Note: This is Part 4 of the “Justice as Conditionals” series.

The conditionals, as exposited so far, are one-sided affairs. They are a single person imposing their preferences, what I’m calling their moralities, upon another who may not share them. Such a conception, however, is not the entirety of how Conditionals may appear. In particular, Conditionals can appear in sets.

               Again, for simplicity, we will consider the two-person case with A and B. When A produces a Conditional to influence the behavior of B, A is taking a preference that B has on A’s behavior and is artificially adhering those preferences onto B’s perceptions of their own behavior. So far, we have tacitly assumed that the Conditionals are absolutely true and that B would not refrain to accept the adjustments to their preferences.

Consider, however, what would happen if A provided B with too strict a Conditional: “if you don’t move to Ohio, I’m not going to pay for dinner.” A is taking the fact that B would like A to pay for dinner and applying it to B’s preferences regarding moving to Ohio. However, even if this is a true statement, it is not enough to meaningfully sway B’s behavior; B very much does not want to move to Ohio. What this Conditional does manage to usefully convey is that A has some meaningful preference regarding B’s moving to Ohio. This solid information about A’s preferences regarding B’s behavior allows B to construct their own, almost certainly more properly-balanced, Conditional: “if you give me $1M, I will move to Ohio.”

This back and forth can continue on, each time providing more and more information about each’s preferences for the other, or at least whatever each can convince the other of. If this process converges to a situation where A and B each have their own behavioral restriction and each Conditional is “I will disobey my restriction if and only if you disobey yours,” what I will call a Small (or unenforced) Contract is formed. The only incentives which hold a Small Contract in place are the parties’ preferences regarding each others’ behavior and the sub-goal of maintaining the reputation of their own Conditionals. In this case, the deal might converge to “B will move to Ohio and A will buy them a nice house there.”

               To clarify things slightly, a Small Contract is not something distinct from Conditionals. Rather, it is a set of Conditionals, one from every agent in question to every other, all of which agree on the behavioral restrictions placed upon each party as well as the behaviors which would result from any given violation.

Lastly, we note that such agreements make the concept of Conditionals’ Acceptable Ranges (Domains and Codomains) all the more important. Small Contracts would be virtually impossible otherwise, as the back-and-forth Conditionals would not then have the capacity to vary enough to allow the convergence to a Contract. Each agent may care more to avoid restricting their own behavior than to actually restrict the other’s, and no convergence would happen. In these cases, the preferences of the parties regarding their own behavior would not significantly change.