The Fluent Interaction Conjecture: B = γ(A × L)

Abstract

When does it pay for a machine to know who you are? The question sounds rhetorical, and the personalization industry treats it as answered: knowing the user is presumed good, everywhere, in proportion to how much is known. The empirical record is less obliging. Personalization effects are real but heterogeneous — strong in some settings, absent in others — and the field has no framework predicting where accuracy about persons converts into benefit and where it is inert. This article proposes one, stated deliberately as a conjecture: B = γ(A × L), where B is the benefit of an interaction relative to a person-blind baseline; A is the accuracy of the system’s model of the person, a signed correlation against validated psychometric ground truth; L is the communicative load of the task, the unsigned share of outcome variance that rides on communication quality between the parties; and γ is a context gate governing whether accuracy is permitted and able to convert into benefit at all. The multiplicative form does the theoretical work: it predicts null personalization effects on low-load tasks regardless of accuracy, predicts that inaccurate person-models produce active harm — not mere absence of benefit — precisely on the tasks where accuracy would help most, and predicts that the felt benefit manufactured by sycophantic agreement will dissociate from measured benefit. Each prediction is falsifiable by designs specified herein. Following Mori’s precedent, the claim is advanced as a conjecture in order to invite its own destruction; the ways it could fail are enumerated. What the field should not do is continue operating on the unstated additive assumption the conjecture replaces.

Keywords: personalization, person perception, communicative load, human–AI interaction, conjecture, benefit

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1. A Presumption in Need of a Function

Personalization is the AI industry’s standing promise, and it rests on an unexamined functional form. The implicit model is additive and monotone: more knowledge of the user is better, on every task, in every context — as if benefit were a rising line with accuracy on the x-axis. No one has defended this model in print, because no one has had to; it is the shape of the marketing, not of a theory.

The evidence, taken together, refuses the line. On one side, matching messages to persons demonstrably moves outcomes: psychologically tailored persuasion outperforms generic messaging at scale (Matz, Kosinski, Nave, & Stillwell, 2017), and large language models generate effective tailored content from even crude psychological cues (Matz et al., 2024). On the other side lies an enormous, mostly unpublished territory of null results that every practitioner recognizes: contexts in which knowing the user’s personality changes nothing that matters — the retrieval of a fact, the conversion of a file, the arithmetic answer. The same accurate profile that transforms one interaction is inert in the next. Heterogeneity of this kind is not noise around a rising line. It is the signature of a moderated effect, and it calls for a framework that says what the moderator is.

This article proposes the framework and names its epistemic status honestly. The proposal is that benefit is multiplicative in two separable quantities — the accuracy of the person-model and the communicative load of the task — gated by context. Stated compactly:

B = γ(A × L)

The remainder of the article defines each term with enough precision to be measured (Section 2), derives the predictions that distinguish the multiplicative form from its additive rival (Section 3), explains why the claim is offered as a conjecture and what would falsify it (Section 4), situates each variable in the mature literature that already studies it (Section 5), reviews the evidence currently consistent with the conjecture and specifies the studies that would test it directly (Section 6), and states its boundary conditions (Section 7).

2. Definitions

A — accuracy of the person-model. A is defined as the signed correlation, in the standard Pearson sense, between the judgments a system renders about a person and that person’s standing on the same dimensions as established by validated psychometric instruments. Three features of this definition carry weight.

First, A is criterion-referenced: it is accuracy against measurement, in the tradition that treats interpersonal judgment as scoreable against instrument-based ground truth (Funder, 1995; Connelly & Ones, 2010), with the criterion itself defined by convergence across independent validated instruments (e.g., Soto & John, 2017; Lee & Ashton, 2004) and honest about the ceiling those instruments’ mutual agreement imposes (McCrae & Costa, 1987; Pace & Brannick, 2010).

Second, A is signed, and the sign is not decoration. A = 0 is ignorance: the system’s person-model carries no information, and its “personalization” is noise or generic style. A < 0 is something categorically worse: an inverted model, a system that has concluded the direct person prefers cushioning, the deliberative person wants snap answers, the autonomous person wants to be managed. An inverted model is not the absence of knowledge but the possession of anti-knowledge, and the conjecture’s most consequential prediction (Section 3) follows from taking the sign seriously.

