• ## Ideal theory in the shadow realm

It’s opposite day! Instead of talking about the ideal, we’re going to talk about the anti-ideal—the worst of all possible worlds. I contend that, if ideal theory is useful, anti-ideal theory is also useful.

Last time, we covered two roles for ideal theory—ideal as destination and ideal as calibration. We’ll examine the anti-ideal from each perspective.

### Ideal as destination

To recapitulate, this line of thinking claims the ideal is useful because it provides a long-term goal and something to work toward. Symmetrically, the anti-ideal is useful because it provides a long-term anti-goal and something to avoid. We operationalize this as seeking to minimize the distance between our current world and the ideal and maximize the distance between our world and the anti-ideal.

This is where the symmetry breaks down. For most reasonable metrics, there is only one world with a minimum distance to the ideal—namely, the ideal itself. Depending on what we believe about the set of possible worlds, there might be none, one or many points which are at a maximum distance from the anti-ideal.

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• ## Ideal theory as calibration

The ideal serves not only as destination but as calibration. Once we acknowledge our ignorance of possible worlds, we must treat the task of social engineering as a problem of statistical inference. From the statistical inference perspective, the ideal (maximum) is very informative about the underlying distribution of possible worlds and helps us make more informed trade-offs.

### Intro

Last time, I described how (Gaus 2016) juxtaposes unidimensional and multidimensional models of justice. I went on to contest the claim that the ideal is otiose in the unidimensional model and made an analogy to the secretary problem.

This time I’ll make the (related) argument directly that there are two distinct uses of ideal theorizing and only one is bad from the unidimensional perspective.

### Dimensionality of justice

Let’s try to formalize ‘unidimensional’ and ‘multidimensional’ models of justice so we can be sure we’re thinking of the same thing. Gaus suggests (and I’ll accept) that a key part of any theory of ideal justice includes a function $$e \colon \mathbb{W} \to \mathbb{R}$$1, a set of possible worlds $$\mathbb{W}$$. In other words, each such theory should be able to assign a ‘justice score’ to every possible world. In terms of this machinery, the unidimensional model simply limits itself to using only $$e$$ and $$\mathbb{W}$$. The multidimensional model on the other hand also gives us a tool to inspect the structure of $$\mathbb{W}$$ in the form of a metric $$d \colon \mathbb{W} \times \mathbb{W} \to [0,\inf)$$. In other words, the multidimensional model lets us determine how similar two possible worlds are in some way that’s not directly related to their justice scores.

To actually use this in a model, we’ll also need a way of finding worlds $$W$$ from $$\mathbb{W}$$ to evaluate. We denote a a random, ‘nearby’ (i.e. one with a small distance $$d(W, W_c)$$ from the then-current world $$W_c$$) world as $$W_r$$.

### Ideal as destination

(Gaus 2016) and the rest of the literature suggest that the an ideal is useful as a destination. According to Rawls, “By showing how the social world may realize the features of a realistic Utopia, political philosophy provides a long-term goal of political endeavor, and in working toward it gives meaning to what we can do today.” (Rawls 1993)

In terms of our model, the ideal is $$\mathop{\mathrm{argmax}}\limits_{W \in \mathbb{W}} e(W) = W_i$$, the possible world that achieves the highest justice score. A wholly naive algorithm would then:

1. Use our ideal $$W_i$$ to orient societal progress by always picking $$\mathop{\mathrm{argmin}}\limits_{W \in \{W_c, W_r\}} d(W, W_i) = W_{bk}$$. In other words, on every ‘step’, someone proposes some random alternative world $$W_r$$ and this naive algorithm compares it to the current world and picks whichever is closer to the ideal.
2. Stop when $$d(W_c, W_i) = 0$$.

With this interpretation, it’s clear that the ideal as destination as not only otiose in the unidimensional model but nonsensical. The unidimensional perspective was defined by its omission of the metric $$d$$ so we certainly can’t use it in our algorithm to find $$W_{bk}$$.

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• ## Utopia and an infinitude of secretaries

The Tyranny of the Ideal juxtaposes a unidimensional model of worlds with a multidimensional model. It goes on to suggest that ideal theory is otiose in the unidimensional model. I disagree and attempt to illustrate the disagreement via analogy to the famous secretary problem.

### Ideals as superfluous

In (Gaus 2016), the author lays out two conflicting views of political philosophy. The ideal theorists insist on the value of having an ideal society in mind when deciding between possible futures. Their opponents, represented by Amartya Sen, suggest this is a bit silly.

The possibility of having an identifiably perfect alternative does not indicate that it is necessary, or indeed useful, to refer to it in judging the relative merits of two alternatives; for example, we may be willing to accept, with great certainty, that Mount Everest is the tallest mountain in the world, completely unbeatable in terms of stature by any other peak, but that understanding is neither needed, nor particularly helpful, in comparing the peak heights of, say, Mount Kilimanjaro and Mount McKinley. There would be something off in the general belief that a comparison of any two alternatives cannot be sensibly made without a prior identification of a supreme alternative. (Sen 2011)

(The mountain climbing metaphor is popular in discussions of ideal theory.)

