capitalism and convexity
Capitalism exacerbates “greed” via assembling increasing marginal utility agents from decreasing ones
I take the terms “concave agent” and “convex agent” from mako yass’ excellent essay: concave agents, the normal kind, experience declining marginal utility, while convex agents experience increasing marginal utility. Convex agents are naturally risk-affine, willing to accept “double-or-nothing” bets.
Convex agents fight more than concave agents: for concave agents, a divided pot is a bigger pot: √4 + √0 < √2 + √2. For convex agents, it’s the unified pot that is bigger: 42 + 02 > 22 + 22. Convex agents could hold a lottery to determine the winner, but the losers of such a lottery have every reason to refuse to cooperate with it once they understand they have lost - since a little bit is worth nothing and a small chance of a lot is still significant. When concave agents lose and are compensated with something, they have much more reason to accept their lot.
All else being equal, you’d rather be surrounding by concave agents - yass’ essay applies this to AIs in particular, but it can be generalized. Convex agents - status-obsessed nutcases who play brinksmanship for fun - suck to be around. Further, it’s rational for convex agents to bully concave ones: concave agents typically, well, cave, particularly when they know their opponents won’t.
human concavity
Humans by default are concave rather than convex. There’s debate about whether the happiness returns to income ever cap out or stay positive forever, but not that the slope of the curve gets at least closer to zero as income rises. However, humans can be put in situations that elicit convexity. Tournaments are the most obvious example: if Bigfuck Blooddrinker kidnaps you and throws you into a tournament of combat to the death, your utility curve looks like an ultraconvex hockey stick:
corporate convexity
Capitalist firms are more convex than individuals. In the generic case, a capitalist firm in the presence of financial markets should be expected to operate with a linear rather than marginally declining utility curve. Some effects (such as managerialism) may move this curve more towards a standard concave one, while other effects (such as returns to market capture) can tip it towards proper convexity.
Why should this be? Investment funding flows towards companies proportional to the expected value of their income stream. A single investor, who has a concave utility function like anyone else, would be stupid to bet all her money on a company with a 51% chance of doubling her money and a 49% chance of folding. However, she would be smart to invest in many such companies, as long as their risk is “diversifiable,” i.e., uncorrelated. (Nondiversifiable risk thus represents a factor that pushes corporate utility functions back towards concavity.)
What are some factors that can push corporate utility functions towards convexity?
First, the presence of monopoly profits. If it is the case that greater market share is associated with higher returns, then success is more valuable the more you have already succeeded. Some sectors naturally have more of this than others, but any laws that increase returns to scale (such as weak antitrust) or barriers to entry (such as strong licensing or intellectual property ones) will increase this as well.
Second, fecal buoyancy. The leadership of firms (and states,) almost by definition, over-represents the highly ambitious; it also almost necessarily over-represents the risk-affine if it selects on those who have bet and won big on some series of gambles in the past.
Third, the “shareholder revolution” and increasing sophistication of financial instruments. These counteract the normal incentives facing incumbent managers, who value keeping the company afloat first and chasing white whales secondarily.
cooperative convexity
Note that not all market participants work this way: family firms and cooperatives sink or swim with their enterprises, and so concave individual utility functions sum to concave collective ones. Indeed, such firms are almost certainly too risk averse, although welfare and full employment policies can be used to bring them up again.
political concavity and complexity
A great advantage of democracy is that you can lose power and retire in peace, or perhaps to contest in the next election. This has vastly reduced the scope of manifest political violence within electoral democracies. Extraordinarily long-running states like the Byzantine empire also accepted making civil wars frequent but non-apocalyptic by making them not all-or-nothing affairs: losers would be retired to monasteries or blinded, rather than killed; while winners knew their ability to gather spoils would be limited by the possibility of the next coup; legitimacy was acquired via being able to credibly demonstrate ability in the next civil war (acclamation by the troops, populace, or bishops) and a system in which openly currying such favor was largely allowed.
Greed is good.
This post insinuates a naturalistic fallacy.
Any collective judgement would prefer a portfolio of risky endeavors for exactly the same reason.
As you say elsewhere on this substack, what is important is the externalities. If risk-seeking makes bad neighbors, it is because they impose negative externalities. But do they do this more under capitalism? If capitalism opens up more options, do these options have more positive or more negative externalities? It is not obvious. The really clear example is war. But war is very old. Maybe it is a poor investment that cannot compete with the incremental options provided by the divisibility of money.
Your other example is monopolies. A competitive market provides consumer surplus, which is a positive externality, whereas a monopoly internalizes the externality, so it is more incentive-compatible. You could say that a monopoly imposes a negative externality compared to a competitive market. Externalities are only a relative concept, so this is a comparison to a hypothetical; it matters what competitive market is actually possible. If the entrepreneur attempts to consolidate a monopoly in place of an existing market, this is bad, but if an entrepreneur attempts to go "zero to one" that is good. Is it bad that Uber is a monopoly? That depends on what is the alternative. It looks very easy to build. Austin kicked out Uber and created a nonprofit replacement, which proceeded to permanently close during covid. Perhaps the value of Uber is that it breaks the law; and this replacement was too cozy with the state. But for a few years it operated without all the investment of Uber. What is Uber spending all its money on? I suspect creating sinecures for programmers, not creating shareholder value. I do not think the Uber monopoly is optimal, but neither do I think it was created by rational investors.
If an agent with logarithmic utility plays the ultimatum game for a stake equal to his current wealth, against one whos utility is linear in money, what distribution do you expect?
Nash bargaining predicts 45:55. Kalai predicts 41:59. That would suggest exploitation through brinksmanship isnt much of a concern in the west today.