is to maintain that she would have a very difficult time making sense that there could be so much difference in what is being evaluated (what the relevant features of the social world are), yet this does not affect their overall justice scores, only the terrain on the x-axis.
2.5 The Fundamental Diversity Dilemma
We can thus see why the Hong-Page theorem, based on their specific notion of a perspective, is inappropriate to ideal theory (but see §III.3.2). A theory of the ideal needs to fix on the justice-relevant features of possible worlds to identify them, and, on the basis of these features, construct a similarity ordering. And so the impressive formal Hong-Page results are not of centra
l relevance to us after all. A more fundamental lesson from the forgoing, though, is that as perspectives become more deeply diverse their ability to communicate with one another is hampered.41 Perspectives that are similar, but see things in somewhat different ways, obviously can help each other to overcome the Neighborhood Constraint. Alf’s perspective may alter the neighborhood or call attention to justice-relevant features that Betty’s overlooks. At some point, however, as the perspectives diverge they simply see things in what will seem to each puzzlingly different ways. Perhaps as with Betty and Ulysses they radically disagree about what constitutes the neighborhood and the features of the world that are relevant. In one way, as Hong and Page show, this should be a great resource, helping perspectives to overcome their own limitations by confronting those who understand the optimization problem differently. However, although embracing deeper diversity improves the odds of identifying the global optimum and/or bringing it into our neighborhood, at the same time it reduces our ability to meaningfully share this information. Betty and Ulysses may disagree about so much that she cannot understand how his purported discoveries are relevant to the ideal that she is trying to find. Empirical analysis tends to confirm this, indicating that those with very different outlooks have difficulty communicating and coordinating with one another.42 Overall, we are apt to disagree about the value of alternative social worlds, the identification of those worlds, and what the reports of other perspectives actually mean. As with the Tower of Babel, our collective effort to reach heaven can collapse into mutual incomprehension.