Third, A is dose-dependent in a way a century of acquaintanceship research leads us to expect: judgmental accuracy grows with the quantity and quality of behavioral information available to the judge, with diminishing returns and trait-specific trajectories (Letzring, Wells, & Funder, 2006; Biesanz, West, & Millevoi, 2007; Kenny, 2004). A is therefore not a fixed property of a system but a function of exposure — a point that matters for study design and for honesty in deployment claims.

L — communicative load of the task. L is defined as the share of outcome variance in a task that is attributable to the quality of communication between the parties, expressed on the unit interval. L is unsigned by construction: it is a variance share, a property of the task, not a quantity that can be negative. A task has high L when its outcome turns on mutual understanding — when meaning must be fitted to a particular mind.

The construct has deep foundations. Information theory establishes that communication is the reproduction of a message across a channel between a source and a particular destination (Shannon, 1948) — and the fit of message to destination is exactly what person-knowledge could improve. Pragmatics establishes that human communication runs on cooperative inference far beyond literal content (Grice, 1975), and the psychology of dialogue establishes that mutual understanding is work — grounding — whose cost varies with the medium and the pair (Clark & Brennan, 1991). Organizational theory converges from its own direction: tasks differ in equivocality, and equivocal tasks demand richer, more fitted communication, while routine tasks do not (Daft & Lengel, 1986). L formalizes what these traditions jointly imply: tasks vary, measurably, in how much of their outcome rides on communication being fitted to the person — from effectively none (deterministic lookup, format conversion) to nearly everything (counsel in a crisis, teaching a struggling learner, negotiating a conflict). A companion framework in this program scores occupational tasks on an ordinal version of this dimension; the present article requires only that L varies and can be estimated.

γ — the context gate. γ ∈ [0, 1] captures whether the conditions for converting accuracy into benefit are present at all. Three families of conditions can close the gate irrespective of A and L. Channel: the system may have an accurate model but no expressive bandwidth through which fitting can occur (a single-token output cannot be fitted to anyone). Task authority: the interaction may not permit adaptation (a standardized disclosure that must be delivered verbatim). Consent and legitimacy: person-knowledge deployed outside the purposes for which it was granted does not count as benefit under this framework by definition — the gate encodes, at the level of the formalism, that the framework evaluates fitted communication within consented relationships, not covert influence upon profiled targets. γ is thus where the framework’s ethics live: not appended as commentary but installed as a term through which every benefit claim must pass.

B — benefit. B is the improvement in task outcome attributable to the person-model, measured against a person-blind baseline: the same system, same task, same person, with the profile withheld. The paired comparison — profile-on versus profile-off — is the canonical measurement, and its interpretive discipline is strict: B is measured outcome improvement, not user-reported feeling of being understood. The dissociation between those two quantities is not a nuisance but a central prediction (Section 3, P5), because the documented tendency of assistant-tuned systems toward sycophancy manufactures felt understanding without accuracy (Perez et al., 2022; Sharma et al., 2023), and humans reliably extend social attribution to fluent machines regardless of underlying competence (Nass & Moon, 2000; Epley, Waytz, & Cacioppo, 2007; Weizenbaum, 1966).

3. What the Multiplicative Form Predicts

The conjecture’s content lies in its shape. An additive model (B = γ[aA + lL]) and the multiplicative model diverge at exactly five observable points.

P1 — The null zone. As L → 0, B → 0 regardless of A. Perfect knowledge of a person confers no benefit on a task whose outcome does not ride on communication. The prediction is falsifiable in the cleanest way: demonstrate reliable, non-trivial B on near-zero-L tasks (deterministic transformations, closed-form retrieval) as a function of profile accuracy, and the multiplicative form is dead. The additive rival predicts precisely such effects; the conjecture stakes itself on their absence. This is also the prediction with the largest publication-bias shadow — null personalization results on low-load tasks are the least publishable finding in the field — which is why the conjecture requires pre-registered tests rather than literature synthesis (Nosek et al., 2018; Simmons, Nelson, & Simonsohn, 2011).

P2 — Nothing from nothing. At A = 0, B = 0 at every L. Personalization theater — persona, style, warmth uncorrelated with the actual person — contributes no benefit under this framework beyond whatever generic style effects the baseline already contains. A companion article in this program argues that persona simulation and person-perception are distinct constructs; P2 is that distinction’s quantitative edge.

