[Repost] An Interactive Toxin Puzzle

This is the summer break and I’m publishing old essays written when the audience of this newsletter was confidential. This post has been originally published March 17, 2022.

Spoiler Alert: the following lines reveal important details of the story told by Ken Follett in his novel Never. You may not want to go further if you intend to read or are already reading Follett’s book. 

I have recently finished Ken Follett’s novel Never. It was somehow weird to read it while a war was starting, with the result that the probability of a nuclear attack is now at a level that has not been reached since the 1960s. Follett’s novel is indeed a story of a geopolitical escalation culminating in the start of total nuclear war between the U.S. and China. It was the first time I was reading a book by this author. I didn’t find it particularly good. I have been struck by the simplicity and naivety of many dialogues. Moreover, the book is long (more than 700 pages in French) and a substantive part of the side stories do not obviously contribute to the main plot. Still, the last quarter of the book is a page-turner, as the tension is growing and events leading to the so much feared outcome multiply.

The main interest of this novel is thus its narration of the escalation process, and of the underlying strategic reasoning of the leaders of the two big superpowers. Schematically, the reasoning takes the following form:

(i)              I – the leader of a superpower – do not want to launch a nuclear attack because I know it would start a nuclear war.

(ii)            I expect you (the leader of the other superpower) to similarly want to avoid launching a nuclear attack for the same reason.

(iii)           On the other hand, for strategic and political reasons (which may differ depending on the superpower), it is necessary to not appear weak and to respond to an attack by more than proportional means (but not too much).

(iv)           (i), (ii), and (iii) are common knowledge between us.

Point (iii) is crucial here. Let’s say that due to contingencies, superpower A launches a conventional attack x on an ally of superpower B. The strength s(x) of the attack is a measure of its material damages and casualties. Denote f a “retaliation function” such that, for any attack of strength s(x) by a superpower, s’(s(x)) = f(s(x)) > s(x). This basically encapsulates point (iii). Now, by launching attack x, A knows that it will start an escalation process s, s’, s’’, …, that will culminate in a nuclear attack. Take any specific moment in this sequence. The reasoning of the superpowers’ leaders leads them (and this is clearly the message that Follett wants to convey to his readers) to entertain two contradictory intentions: an intention to retaliate and an intention to not feed the escalation until the nuclear threshold is reached. But, by (i)-(iv), it is common knowledge that each leader, when she retaliates at time t without the intention to further retaliate at time t+n, will nonetheless have to. In other words, both parties form present intentions to act in a certain way in the future for which it is common knowledge that, when the time will come, they will not intend to act according to them. This sounds paradoxical: can we intend to act in a certain way when we know that when we will have to act, we will no longer have this intention? 

The paradox I have just described looks like an interactive version of the “toxin puzzle” elaborated by the philosopher Gregory Kavka. Kavka asks us to consider the following scenario.

The Toxin Puzzle. An eccentric billionaire offers you a deal. You can drink a small glass of liquid containing a toxin that will make you seriously ill for one day, after which you will have fully recovered. You’ll be paid one million dollars tomorrow morning, if at midnight tonight, you intend to drink the toxin tomorrow afternoon. However, you do not need to actually drink the toxin to receive the money. Only forming the right intention matters.

Assume that your preferences are the following:

Winning 1 million $ and not drinking the toxin > Winning 1 million $ and drinking the toxin > Winning nothing and not drinking the toxin > Winning nothing and drinking the toxin

The best strategy seems therefore obvious: you should intend to drink the toxin at midnight and then just not drink it tomorrow afternoon. But as Kavka points out, as soon as you have formed this plan, it seems paradoxical to intend today to drink the toxin tomorrow, knowing that tomorrow you will not intend to drink it! A potential solution would be to settle today on the use of a commitment device to force you to drink the toxin tomorrow. But suppose that such commitment devices are not available. The puzzle then comes from the fact that while you don’t have any reason to drink the toxin, you have reason to intend to do so. Kavka nails it perfectly:

“we are inclined to evaluate the rationality of the intention both in terms of its consequences and in terms of the rationality of the intended action. As a result, when we have good reasons to intend but not to act, conflicting standards of evaluation come into play and something has to give way: either rational action, rational intention, or aspects of the agent’s own rationality.”

Return now to the strategic reasoning of the leaders of our two superpowers. Clearly, they have reasons to intend to not escalate until the nuclear threshold is reached. But while forming this plan, they also know that they will have no reason to not escalate, or rather that stronger contrary reasons will prevail. We are in the same situation as in Kavka’s toxin puzzle, except that here the conflict of reasons is triggered by interactive reasoning: I know that I will not be able to act later as I’m intending to now because I know that this is also true for you, because I know that you know that this is also true for me, and so on. This is a tragic situation in which, as Kavka points out, it is impossible to be fully rational.