Small rules, unequal resources: an attention ecology for protocol design

Research question. Can a small recognition-and-correction loop support useful work without turning initial visibility into entrenched access to scarce review?

Bounded answer. Capping credit and preserving exploratory access yield simple mathematical bounds on offered group attention. They do not guarantee completed coverage, accurate checks, repair capacity or equitable outcomes. A small synthetic ecology exhibits those gaps and compares the mechanism against plain uniform routing rather than assuming reputation machinery is necessary.

Contribution and claim ledger

The prior mathematical ingredients are ordinary softmax mixtures, convex updates, finite resource accounting and queue dynamics. This manuscript applies and connects them; it does not claim to invent these methods. The earlier dossier’s local-feedback model motivates the diagnostic. This study is standalone synthetic evidence, not a fitted or externally validated social model. AI agents drafted and internally critiqued it under the same orchestration; external and human review remain separate.

Four rules, three comparison policies

Six accountable groups differ in capacity, skill coverage, submission volume and stipulated review diligence. A large collaboration has more internal capacity and offers but remains one group. Offers contain a required skill and a synthetic latent defect. Reviewers are different qualified groups. Checks and independent audits consume scarce effort; flagged or audit-discovered defects create persistent correction work. Oldest corrections get first access to the same experts next period.

The routing alternatives are: cumulative attention reinforced by pending volume (prestige); decayed capped check/correction credit with exploration (bounded); and a uniform active-group lottery. Each uses the same reviewer selection and cost model. Uniform routing is the serious simplicity baseline. Prestige intentionally models both feedback and volume multiplication; the experiment cannot identify which of those two components alone caused a difference.

The word “trust” here names a proposed interpretation of recognition, not a computed probability that a claim is true. “Dominance” names the hypothesized advantage of visibility feeding future access, not a demonstrated account of human motivation. Agents do not optimize effort or voluntarily join; their stipulated diligence creates tasks accomplished or missed. The separate coupled study addresses limited honest/shallow/refuse responses. Neither model supplies a general cooperation theorem.

A conditional bound, not a promised outcome

For an active group set of integer size $K\ge1$, finite score $s_i$, $0\le\epsilon\le1$ and finite feedback strength $\beta\ge0$, bounded routing uses

$$P_i(s)=\frac{\epsilon}{K}+(1-\epsilon) \frac{e^{\beta s_i}}{\sum_j e^{\beta s_j}}.$$

At period end, qualifying credit $r_i\ge0$ produces

$$s_i(t+1)=(1-\mu)s_i(t)+\mu\min(1,r_i(t)),\quad 0\le\mu\le1.$$

Starting in $[0,1]$, scores remain in $[0,1]$ because the update is a convex combination of two points in that interval. Therefore, while the active set and its declared identity partition are fixed,

$$\frac{\epsilon}{K}\le P_i\le \frac{\epsilon}{K}+(1-\epsilon)\frac{e^\beta}{e^\beta+K-1}.$$

The upper bound follows by putting the selected score at one and all others at zero. Strong reinforcement can make it close to one despite bounded credit. A positive proposal floor is not a completion floor: selected work can lack an independent specialist, sufficient indivisible capacity or a feasible audit. An actor hidden behind multiple asserted groups also violates the fixed-group premise. The prestige comparator multiplies weights by queued volume after its mixture, so it does not inherit the uniform exploration floor.

A local self-organization diagnostic

For $K\ge2$, to isolate feedback, consider the separate deterministic approximation in which expected credit is exactly group attention, so $s'=(1-\mu)s+\mu P(s)$. It has a symmetric fixed point $s_i=1/K$. On the zero-sum perturbation subspace the softmax Jacobian acts as $(1-\epsilon)\beta/K$, giving update multiplier

$$\lambda=1-\mu+\mu(1-\epsilon)\beta/K.$$

For $0<\mu\le1$ and nonnegative $\beta$, local asymptotic stability holds when $(1-\epsilon)\beta<K$. Equality is inconclusive by this linearization; above it, small asymmetries grow locally. The common-score direction has multiplier $1-\mu$. This is a local result for the stated map. The actual simulator has heterogeneous queues, capacity filters, capped event credit, audit access and repair obligations; it is not this symmetric system and no threshold transfer is asserted. The calculation explains why feedback deserves testing even with a small rule set.