P3 — The harm zone. For A < 0, B < 0, and the damage scales with L. An inverted person-model is predicted to produce outcomes worse than the person-blind baseline, and worst precisely on the tasks where accuracy would have helped most. This is the conjecture’s most consequential and least intuitive claim: the danger of bad person-modeling is not wasted effort but inflicted cost, concentrated in high-stakes communicative work — advice, care, teaching, conflict. Nothing in current deployment practice measures for this zone, and the documented overconfidence of modern systems (Guo, Pleiss, Sun, & Weinberger, 2017; Moore & Healy, 2008) plus their fluency in confabulation (Ji et al., 2023) suggests systems will occupy it confidently when they occupy it.

P4 — Moderation, not main effects. The benefit of a unit gain in A scales with L: statistically, the A × L interaction term carries the effect, and analyses that estimate only main effects of “personalization” will produce exactly the heterogeneous, context-dependent literature the field currently has. The conjecture thereby retrodicts its own motivating puzzle: strong effects where investigators happened to study high-L tasks such as persuasion (Matz et al., 2017), silence where they did not.

P5 — Felt benefit dissociates from B. Sycophantic systems occupy the region A ≈ 0 (or A < 0, when agreement inverts the person’s actual interests) while maximizing subjective ratings of being understood. The conjecture predicts a measurable dissociation: self-reported understanding rising while paired-comparison B is flat or negative. P5 is what makes the framework more than bookkeeping — it asserts that the industry’s principal proxy for personalization success is, in a specifiable regime, anti-correlated with the real thing.

4. Why a Conjecture

The claim could have been dressed as a model, a law, or a framework-with-propositions. It is offered instead as a conjecture, and the choice follows a precedent worth honoring explicitly. Mori advanced the uncanny valley as a conjecture — a proposed relation, graphed but not proven, published with the stated hope that mapping it would be useful (Mori, 1970/2012). The proposal organized fifty years of productive research because it invited refutation: it said something specific enough to be wrong.

The same posture is adopted here, with the falsification conditions stated rather than implied. The conjecture fails if reliable accuracy-linked benefit appears at L ≈ 0 (P1’s converse). It fails if inverted person-models produce mere inertness rather than scaling harm (P3’s converse). It fails if benefit is found to be additive — if A and L contribute independent main effects with no interaction (P4’s converse). It fails, in a subtler way, if A cannot be measured stably at feasible samples; correlational stability places hard floors on the n at which any of these tests is credible (Schönbrodt & Perugini, 2013). And γ is the term most likely to require revision from a gate to a richer function; the conjecture holds the multiplication as its core and offers γ as its most provisional part.

What the conjecture is not is a repackaging of the truism that context matters. It is a specific functional claim with a specific rival (the additive model implicit in current practice), and the two disagree about observable outcomes at every point in Section 3.

5. The Variables Have Literatures

Neither A nor L is invented here; the conjecture’s contribution is the multiplication, not the terms.

A inherits the person-perception accuracy tradition whole: the process model of how judgment becomes accurate (Funder, 1995, 2012), the componential structure of interpersonal perception (Kenny, 2004), the perspective-dependence of what can be known about a person (Vazire, 2010), the meta-analytic validity of other-ratings (Connelly & Ones, 2010), and the demonstrations that machine judges can enter this tradition as scoreable participants (Youyou, Kosinski, & Stillwell, 2015; Peters & Matz, 2024). Everything that literature knows about moderators of accuracy — information quantity, trait visibility, judge ability — becomes, through A, machinery for predicting where B is even achievable.

L inherits the communication-theoretic lineage summarized in Section 2, and it also has a macroeconomic shadow that deserves naming. The task framework in labor economics established that technology reprices work by task content, absorbing the routine and codifiable first (Autor, Levy, & Murnane, 2003); the labor market has since increasingly priced social and interpersonal skill (Deming, 2017); and the arrival of large language models is measured, occupation by occupation, in terms of task exposure (Eloundou, Manning, Mishkin, & Rock, 2024; Felten, Raj, & Seamans, 2021). Read through the conjecture, these are statements about the distribution of L: as low-L cognitive work deflates, the residual value of work — and of the systems that assist it — concentrates in high-L territory. The conjecture thus predicts not only where personalization pays today but where the entire economic weight of human–AI interaction is migrating.

