Order Only Matters at the Forks

An executive with a deputy, a chief of staff or a capable assistant hands over a great deal of ordering: which meeting comes first, and whether the finance conversation happens before the board pack or after it. Most of that ordering is safe to hand over. A small part of it carries a decision about the outcome, and from the outside the two kinds look the same.

The Lam System for Political Interaction draws the line exactly. Fix the actor's judgments, every reading of the world and every election at the points where the maneuver forks, and the outcome is settled: the entries the record gains, what the actor holds at the end, and how each cycle ends. Wherever two moves could be made in either order, the order between them leaves that outcome where it was. Interpretation and Sequencing goes through which choices of order matter between levers and why each rests on a reading. The guarantee behind it says more than a list of forks can: the forks are the only places order can matter, in any maneuver the system records, however the actor chose to run it.

When either move could come next

When two moves both look as if they could come next, the pair falls into one of a few kinds, and only one kind leaves the order genuinely free.

Sometimes the structure never lets both be open. The target cannot select while a lever is still waiting to be played: the selection waits for that lever's reading, or for the actor to give it up. Within a single lever the steps come one after another, declared, resourced, tested, played and read, so two moves of this kind look like rivals only in the abstract.

Sometimes a reading of the world decides which of two entries is written. The gate passes, or it fails and the actor escalates. The target's reading of a lever validates, or it fails. Both continuations are possible beforehand, and the actor's reading of the situation picks one, so there is no order to choose.

Sometimes the choice is one of the actor's forks: mooting a lever, abandoning or mooting the cycle, revising the aim, taking the last place in the budget of levers, choosing which failed gate to escalate first, adding a lever or letting the target decide. Each closes something off, and the order is the actor's election.

Everything else is scheduling: two moves on different levers, touching different resources, neither closing anything. Once the judgments are fixed, the readings and the forks are settled, the structural pairs never arise, and scheduling is all the freedom left. The guarantee says that freedom never moves the end.

Why free order stays free

A scheduled pair commutes because neither move reads what the other writes, and because their effects on what the actor holds combine the same way in either order. Spending the invoices and then the letter leaves what spending the letter and then the invoices leaves.

That alone would not make the order free. It also depends on how each lever's progress is kept. What a lever may do next depends on that lever's own entries, together with facts about the cycle as a whole, and never on which entry in the cycle happens to have been written last. Had each lever's next step been read off the latest line of the cycle, the order in which two siblings were written would change what each of them could do next, and every schedule would become a fork. Because each lever answers only to its own history, the order of two levers' entries is free in fact as well as in appearance.

The cycle's shared moments are fixed in place. Opening the cycle, the target's selection, the outcome and the close are each written at a point where no lever's entry can fall on the wrong side of them. The free order is confined to the middle of a cycle, between levers, and everywhere else the order of the record is a fact.

From one swap to a whole maneuver

Schedules of one maneuver can differ in many places. At the first place they differ, the two moves are free, and a step later the schedules have come back together, with the same holdings, the same moves open and the same entries up to their order. From there the same reasoning applies at each later difference in turn.

For the two schedules to end in the same place, that process has to stop, and it stops because the maneuver ends. There are only finitely many differences to close. This guarantee leans on Every Maneuver Ends for exactly that reason: a maneuver that could run forever would give two schedules room to go on differing, and they would never arrive anywhere that could be compared.

The promise also holds for every pattern of choices. An actor who takes the batched stance described in Stances Toward Uncertainty, declaring every lever and naming everything each needs before testing any gate, will often have several levers ready to play at once, and a great deal of order is free. An actor who runs adaptively, adding one lever at a time after reading the last, has almost nothing free, since each lever waits on what the one before it taught. The stance changes how much of the order is free, and in no stance does the free part change the end.

What can be handed to someone else

Illustrative. The people and the company are invented. Liesel Harrow runs the testing division at a rail signaling contractor, and she wants the president, Casimir Thorne, to bring in-house the test rig the company now rents from an outside laboratory, under her. His adverse alternatives are to keep renting, or to give the rig to the projects division. She declares two levers at the outset: a cost comparison of two years' rental against owning, built from invoices she holds; and a letter she already holds from the client's chief engineer, Margit Sorensen, saying that in-house testing would shorten approvals. Both gates pass. Liesel means to read the play, Casimir's view once both levers are in front of him, and then let him decide.

She is away for the week, and her deputy, Wes Okoro, arranges the meetings. Whether the letter goes on Monday and the cost comparison on Thursday, or the other way around, is scheduling. Each lever spends its own resource, neither reads anything the other writes, and Casimir's reading comes once both are in, so Wes can fit them to Casimir's diary without settling anything of Liesel's.

On Tuesday, after the letter, Casimir tells Wes he has seen enough and asks whether Thursday is still needed. Wes cancels it. In the system, that is a moot: a lever given up because its purpose looks met, made on a reading that Casimir is persuaded, and closed for good. Casimir approves the move. The record holds a mooted lever that Liesel never decided, written as hers because she is the actor. Had Casimir read the letter as a benefit more rented rig time could buy, the cost comparison was the lever that answered him, and it had already been given up.

Two of the six decisions in the figure were Wes's to make. The other four were Liesel's, and three of them look like scheduling: a canceled meeting, a suggestion to decide now, a judgment about old invoices. The guarantee is what makes the first two safe to hand over without a second thought, and the same reasoning picks out the others. Each of them either closes something off or rests on a reading, and anyone who makes one makes it in the actor's name.

Where the guarantee stops

The guarantee says the outcome follows from the judgments. It says nothing about whether they were good, or whether two actors would make the same ones. Two actors with different readings of Casimir reach different outcomes, each of them fully determined by its own judgments.

Its scope is also deliberate. It covers levers that need different resources and gates that find one resource missing at a time. Two levers drawing on the same resource would compete for it, since playing one could leave the other's gate short, and the order between them would become a fork of a new kind. A gate that found two resources missing at once would raise the question of which to fetch first, another fork. The system names both as extensions and leaves them outside the guarantee as it stands; the essay What the System Cannot Yet Represent takes them up. And the record follows the same line as the outcome, exact for what was sequenced and exact up to order for moves that ran side by side, which The Record explains.