Should we allow AI-written articles in the Alignment Journal?

1 Setup

We assume there are two types of authors, high-quality authors (Type \(H\)) and slop authors (type \(L\)), who differ only in the substance of their manuscripts. The proportion of high-quality authors is \(\lambda\), and the rest are slop authors. Articles have apparent substance \(s\), which is the quality the manuscript presents to a reviewer—the metric a reviewer can measure, at any depth. They also have delivered substance \(v\), which is what a reader gets if the manuscript is published.

High-quality authors, given substance time \(t\), produce a manuscript whose apparent substance \(s_H\) equals its actual substance \(v_H\) and is

\[ v_H =s_H = \theta \sqrt{t}. \]

The rest produce slop, which in our model means manuscripts presenting an apparent substance \(s_L\), and an actual substance: \(v_L = 0\), taking time \(t_{\min}\). All of which is to say, the \(H\) authors aren’t deceptive but may vary in the quality they deliver, whereas the \(L\) authors produce low-quality outputs masquerading as adequate.

Every manuscript additionally requires drafting time \(d\): hand-drafting costs \(f\), AI drafting costs \(\delta = f/a\), where \(a\) is the AI’s drafting efficiency. An author producing \(n\) manuscripts at substance time \(t\) satisfies \(n(t + d) = T\).

Reviewing a manuscript to the journal’s standard takes \(h\) reviewer-hours and there are \(R\) total reviewer-hours, so the journal can review at most \(M = R/h\) manuscripts. Facing \(N\) submissions, it reviews \(\min(N, M)\) of them and rejects the rest unread, so a submission’s chance of being read at all is the coverage rate

\[ r = \min\!\left(1, \tfrac{M}{N}\right). \]

To control the volume of papers, we assume there is a noisy, cheap desk-reject process, which rejects a fraction of submissions without a full review; this is where we might consider a stylometric classifier to detect AI drafting.² A manuscript that receives a review is accepted with a probability depending on both its substance \(s\) and the review time \(h\),

\[ \Pr(\text{accept} \mid s, \text{reviewed}) = \Lambda\big(h\,(s - \bar{s})\big), \qquad \Lambda(x) = \frac{1}{1+e^{-x}}. \]

i.e. deeper reviews detect substance more precisely. Call \(h\) the depth of review. The journal holds \(h\) fixed with respect to queue size.

Authors are assumed careerist in that they care only about a payoff \(b\) per accepted paper. A high-quality author facing a drafting cost \(d\) thus solves

\[ \max_{t \ge t_{\min}} \; \frac{r\,b\,\Lambda\big(h\,(\theta\sqrt{t} - \bar{s})\big)}{t + d}, \]

maximizing accepted papers per unit of time. No single author can move the coverage rate \(r\), and it scales the payoff of every candidate \(t\) identically, so it drops out of the optimum; as such, congestion never influences the choice of how much substance we write. What does influence the choice is the drafting cost \(d\) — whichever of the two technology costs the author currently pays, \(f\) by hand or \(\delta = f/a\) with AI — which prices the marginal foregone manuscript in the first-order condition

\[ \frac{\Lambda'}{\Lambda} \cdot \frac{h\,\theta}{2\sqrt{t}} \;=\; \frac{1}{t+d} \; : \]

As AI capability rises, \(\delta\) falls, the marginal foregone manuscript becomes cheaper, and the optimum tilts toward more, thinner papers.

Now let us consider the target audience, the readers. We attempt to maximize their welfare; there are two ways we might describe this.

Firstly, we might consider the average delivered substance of the articles,

\[ W \;=\; \mathbb{E}\left[\, v \mid \text{accepted} \,\right]. \]

Recall that \(v = s_H\) for high-quality manuscripts, while for slop \(v = 0\) even though its apparent substance \(s_L\) is positive. Secondly, we might consider the number of good papers published per period. Of the \(\lambda\,n_H\) high-quality manuscripts written, a fraction \(r\) get reviewed and a fraction \(\Lambda_H\) of those pass, so the flow of high-quality papers into print is the throughput

\[ Q \;=\; r\,\lambda\,n_H\,\Lambda_H. \]

Either seems a reasonable objective for the journal, and they measure different things: \(W\) depends on the ratio of accepted slop to accepted good work, \(Q\) on the level of accepted good work. Happily, every policy comparison below comes out the same way under both, so we can track the pair without choosing between them.

