# Tag Archives: short

## The Corporation, Slavery, and Optionality

It has been said before that a corporation is a kind of “person” under the law. For example, see the documentary The Corporation (about 10:54 to 12:08). However, later on in The Corporation, the narrator asks what sort of “person” the corporation may be. Nassim Taleb has pointed out that this “person” does not have honor, or experience shame, or have many of the features of other “persons”.

In a similar vein, there is an inherent optionality in the “limited liability” corporation (or its international equivalents, for example the mbH of GmbH, but it doesn’t have to be in the name). Taleb noted that recognition of this optionality could be traced back to the time of the first joint stock companies (and to Adam Smith, I believe). With limited liability, the owners get the upside of the corporation, but not the downside (for a discussion of this and other ethical asymmetries see the works of Taleb, particularly Antifragile). The downside lands somewhere else.

It occurred to me that if a corporation is a person, it is not a free person: what free person is owned by other people? The corporation seems to be a slave.

The optionality of the corporation – for the owners – extends to slavery as well. Harriet Beecher Stowe in Uncle Tom’s Cabin tells the story of a slave who is an ingenious inventor – but the fruits of his ingenuity go to his “owners” (while his suffering, presumably, is his alone):

This young man had been hired out by his master to work in a bagging factory, where his adroitness and ingenuity caused him to be considered the first hand in the place. He had invented a machine for the cleaning of the hemp, which, considering the education and circumstances of the inventor, displayed quite as much mechanical genius as Whitney’s cotton-gin. […] Nevertheless, as this young man was in the eye of the law not a man, but a thing, all these superior qualifications were subject to the control of a vulgar, narrow-minded, tyrannical master. This same gentleman, having heard of the fame of George’s invention, took a ride over to the factory, to see what this intelligent chattel had been about. He was received with great enthusiasm by the employer, who congratulated him on possessing so valuable a slave.

It is clear that a corporation cannot “suffer” in the same way. Nevertheless, on rewatching part of The Corporation, I discovered what might have been the germ of this idea of the “corporation as slave”: a discussion of how the 14th Amendment to the US Constitution was applied to corporations (8:40 to 10:50). Despite this interesting interpretation, ownership of a limited liability corporation was not deemed illegal, and the essentially free option remains.

## The ex post probability is either 0 or 1

The things you think of while doing the dishes. At the Maths Faculty in Cambridge, there are cunningly no dishwashers. Allegedly there are showers, a proven idea-generating tool. But I think they are there for other reasons.

Intuitively, it feels as if “after the fact” the probability of any event should either be 0 or 1. Either it happened or it didn’t. Well, except if your last name is Clinton.

Framing this in terms of rigorous axiomatic probability theory: consider the filtered probability space $(\Omega,\mathcal{F},(\mathcal{F}_t)_{t\in I},\mathbb{P})$. Consider real-valued random variables on this space and use the notion of conditional expectations. Define conditional probability in terms of conditional expectation as follows: for $A \in \mathcal{F}$ and $\mathcal{G} \subseteq \mathcal{F}$ a sub-$\sigma$-algebra we have $\mathbb{P}(A | \mathcal{G}) := \mathbb{E}(\mathbf{1}_A | \mathcal{G})$.

Now take $A \in \mathcal{F}_t$ – we are thinking of $t$ as being the current time, and we are looking at the event $A$ which occurred at or before the current time. Since $A$ is $\mathcal{F}_t$-measurable, $\mathbf{1}_A$ is an $\mathcal{F}_t$-measurable random variable. Thus we can “take out what is known”: $\mathbb{P}(A | \mathcal{F}_t) = \mathbb{E}(\mathbf{1}_A | \mathcal{F}_t) = \mathbf{1}_A$.

But indicator functions are always either 0 or 1. Hence the result.

This is a (very, very simple) 01 law. And you don’t really need maths for it.