Shared labor and persistent debt

A period gives each actor capacity $C_i$. The costs are two effort tokens per invitation/intake, ten per completed check, five per independent audit and twenty per correction (scaled in a stress regime). All draw from the same balance. Thus for every actor-period, the implementation preserves

$$L_i^{\mathrm{intake}}+L_i^{\mathrm{check}}+L_i^{\mathrm{audit}}+L_i^{\mathrm{repair}}\le C_i.$$

That accounting bound cannot prevent queues from growing. If recognized correction arrivals exceed feasible qualified correction completions, known debt accumulates. A low-resource specialist may check one offer yet be unable to complete an indivisible repair. Spare effort elsewhere does not solve that skill/size mismatch. Tasks cannot be fractionally carried across periods in this model. This modeling choice deliberately exposes indivisibility; it is not a recommended real scheduler.

An even more troubling case is a small correction queue with many hidden defects. A shared blind period makes all checks support their claims. Without independent audits, defects create no repair requests. The negative-control test gives every offer a defect, every period blindness and no audits: some work completes, every judgment is wrong, and repair debt remains zero. Neither throughput nor a quiet queue should be a proxy for scientific reliability.

Exploratory design and honest denominators

Nine regimes perturb arrival load, feedback, exploration, repair cost, common-mode blindness, audit access bias and absence of audits. Each runs eight seeds for eighty periods under all three policies: 216 retained runs. Exogenous offers, true defect states and blind periods match across policies within each seed/regime, verified by an offer-stream hash. Policies induce different processing orders and hence different signal draws; this is not pathwise matching of every check outcome.

Outputs include all offers, checks, unresolved work, correctness among completed checks, correct checks per offered task, defect discovery divided by all offered defects, author-attention concentration, every group’s coverage, known repair debt and all charged labor. Capacity refusals and invitations count attempts rather than unique offers; retrying a pending offer next period is visible in those totals. There is no claim to include author drafting labor, routing compute or institutional administration. Group concentration must be read beside offered volume: equal attention shares and equal per-offer service are different objectives.

The summary reports means and minimum/maximum across seeds, with paired differences from uniform routing. These are descriptive sensitivity results, not significance tests, inferential confidence intervals, real-world predictions or a preregistration. The run manifest identifies source/test and CSV hashes. Parameters are illustrative; none is estimated from scientific communities.

Selected numerical outcomes (synthetic implementation results)

Means over the eight retained seeds; full seed ranges and all regimes are in models/ecology/results/summary.json. “Correct/offer” includes unresolved offers in its denominator. HHI measures completed attention concentration, and debt counts recognized correction tasks remaining after eighty periods.

Under overload, uniform routing has the lowest concentration but also the lowest minimum per-group coverage; bounded routing improves that coverage metric while slightly reducing correct checks per offer relative to uniform. Total charged labor is similar: 10,404 tokens for bounded versus 10,373 for uniform out of 10,800 available. This is a tradeoff, not domination by the proposed mechanism.

Known debt persists even under default load because the large team’s rare-skill repairs require a different qualified actor; its small rare-skill peers each have fifteen tokens, below an indivisible twenty-token repair. Uniform or prestige routing cannot create the missing independent repair capacity. Doubling repair cost raises debt for every policy. Under common blindness, the lower debt is misleading: fewer than half of all offered defects are found, even while correct checks per offer remain above .85 because most offers are nondefective.

The missing incentive bridge: manufacturing work to earn correction credit

The adversarial replication exposed a structural gap: in a no-audit fixture, an all-clean population finishes with total recognition about .042, while an all-defective population finishes around 1.344 after 22 completed repairs. This is an implementation counterexample about the reward rule. The agents in the ecology cannot choose their defect rates, so those numbers do not establish strategic behavior or an equilibrium. They motivate an explicit deviation model instead of a verbal claim that correction rewards induce cooperation.