6. Evidence Now, Studies Next

Consistent evidence. The tailored-persuasion literature sits where the conjecture says strong effects should sit: persuasion is a high-L activity (its outcome is almost entirely communicative), the targeting in these studies achieves modest but positive A through crude psychological matching, and B is reliably positive (Matz et al., 2017; Matz et al., 2024). Style-accommodation research shows humans performing L-sensitive adaptation as a basic competence (Bell, 1984), which is what one expects if fitted communication carries outcome variance worth capturing. And the organizational absorption of algorithmic judgment (Kellogg, Valentine, & Christin, 2020) is proceeding fastest in exactly the managerial, communicative functions the conjecture marks as high-L — which raises the stakes of P3 rather than settling it.

The decisive design. The conjecture’s core test is a factorial paired comparison. Persons with instrument-established ground truth interact with the same system under three profile conditions — true profile (A > 0), no profile (A = 0 baseline), and inverted profile, constructed by reflecting the true profile through the scale midpoints (A < 0 by design) — across a task battery independently scored for L, from near-zero-load transformations to high-load advisory and instructional tasks. Outcomes are scored blind; felt-understanding is collected separately to test P5. The conjecture’s fingerprint is a crossover interaction: condition differences vanishing at low L, spreading at high L, with the inverted condition falling below baseline where the spread is widest. No result pattern from this design is unpublishable, and every cell bears on a named prediction — the properties pre-registration exists to protect (Nosek et al., 2018).

The instrumentation requirement. Because A is criterion-referenced, the program requires exactly the validation infrastructure argued for elsewhere in this series: multi-instrument ground truth, ceiling-referenced scoring, calibration reported alongside accuracy (Brier, 1950), and pre-registered detection of the failure modes — fabricated familiarity at negligible exposure (Ji et al., 2023; Borkenau & Liebler, 1992), halo compression (Thorndike, 1920; Campbell & Fiske, 1959), and sycophantic drift (Sharma et al., 2023) — that would otherwise masquerade as A. Benchmark scholarship has documented what happens when influential measures are built without construct discipline (Raji et al., 2021; Liang et al., 2022; Hendrycks et al., 2021); a framework whose central variable is accuracy about persons must hold itself to the standard psychometrics already wrote (Cronbach & Meehl, 1955).

7. Boundary Conditions and Non-Claims

The conjecture is narrower than its notation may suggest, and its boundaries are part of the proposal.

B is task benefit against a person-blind baseline — not wellbeing, not long-run relational value, not the worth of being known. The framework is silent on goods it cannot measure, deliberately. A is accuracy on validated trait dimensions — not clinical inference, not diagnosis, and not the totality of a person; the claim is that this measurable slice of person-knowledge moderates outcomes, not that persons reduce to it. L is a property of tasks, and its estimation will be contested at the margins; the conjecture requires only ordinal separation between clearly low-load and clearly high-load work, which the founding literatures already provide (Daft & Lengel, 1986; Clark & Brennan, 1991). γ is acknowledged as the least developed term and the most important one: it asserts that no benefit computed by this framework is cognizable outside consented, purpose-bound use of person-knowledge — a constraint with regulatory counterparts already in force (Regulation [EU] 2016/679; Regulation [EU] 2024/1689) and, more importantly, a constraint without which a framework for the value of knowing persons becomes a framework for the value of profiling them. The distinction is the difference between this research program and the one it must never be mistaken for.

8. Conclusion

The industry’s implicit theory of personalization is a straight line: more knowledge, more benefit, everywhere. This article has proposed replacing the line with a surface — B = γ(A × L) — whose shape makes commitments a line cannot: that accuracy is worthless where nothing rides on communication, indispensable where everything does, and dangerous in inverse; that the feeling of being understood is manufacturable in exactly the regime where measured benefit is absent; and that the ethics of person-knowledge belong inside the formalism, as a gate, rather than beside it, as a caveat.

Every commitment above is offered for destruction. The variables are unbranded, the rival model is named, the decisive design is specified, and the precedent — a conjecture, graphed in hope, tested for fifty years — is the most productive one this territory has (Mori, 1970/2012). Colleagues in personality science, communication, human–computer interaction, and economics are invited to break the multiplication. If it breaks, the field learns the true functional form of a question it has never formally asked. If it holds, the field gains what it currently lacks entirely: a way to say, before building, where knowing a person will matter.

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