Definition
In CLAIM-347’s notation, let an organization 𝒪 face, at time t, the attainable options X_t. Each of its perspectives i ranks X_t by a preorder ≿ᵢ and holds an authority that the organization’s endorsement dynamics set (CLAIM-277, CLAIM-283). The organization’s appraisal is the negotiation N_t that takes the profile of rankings and authorities to a collective relation R_t on X_t.
- A common currency at t, in the owner’s sense, is ordinal extendibility: the negotiation has an ordinal potential on a window around t, so some complete ordering agrees with every win (TERM-077). It requires only that a compatible extension exist, not an observed shared evaluation of every option; how options never contested compare is open across the class. It is not ordinal comparability of every pair, not a scalar currency, a real-valued representation, and not a cardinal trade-off structure with fixed exchange rates; on continua the last two come apart from the first (CLAIM-436), and this term uses only the first.
- Potential. Read the perspectives as players, each with its own ranking. A ranking ≿_v is a potential of the negotiation when every move that wins one of its conflicts is an improvement along ≿_v: the perspectives’ rankings differ, but what prevails among them climbs one shared ordering. This is Monderer and Shapley’s ordinal potential (LIT-1462), carried from a game’s unilateral deviations to a negotiation’s conflicts. Exact potentials are rare, so the term says approximately, and the approximation is ordinal: the least fraction of the window’s wins whose reversal leaves them acyclic (TERM-077). The Hodge decomposition (Candogan, Menache, Ozdaglar and Parrilo for games, LIT-1442; Jiang, Lim, Yao and Ye’s HodgeRank for pairwise comparisons, LIT-1439; THEORY-894) is not the test of existence: its gradient is a least-squares fit to margins and can reverse a comparison the wins settle (CLAIM-434, part 4). It is kept as a measure of cardinal inconsistency, for records whose margins are intensities. Frijda’s three marks of control precedence (THEORY-055), priority, persistence and resumption, are how a potential shows itself in time; an ordinal potential that has them is a persistent potential (TERM-078), and this term is a persistent potential of a particular kind.
- Existence and kind are separate. That the negotiation has a potential at all is its common currency; on a finite set of outcomes it is exactly that no chain of winning moves cycles (CLAIM-434, part 1; Monderer and Shapley, THEORY-896). Which ordering the potential is, and whether it ranks the system’s own states by their bearing on its maintenance, is a further fact. The potential is nobody’s ranking until it is shown to be one.
- Nonvacuity. A window with no contested pairs has an acyclic, empty relation of wins, so every ordering is trivially its potential. Valence is undefined there, not zero or neutral: the term applies only over a non-empty set of contested pairs on which ≿_v and some rival ordering disagree. It is the thesis’s first consequence (CLAIM-440), now a condition of the definition, stated for contest: what it needs is contested pairs in the record of wins, not demands that are jointly infeasible (TERM-060). The two come apart both ways (CLAIM-449).
- The kind. ≿_v ranks the system’s own states by their bearing on its maintenance: its essential variables in Ashby’s sense (THEORY-324), the graded norm of Di Paolo’s adaptivity (THEORY-628), what THEORY-045 calls a regulatory state’s meaning “for staying alive”.
- Identification. A record of wins fixes a class of potentials, not one: increasing transforms aside, orderings that differ only on pairs never contested fit it equally (CLAIM-434, part 7). So the claim that the potential is an ordering of this kind, or is a particular perspective’s ordering, is identified only by intervention: devaluing an outcome or perturbing the system and contesting the pairs on which the candidate orderings differ (QUESTION-268). Until then the term is reported as holding of the class.
- Goal-conduciveness valence is a regime in which a ranking of that kind
is a persistent potential of the negotiation over a non-empty set of
contested pairs.
