# Forks and Threats

Wed 19 February 2020 by Moshe Zadka

What is a threat? From a game-theoretical perspective, a threat is an attempt to get a better result by saying: "if you do not give me this result, I will do something that is bad for both of us". Note that it has to be bad for both sides: if it is good for the threatening side, they would do it anyway. While if it is good for the threatened side, it is not a threat.

Threats rely on credibility and reputation: the threatening side has to be believed for the threat to be useful. One way to gain that reputation is to follow up on threats, and have that be a matter of public record. This means that the threatening side needs to take into account that they might have to act on the threat, thereby doing something against their own interests. This leads to the concept of a "credible" or "proportionate" threat.

For most of our analysis, we will use the example of a teacher union striking. Similar analysis can be applied to nuclear war, or other cases. People mostly have positive feelings for teachers, and when teacher unions negotiate, they want to take advantage of those feelings. However, the one thing that leads people to be annoyed with teachers is a strike: this causes large amounts of unplanned scheduling crisis in people's lives.

In our example, a teacher union striking over, say, a minor salary raise disagreement is not credible: the potential harm is small, while the strike will significantly harm the teachers' image.

However, strikes are, to a first approximation, the only tool teacher unions have in their arsenal. Again, take the case of a minor salary raise. Threatening with a strike is so disproportional that there is no credibility. We turn to one of the fundamental insights of game theory: rational actors treat utility as linear in probability. So, while starting a strike that is twice as long is not twice as bad, increasing the probability of starting a strike from 0 to 1 is twice as bad (exactly!) as increasing the probability from 0 to 0.5.

(If you are a Bayesian who does not believe in 0 and 1 as probabilities, note that the argument works with approximations too: increasing the probability from a small e to 0.5 is approximately twice as bad as increasing it from e to 1-e.)

All one side has is a strike. Assume the disutility of a strike to that side is -1,000,000. Assume the utility of winning the salary negotiation is 1. They can threaten that if their position is not accepted, they will generate a random number, and if it is below 1/1,000,000, they will start the strike. Now the threat is credible. But to be gain that reputation, this number has to be generated in public, in an uncertain way: otherwise, no reputation is gained for following up on threats.

In practice, usually the randomness is generated by "inflaming the base". The person in charge will give impassioned speeches on how important this negotiation is. With some probability, their base will pressure them to start the strike, without them being able to resist it.

Specifically, note that often a strike is determined by a direct vote of the members, not the union leaders. This means that union leaders can credibly say, "please do not vote for the strike, we are against it". With some probability, that depends on how much they inflamed the base, the membership will ignore the request. The more impassioned the speech, the higher the probability. By limiting their direct control over the decision to strike, union leaders gain the ability to threaten probabilistically.

Nuclear war and union strikes are both well-studied topics in applied game theory. The explanation above is a standard part of many text books: in my case, I summarized the explanation from Games of Strategy, pg. 487.

What is not well studied are the dynamics of open source projects. There, we have a set of owners who can directly influence such decisions as which patches land, and when versions are released. More people will offer patches, or ask for a release to happen. The only credible threat they have is to fork the project if they do not like how it is managed. But forking is often a disproportinate threat: a patch not landing often just means an ugly work-around in user code. There is a cost, but the cost of maintaining a fork is much greater.

But similar to a union strike, or launching a nuclear war, we can consider a "probabilistic fork". Rant on twitter, or appropriate mailing lists. Link to the discussion, especially to places which make the owners not in the best light. Someone might decide to "rage-fork". More rants, or more extreme rants, increase the probability. A fork has to be possible in the first place: this is why the best way to evaluate whether something is open source is to consider "how possible is a fork".

This is why the possibility of a fork changes the dynamics of a project, even if forks are rare: because the main thing that happens are "low-probability maybe-forks".