Gaus goes on to characterize Sen’s perspective as fundamentally unidimensional. He concludes the discussion with the following, “In this book, then, I shall explore multidimensional ways of thinking about justice, for they provide the most compelling response to Sen’s elegant unidimensional analysis—an analysis that makes the ideal otiose.”

### Counterclaim

But I, random Internet blogger, claim they are both wrong. Or, at a minimum, very misleading. The ideal serves a role even from the unidimensional perspective.

Implicitly, they are both modeling the unidimensional search for a better world as one across a known set of worlds with a well-order guiding the way. But this assumes too much. Even if we (unrealistically) suppose we can flawlessly evaluate each world or pair of worlds, we do not know the full set of possible worlds. Rather than perfect information, we are in a state of relative ignorance, groping in the dark. Given our ignorance, any information about the distribution of possible worlds (including the maximum—the ideal) is valuable.

#### Secretary problem

To see that distributional information is valuable even in a unidimensional context, we’ll model ideal theory as a classic unidimensional problem: the secretary problem. In this problem, an employer wants to hire a secretary and starts to interview applicants. After each interview, the employer can decide to continue interviewing or hire the last interviewee and end the process. Their goal is to stop optimally so that they hire the best possible applicant.

The crucial consideration for us is that the employer doesn’t know in advance the quality of the best secretary in the applicant pool. After each interview, the employer must decide if this is as good as it gets or whether to gamble by continuing on. If the employer knew in advance what the best applicant looked like, the problem would be trivial—just keep interviewing until you reach the best applicant.

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• ## How not to write a book

How to Read a Book was a pretty big waste of time for me. It probably would be for you too.

### Intro

Multiple-choice questions are in turn of many kinds; usually they are presented in homogeneous groups. Sometimes a series of statements follows the reading exercise, and the person being tested is asked to indicate which statement best expresses the main idea or ideas of the passage read. In other cases the reader may be offered a choice of statements about a detail in the text, only one of which is a valid interpretation of the text, or at least is more apt than the others; or it may be the other way around; one is an incorrect choice, and the others are correct. Or a verbatim quotation may be given from the text to discover whether the reader has taken note of it and remembered it. Sometimes, in a statement either quoted directly or simply drawn from the text the reader will find a blank indicating that one or more words that will make sense of the statement have been omitted. Then follows a list of choices, lettered or numbered, among which the person being tested is asked to choose the phrase that, when inserted in the blank, best completes the statement.

Yes, that’s 200 words explaining what multiple-choice questions are. If you’d like 426 more pages of mildly condescending prose explaining the obvious, boy, do I have a book for you. Mortimer J. Adler’s How to Read a Book is saved from the appellation ‘worst publication of 1940’ only due to stiff competition from Ba’ath propagandists.

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• ## Deposition schemes

We’ve spent a lot of time recently talking about Acemoglu and Robinson’s work—in particular, about autocrats. Now, we’ll try to turn our new understanding to constructive ends. The first scheme is for an international organization to facilitate abdication by organizing and enforcing retirement payments for dictators. The second scheme is for the ICC to offer abdication ‘credits’ that reduce the severity of criminal punishment for autocrats in the event of voluntary abdication.

We’ve been talking about autocrats lately. It’d be good if we could put our new understanding to use. In that spirit, here are a couple of constructive schemes.

### Retirement plans

#### The problem

(Acemoglu, Johnson, and Robinson 2005) describe the difficulties an autocracy faces in the voluntary relinquishment of power:

A similar problem plagues the reverse solution, whereby the dictator agrees to a voluntary transition to democracy in return for some transfers in the future to compensate him for the lost income and privileges. Those who will benefit from a transition to democracy would be willing to make such promises, but once the dictator relinquishes his political power, there is no guarantee that citizens would agree to tax themselves in order to make payments to this former dictator. Promises of compensation to a former dictator are typically not credible.

#### A solution

If, as proposed in the previous post, autocrats would prefer a guarantee of somewhat reduced income to a chance of somewhat greater income, this transition would be a Pareto improvement. The autocrat gets stability and in exchange the people suffer less expropriation/taxation. So indeed, the only problem is one of commitment.

We can solve this problem by moving ‘up a level’. The citizens of any particular country can’t credibly commit to honoring such an agreement. But if we turn the one-shot game into an repeated game by asking an international organization (e.g. the UN) to facilitate and enforce all such agreements, we create a new equilibrium. The UN (or another international org) would have an incentive to honor these agreements because their credibility when it comes to future such agreements relies on their past behavior.

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