- Its sign is whether the system runs ahead of or behind a reference course along ≿_v: ahead is positive, behind negative, on course neutral. This is Carver and Scheier’s account, whose neutral point is a reference rate of progress, not rest (LIT-1441, read through LIT-1449 and NOTE-1102): a system standing still where it expected to advance is behind. Comparing positions on an ordering needs no measure, so the clause stays ordinal. Where the class of potentials 𝒫_t the record admits is not a singleton, the sign is set-valued: V_t = {sgn_P(x_t, r_t) : P ∈ 𝒫_t}, for the system’s state x_t and reference state r_t. The system has a determinate sign, positive, neutral or negative, only when V_t is a singleton, that is, when every admissible potential ranks x_t and r_t alike; otherwise the sign is partially identified, and narrowing it needs an intervention that contests the pair. With the two orderings of CLAIM-434, part 7, one puts a state ahead of its reference and the other behind it (part 10).
- Its intensity is the potential’s strength: the share of the window’s contested wins that agree with ≿_v, on the pairs where ≿_v and a rival ordering disagree. It is ordinal, counting wins without weighing them; a weighted version that counts margins is cardinal and is stated as such where margins are intensities. Coherence, a low least reversal fraction, is a precondition and not the measure: a stable compromise is as coherent as one perspective deciding everything (CLAIM-434, part 3). Where ≿_v is fixed in advance, as the maintenance ordering or a perspective’s ranking, its agreement can be scored on the contests at hand. Where it is selected from the record, as a best-fitting ordering, it is scored on contests held out from the selection: on wins drawn at random, a best-fitting ordering agrees with 0.87 of the contests it was fitted to and 0.50 of fresh ones (part 11). Like the sign, intensity is reported across the class where the class is not a singleton, as the range of agreements its members attain.
- Ambivalence is conflict that no ordering absorbs, read in the sequence of windows and not in a netted record: circular triads or a positive least reversal fraction within a window, and reversals of the same pair’s outcome across windows, against a null model that keeps the record’s graph of contested pairs. A pair won alternately by each side is ambivalent although its net flow is zero (CLAIM-434, part 5). The Hodge cyclic share’s baseline of (n − 2)/3n holds only for a complete tournament with every pair contested once (part 2); on a sparse graph the baseline depends on the graph. No ordering absorbing the conflicts is what Sen’s theorem allows (THEORY-027) and Tversky’s cycles show (CLAIM-436, part 3b). Neutrality is a persistent potential with the system on its course.
Revision of 2026-10-23: goal conduciveness, not hedonic
Drafted as “hedonic valence”, the owner’s word. Revised before merge, at the owner’s direction, after Berridge’s liking–wanting dissociation showed that the regime this term defines tracks ‘wanting’, not ‘liking’ (THEORY-893, CLAIM-438). On the component process model’s levels of valence (LIT-1458, CLAIM-433) the ordering defined here is goal conduciveness, need satisfaction and goal attainment, and intrinsic pleasantness, ‘liking’, is a separate appraisal with its own ordering. Hedonic valence in that sense is not what this term defines.
Revision of 2026-10-23: the review of PR #327
A review of the pull request that filed this term found six faults, and all six were conceded before merge:
- It defined a common currency as a complete, transitive relation, which CLAIM-436 shows is not a currency on continua. The definition now separates ordinal extendibility (first named comparability), ordinal comparability, scalar currency and cardinal trade-off structure, uses only the first, and weakens it from complete and transitive to acyclic.
- Existence alone made a conflict-free system vacuously eligible. A nonvacuity condition now makes valence undefined there.
- It measured approximation and intensity with the Hodge gradient, which can reverse an ordinal comparison. Both are now ordinal; Hodge measures only cardinal inconsistency.
- Its ambivalence measure read a netted record, which erases alternation, and applied a complete-tournament baseline everywhere. It now reads windows in sequence against a graph-preserving null model.
- QUESTION-266 predicted that intrinsic pleasantness and goal conduciveness coincide, which this term does not imply. The question now makes their covariation conditional.
