… but an unweighted directed graph doesn’t encode that information. An unweighted directed graph really encodes structure and direction. It can encode what transitions are possible, and it can be used to infer the sequences of events that can happen. However, unless you endow the graph with a weight function (how much space/time/energy/money/whatever it “costs” to “traverse” an edge), you can’t mathematically conclude that taking a sequence that loops a bunch of times before reaching the destination is better than taking a direct path just once, because you haven’t established a metric for what “better” means.

And the liberal argument would in fact be that even though direct action takes only one branch, it is a more “costly” branch than taking an average path through their graph, which consists of a series of low-“cost” steps. My argument from an anarchist perspective is that the liberal notion that the steps in the directed graph of the liberal political system are “low-cost” — in terms of time, energy, or money — is privileged nonsense. But unfortunately, seeing merely the unlabeled graph doesn’t bring this to light.

So an informal way to do this might be to mark the branches with text that indicates the character of the branch. Or if you don’t mark it, then this would be the character of the arguments liberals will use to misread your approach (because they always will misread your argument).

Here’s a counterexample that demonstrates my point:

I got this from Neighborhood Anarchist Collective’s Facilitation Guide. Just like your graph, there is are loops which can be traversed an unbounded number of times (i.e., there is nothing stopping you from going around the loop zero times, once, ten times, a billion times, etc.). In my view, this is a workable specification for consensus-based anarchist decision making. It is excellent reading for any anarchist.

Now taken in isolation, their raw directed graph has the same issue as the one your directed graph would be used to argue is a bad system. But NAC’s diagram is a summary of an article which, in my view, makes it clear in prose that the time and energy spent traversing each branch is vastly lower than the cost of electoralism. Additionally, they even surrounded some of the branches with that nice circle, which suggests that these items have similar weights. So with that context, their argument pushes through.

It also reveals that another way to encode cost is to give the nodes (not necessarily the edges) a weight. This is what NAC does informally by putting prose inside some of the nodes.

In contrast, your directed graph might benefit from a bit more information, unless you intend to include it as part of prose explaining why, in your context, simplicity of the graph maps to better outcomes.

Sorry about being such a pedantic fuckweasel here, but my research uses directed graph theory. One thing I’ve learned is that your modelling representation is super important when doing stuff with graph and digraph objects, because it can either vastly simplify or complicate the solution to your problem. So I kinda have to be pedantic 🤓