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  • Max Stearns

Dimensionality and its Discontents

In 1930, Sigmund Freud published his masterwork, "Civilization and its Discontents" (available here: Freud explained that although our happiness critically depends on living in a society empowered to limit how we all manifest our most basic urges and behaviors, personally subjecting ourselves to the resulting societal constraints ironically limits our happiness. Freud's critical insight corresponds to what game theorists cast as a prisoners' dilemma. We all benefit from societal rules and norms, and we certainly wish others to comply with them. At the same time, if we could capture those benefits, while sometimes cheating ourselves, we would be happier still. Yet if everyone did that, we'd be back to where we began, inviting the need for societal constraint. (For a thoughtful article exploring this theme by Debra Friedman and Barry R. Weingast, see

The prisoners' dilemma game operates along two dimensions and is typically presented in a two-by-two matrix. Each player confronts the choice to defect (here failing to abide society rules) or to cooperate (obeying those rules). With proper payoffs, and absent some means of coordination, mutual defection predominates. This happens even though despite the personal costs of complying with societal norms, each participant would be have been happier had both somehow managed to be constrained by them.

Cycling preferences likewise arise from dimensionality. In the classic presentation, three persons hold the following preferences (1) ABC, (2) BCA, (3) CAB. There's no first choice winner, and if the three participants vote sincerely in binary pairs, the group will discover that it prefers A to B and B to C, yet C to A. By contrast, with a tweak in Person 3's ranked preferences, (1) ABC, (2) BCA, (3) CBA (from CAB), B defeats both A and C in binary pairs. The second listed preferences can be neatly arrayed--A then B then C (a straight line)--with Person 1's ranking starting at the left and moving right (ABC), Person 3's preferences starting at the right and moving left (CBA), and with each preferring the Person 2's first choice (B), to the opposite extreme. By contrast, the earlier set of cycling preferences cannot be so neatly aligned. They instead force a triangle, for example, A to the upper left, B to the upper right, C centered below. Beginning with each person's first choice, the rankings proceed clockwise (A then B then C then A, etc.). (For more general background, see, especially chapter 3).

Dimensionality yields discontent because it often exposes an uncomfortable reality: those we naturally consider opponents turn out to share something significant in common. Worse still, whatever that common ground is, some other person or group fails to embrace it, and perhaps thinks the others are profoundly mistaken in doing so. Sorting this out is like finding a magical key. It opens the door not to some cluttered closet, but to an elegant hallway, with staircases and other doorways in all directions, up-down, left-right, in-out. Despite its discontents, dimensionality is a key to understanding.

Dimensionality also invites frustration because grasping it requires suspending disbelief, allowing for over-simplication. As I tell my students: "Don't fight the models, at least until after you have allowed yourselves the chance to understand them." To illustrate dimensionality, we must express two things in tension: first demonstrating that two positions can be meaningfully juxtaposed, deliberately eschewing a more nuanced framing, and second, identifying a third position that rejects a premise the two juxtaposed positions nonetheless share. At the root of dimensionality is the simultaneous recognition of opposition and similarity, a kind of suspended cognitive dissonance.

Some examples:

In the Supreme Court's race jurisprudence, it seems intuitive to juxtapose modern liberals with adherents to Jim Crow. After all, the latter would allow policies that entrench a racial caste, whereas the former would not only disallow such policies, but would also go further, permitting race-conscious measures intended to advance the interests of those who were historically oppressed based on race. And yet, this sharp dichotomy is oversimplified. A third position, color-blindness, rejects a premise these other seemingly opposed positions share. The color-blind position does not stand neatly between modern liberals and Jim Crow. Unlike either of these other camps, color-blinds disallow any express reliance on race. Modern liberals and Jim Crow are opposed on the question whether to permit racial subordination, but not on the question whether to condone some form of discrimination, or differentiation, based on race. Among the three groups, color blinds stand alone in their absolute unwillingness to discriminate based on race. The positions thus implicate two dimensions, forming a triangle. (For my more detailed analysis, see Obergefell, Fisher II, and the Inversion of Tiers, 18 U. Pa. J. Const'l Law (forthcoming), available here

In an earlier post [see, I juxtaposed environmentalists (liberal) and fiscal hawks (conservative). Certainly many liberals care about the debt, and many conservatives care about the environment. Nonetheless, these issues tend to animate constituencies that generally occupy opposing ends of the conventional left-right, or liberal-conservative, spectrum. Even so, both groups couch their arguments using a common analytical framework: "We must aggressively tackle global warming to protect the grandchildren" (liberals) versus "We must aggressively tackle the looming debt to protect the grandchildren" (conservatives). We might infer universal agreement on the kind of restraint that protects the interests of our progeny. But of course we know that's not true. For reasons that implicate another prisoners' dilemma, elected officials prefer each other to be restrained, while themselves remaining free to cater to those whose support is politically important (for more background, see, especially chapter 2). The result is a systemic myopia, focusing on immediate political pressures, and declining to make hard fiscal or environmental policy choices that we all know matter greatly to future generations. The great middle implicitly rejects (through actions if not words) the pleas on behalf of our children and our children's children. Once more, the positions force a triangle.

(For another illustration, consider this recent post by my brilliant colleague, Mark Graber, reviewing Michael Klarman, The Framers' Coup: The Making of the United States Constitution (book available here; review available here:, in which Graber reveals a problem of dimensionality among electoral constituencies at the time of constitutional ratification.)

From this we might come away thinking that dimensionality only affects our collective selves, once more showing that it is civilization, or at least society, that brings about our discontent. This too is mistaken. The explanation returns us to psychology. Consider emotion. We develop intellectual constructs concerning such matters, but ones that ultimately fail: love is opposite hate; happy is opposite sad. And yet, intense love and intense hate both lead to obsession, whereas normal emotional states typically do not. Intense happiness and intense sadness both lead to tears, whereas we do not cry most of the time. (The psychologist, Leon Seltzer, refers to this phenomenon as "emotional bipolarity." See Even our seemingly singular minds invite dimensionality. What seems juxtaposed unites, loops around, forms a triangle.

Dimensionality has its discontents, to be sure. But it is part of the human condition. And when we see it, we are richer. It's like finding the right key.

As always, I welcome your comments.

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