- It named the potential as one ordering, which a record cannot fix. It now reports the class and identifies a member only by intervention.
The review also proposed the hierarchy that the three terms now carry: ordinal coherence (TERM-077), its persistence over time (TERM-078), goal-conduciveness valence (this term), and felt valence as a candidate only (CLAIM-439). The review called the second level “dynamical ascendancy”; it is named for the potential instead, keeping the rename below. The synthetic cases behind each fix are in scratch/formal/valence.py.
A second review, of the revised pull request, found three more faults, also conceded before merge. Acyclicity establishes ordinal extendibility, not comparability, and the first level was renamed (TERM-077). An approximate persistent potential is no Lyapunov function, and the second level now separates exact from approximate (TERM-078). And where the class of potentials is not a singleton, sign and intensity are set-valued, and an ordering selected from the record is scored on held-out contests (above).
What it is not
- Not “dominance”, and not “ascendancy”. The notion was drafted as “dominance” and renamed on 2026-10-23, because the word is taken: in affective science “dominance” is the third axis of Mehrabian and Russell’s pleasure–arousal–dominance model, the felt sense of being in control, which Fontaine and colleagues’ potency–control dimension continues (LIT-1437) and which the component process model’s own authors call “dominance” (LIT-1458, p. 4); in decision theory a dominated option is one worse on every count. It was renamed “ascendancy” the same day, and renamed again, at the owner’s direction, to “potential”, because the game-theoretic notion says exactly what was meant and brings its theorems with it: an ordering prevails when the negotiation has it as a potential, and how far it prevails is the share of contested wins that follow it. “Precedence” was not used, because CLAIM-283 uses it for the priority a motive claims, as against the authority it is granted. “Potential” in physics and in free-energy accounts is compatible: a function the dynamics descend or climb.
- Not intrinsic pleasantness. ‘Liking’, the hedonic impact of a stimulus, is a separate appraisal (see the revision above). Whether it can be the potential of some ordering is open (CLAIM-433).
- Not a felt state. The term is functional. Whether the regime is felt is QUESTION-059, and whether it is identical with felt valence is Veit’s thesis (THEORY-101), not this term’s.
- Not frustration (TERM-060). Frustration is a relation among demands that no admissible transformation meets jointly. Valence on this term presupposes contest, not frustration: rankings can contest while every demand is satisfiable, and demands can be jointly infeasible before any contest is recorded (CLAIM-449). Where no pair is contested, no ranking has anything to prevail over, and the nonvacuity condition leaves valence undefined whether or not the demands are frustrated.
- Not any potential goal. A ranking of world states, however potential, is not valence until it ranks the system’s own states by their bearing on its maintenance. Whether a firm’s potential metric is a ranking of that kind is a question about the firm (QUESTION-267).
- Not a potential game in the strict sense. A potential game has players changing their own coordinates of a joint profile; a negotiation over one indivisible choice has no such coordinates. The finite result needs only the relation of winning moves, so it applies to either; for contested indivisible choices it is read on the options themselves, with HodgeRank (THEORY-894) as the cardinal measure where margins are intensities. The reading also needs a dynamics, one winning move at a time, under which the potential is climbed; it does not hold for simultaneous moves.
- Not a scale. Neither sign nor the ordering needs a measure. Where the potential ranking is continuous it has a numerical representation; where it is a graded lexicographic override it has none (CLAIM-436).
Note of 2026-10-30: what holds it back
CLAIM-441’s flow case is still unanswered. Abuhamdeh’s review (LIT-1853) shows the literature divided on whether flow is positive during the episode and settles it by definition, so which exit holds is open; its fourth exit would change this definition’s nonvacuity condition. The intensity clause is CLAIM-440’s clause 3, and Orehek et al. (LIT-1854) find positive affect lowering a goal’s priority where goals compete, which CLAIM-468 presses against it.