nucleation

TERM-078: persistent potential: an ordinal potential of a negotiation that is the same, up to its class, across successive windows of time, that decides the conflicts it bears on (priority), and towards which the dynamics climb again after a perturbation (resumption); exact when no move outside a perturbation descends it, and then a Lyapunov function of the one-move-at-a-time dynamics, and approximate when some do, and then no Lyapunov function, short of a drift condition that needs a cardinal potential and further assumptions

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Properties8
StatusActive
Version3
Tagsemotion-and-affect, game-theory, mathematics
Lineorganizational-affect
Used byCLAIM-440 — An organization's appraisal is the negotiation among its perspectives, a common currency is that negotiation's admitting an ordering of the options it faces, and goal-conduciveness valence is a regime in which an ordering of the organization's own states by their bearing on its maintenance prevails in the negotiation; so valence presupposes contested rankings, not frustrated demands, its sign is whether the organization runs ahead of or behind a reference course along the potential ordering, its intensity is how far the negotiation's decisions follow that ordering, and ambivalence, where no ordering prevails, differs from neutrality, where one prevails and the organization keeps to its course, CLAIM-448 — An ordinal potential describes only the winning-move relation it is computed on; where an organization's legibility regime selects which contests are admitted or recorded, an acyclic record, even a persistent potential, can be the product of selective contestation, so observed coherence is not evidence that the organization's perspectives are integrated, and an intervention that improves its self-governance may at first increase the disagreement observed, CLAIM-451 — When an organization's record of winning moves cycles, the failure is organizational nonintegrability, distinct from a perspective's own preference instability and from switching of the governing regime; it becomes organizational tension only when realized as costly reversal against demands the organization maintains, and cognitive dissonance only when that tension is detected and appraised as aversive; learning can relieve it by accommodation, by entrenched precedence or by cheap periodic coordination, which observed coherence does not tell apart, and ambivalence and nonintegrability entail neither one another
RefinesTERM-077 — ordinal potential: of a negotiation over a finite set of options in a window of time, an ordering of the options that every move winning one of its conflicts climbs; it exists exactly when the wins never cycle, which is ordinal extendibility, that some complete ordering agrees with every win, and not observed comparability, since pairs never contested are not compared; and it is fixed only up to a class: every strictly increasing transform of one is one, and on a sparse record several orderings can be
Refined byTERM-076 — goal-conduciveness valence, organizational: a regime in which the negotiation among a system's perspectives has, approximately, a potential, an ordering of the system's own states by their bearing on its maintenance along which the moves that win its conflicts are improvements, persisting and restored after interruption; signed by whether the system runs ahead of or behind a reference course along that potential, and as intense as the negotiation's decisions follow it rather than any rival ordering
Cited as “complements” byTERM-094 — action readiness, with control precedence, in Frijda's sense: a state of preparation for action, not a representation of a desirable state, that claims control over behaviour by persisting until an end state, resuming after interruption, capturing attention and taking priority over other actions

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Definition

Let W₁, W₂, … be successive windows of a negotiation’s history, each with its relation of wins and its class of ordinal potentials (TERM-077). An ordering ≿_v is a persistent potential over the windows when Frijda’s three marks of control precedence (THEORY-055) hold of it:

  • Priority. In each window, on contested pairs where ≿_v and some other perspective’s ordering disagree, the wins follow ≿_v, up to the window’s least reversal fraction.
  • Persistence. ≿_v is in, or within a stated reversal fraction of, each window’s class. A sequence of per-window potentials that are different orderings is not one persistent potential, however coherent each window is (CLAIM-436, part 4).
  • Resumption. After a perturbation moves the system down ≿_v, the one-move-at-a-time dynamics climb it again.

Exact and approximate. The marks admit a tolerance, and the tolerance changes what follows.

  • An exact persistent potential is one that no move outside a perturbation descends. Then ≿_v is a Lyapunov function of the one-move-at-a-time dynamics, non-decreasing along them. That is monotonicity, not return. If a perturbation moves the system to a lower state that is absorbing, no endogenous move descends ≿_v and none climbs it, and the system never resumes. Resumption stays a separate mark, read off the record or derived from further assumptions: reachability of higher states, strict progress away from the top, or stochastic recurrence.
  • An approximate one fits each window only up to a reversal fraction, so some moves descend it. It is then no Lyapunov function. A recurring cycle of moves A → B → C → A has a best-fitting ordering that misfits one move in three, yet no function is non-decreasing along all three moves except a constant (CLAIM-434, part 9). The ordering’s fit does not make the system climb it.
  • What can stand in for the Lyapunov reading in the approximate case is a drift condition: the expected change of the potential along the dynamics is non-negative, or positive away from the top. That needs more than this term supplies. An expectation of changes needs a cardinal potential, differences that mean something, which is the fourth sense of currency, not the first (TERM-077). It also needs a stochastic model of the moves, Markov or stationary over the windows, under which the expectation is taken. Where those are not stated, an approximate persistent potential claims priority and persistence only, and resumption is read off the record as the ordering’s return after perturbations, not inferred from a Lyapunov property.
  • An ordinal surrogate, that moves climb the ordering more often than they descend it, is not a drift condition and does not by itself give return: frequent small climbs and rare long descents can coexist with no tendency to return.

The record of wins is kept per window and in sequence, never netted over the whole history. Netting erases exactly what the term needs: a pair won alternately by each side nets to no conflict (CLAIM-434, part 5). Direction, the number of contests and their variability are three quantities, not one.

What it is not

  • Not “ascendancy”. The review of PR #327 named this level “dynamical ascendancy”. The record had retired “ascendancy” earlier the same day for “potential”, the mathematical word (TERM-076), and this term keeps that choice; “persistent” names what is added.
  • Not an ordinal potential on the pooled record. Pooling the windows can produce an acyclic record from alternating ones, or a cyclic one from windows each acyclic.
  • Not valence. A persistent potential can rank anything. It becomes goal-conduciveness valence (TERM-076) only when it ranks the system’s own states by their bearing on its maintenance, over a non-empty set of contested pairs.
  • Not a Lyapunov function when approximate. See above; the distinction was added before merge after a second review of the pull request.
  • Not stable under simultaneous moves. The Lyapunov reading needs winning moves one at a time; simultaneous moves can cycle even in an exact potential game (CLAIM-434).

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