models/ecology/correction_game.py compares clean work with deliberately manufacturing one correctable defect and obtaining a completed repair. It uses the actual bounded score update and allocation function from the ecology. Let $q^0$ be the next allocation vector after clean work, $q^1$ after manufactured and repaired work, and $V$ the utility value of one full unit of future attention. The two actions concern the same final corrected claim: the manufactured path adds no assumed scientific value. Let $c$ be manufacture cost, $h$ repair effort, $\ell$ utility cost per effort token, $\theta_A$ the repair cost share borne by the author, $d$ the probability that intent to manufacture is established, and $F$ a credible enforceable loss conditional on that finding. The one-step deviation gain is

$$\Delta U_A=V(q^1_A-q^0_A)-c-\theta_A h\ell-dF.$$

Within this risk-neutral one-step model, manufacturing a successfully repaired defect is strictly preferred if and only if independent repair is feasible and $\Delta U_A>0$. Equality means indifference. This is a comparison of two specified actions, not a complete action set, participation model or repeated-game equilibrium. An infeasible repair blocks this particular path; it does not prove that other misconduct is unprofitable. Intent detection $d$ is a separate strong assumption: finding an ordinary error does not establish deliberate manufacture, and ordinary check accuracy cannot be substituted for $d$.

For an author–repairer coalition $C=\{A,R\}$, the corresponding comparison is

$$\Delta U_C=V\sum_{i\in C}(q^1_i-q^0_i)-c-\theta_C h\ell-dF,$$

where $\theta_C\ge\theta_A$ is their joint internalized share and transfers inside the coalition cancel. The model assumes a common attention valuation solely to keep this counterexample small. Distinct declared control groups can still coordinate; declaration-level independence is not coalition-proofness.

Three allocation-credit choices are retained: credit author and repairer; credit only the independent repairer; and no allocation credit for correction. Default parameters are three equal zero-score groups, $\epsilon=.15$, $\beta=4$, $\mu=.4$, $V=100$, $c=1$, $h=20$, $\ell=1$, $\theta_A=\theta_C=.1$, and no intent detection. Independent repair capacity is twenty tokens. Clean work has zero verified credit in this no-audit fixture. This last premise is explicit and important: an exogenous clean-author-credit sensitivity is also supplied under the result key verified_clean_baseline. It does not replay a complete ecology audit, which can also credit the checker and consumes additional audit labor.

These values use the exact softmax, not a linearized benefit. Repairer-only credit removes this author’s unilateral gain but leaves a profitable coordinated path. The no-credit baseline removes this channel under the stated utility function; it is not asserted optimal, since willingness to perform genuine repairs, intrinsic motives and useful recognition are absent from this one-step comparison. Full exploration removes this attention reward channel. Full cost internalization, credible intent detection, verified clean-work credit and insufficient independent repair capacity are separate retained sensitivity cases.

The descriptive social-cost proxy is $c+h\ell+H$, with $H=5$ for temporary harm; attention transfer is excluded as a social benefit because the opportunity pool is fixed. This is an assumed common utility scale, not measured scientific welfare. A twenty-token repair also consumes the entire modeled available repair capacity, leaving none for another case. Costs borne by a shared sponsor or volunteer pool still exist even if a strategic coalition does not internalize them. The default coalition includes the credited repairer yet bears only ten percent of the cost; this assumes substantial externalization or compensation. If the repairer bears the full private effort cost without an offset, the coalition share must reflect that, as in the full-internalization sensitivity.

The scalar capacity comparison is for one case. It does not reserve capacity across repeated calls or provide a multi-case schedule; the separate coupled simulator supplies the stateful shared-ledger experiment.

The design consequence is not to punish ordinary corrections or treat disclosed mistakes as misconduct. An honest author who repairs a claim has made information more useful and should retain a safe correction path. Distinguish recognizing responsible conduct from automatically increasing scarce review priority whenever repair volume rises. Whether to credit independent repair, baseline clean work, or neither in allocation requires testing with genuine repair participation and collusion incentives; no choice here has earned an institutional recommendation.

Interpretation and failure of mitigation

The retained runs should decide how much additional mechanism is worth exploring. Do not select only the regime in which bounded credit looks best. Uniform routing can match or exceed it, high exploration can change little when skill constraints bind, and expensive repair can defeat every allocation policy. Audit access bias can turn “verified credit” into a proxy for privileged access. Even idealized audits cannot help when independent expertise or capacity is absent.

A human-facing protocol can retain four simple actions while machines expose these resource and uncertainty states. But complexity inside the institution has not been abolished: someone must establish accountable control, decide check scope, supply independent auditing and carry correction duties. The model helps locate those burdens; it does not prove that people will accept them.

Before a pilot, compare a plain structured-template interface and uniform routing against the additional credit mechanism under matched total labor. A finding of no material advantage is a reason to omit the mechanism. Keep portable receipts, explicit unknowns and inspectable correction paths even if recognition feedback fails its test.