And now we are set up to estimate the effects of AI drafting and automated AI bans.

We make three other simplifying assumptions:

1. AI drafting here introduces no errors and incurs no cognitive debt³
2. Accepted slop delivers zero value but is not actively harmful.
3. The review budget is exogenous: \(R\) is money divided by the going wage for qualified attention, and the model holds both fixed.

import numpy as np
import matplotlib.pyplot as plt
from livingthing.matplotlib_style import set_livingthing_style
set_livingthing_style()

P = dict(theta=1.0, s_L=0.30, sbar=0.50, t_min=0.05, f=0.50,
         T=1.0, lam=0.25, R=16.0, h=10.0, b=1.0)

T_GRID = np.geomspace(P["t_min"], 25.0, 4000)

def logistic(x):
    return 1.0 / (1.0 + np.exp(-np.clip(x, -60, 60)))

def accept_H(t, p=P):
    return logistic(p["h"] * (p["theta"] * np.sqrt(t) - p["sbar"]))

def accept_L(p=P):
    return logistic(p["h"] * (p["s_L"] - p["sbar"]))

def best_H(d, p=P, fee=0.0):
    """Substantive author's optimum: maximize (b*accept - fee)/(t+d).
    The coverage rate r is a common factor, so it never appears here.
    Returns (value per unit time, t*)."""
    obj = (p["b"] * accept_H(T_GRID, p) - fee) / (T_GRID + d)
    i = int(np.argmax(obj))
    return obj[i], T_GRID[i]

def outcomes(nH, wH, tH, nL, wL, p=P):
    """Coverage, mean substance per article, and good-paper flow."""
    N = p["lam"] * nH * wH + (1 - p["lam"]) * nL * wL
    r = min(1.0, (p["R"] / p["h"]) / N) if N > 0 else 1.0
    aH = p["lam"] * nH * wH * accept_H(tH, p)
    aL = (1 - p["lam"]) * nL * wL * accept_L(p)
    sH = p["theta"] * np.sqrt(tH)
    W = aH * sH / (aH + aL) if aH + aL > 0 else 0.0
    return dict(r=r, W=W, thruH=r * aH, tH=tH, sH=sH)

def solve_A(a, p=P):
    """Free-for-all: everyone AI-drafts, triage to capacity."""
    delta = p["f"] / a
    _, tH = best_H(delta, p)
    return outcomes(p["T"] / (tH + delta), 1.0, tH,
                    p["T"] / (p["t_min"] + delta), 1.0, p)

def mu_star(a, p=P):
    """Recall above which slop producers abandon AI drafting."""
    return 1.0 - (p["t_min"] + p["f"] / a) / (p["t_min"] + p["f"])

def mu_sub(a, p=P):
    """Recall above which high-quality authors abandon AI drafting."""
    Vh, _ = best_H(p["f"], p)
    Va, _ = best_H(p["f"] / a, p)
    return 1.0 - Vh / Va

def solve_B(a, mu, p=P):
    """Classifier ban: AI-drafted papers desk-rejected with recall mu."""
    delta = p["f"] / a
    dH, wH = (delta, 1 - mu) if mu < mu_sub(a, p) else (p["f"], 1.0)
    dL, wL = (delta, 1 - mu) if mu < mu_star(a, p) else (p["f"], 1.0)
    _, tH = best_H(dH, p)
    return outcomes(p["T"] / (tH + dH), wH, tH,
                    p["T"] / (p["t_min"] + dL), wL, p)

def solve_C(a, p=P, eps=1e-3):
    """Fee at slop's uncongested break-even: slop exits entirely."""
    delta = p["f"] / a
    fee = p["b"] * accept_L(p) + eps
    _, tH = best_H(delta, p, fee=fee)
    out = outcomes(p["T"] / (tH + delta), 1.0, tH, 0.0, 0.0, p)
    out["fee"] = fee
    return out

2 Policy A — Free-for-all

Anyone may use AI, and we triage submissions according to capacity as always. Everyone drafts with AI, as it is cheaper and goes unpunished. The equilibrium is easy to compute: the substance choice depends only on the drafting cost \(\delta = f/a\), submission counts follow from the time budget, and coverage follows from the counts.

One reading note for this figure and every figure below: since we expect \(a\) to keep rising, moving right along the horizontal axis is, roughly, waiting. That reading holds everything else fixed — slop quality, the detector, the author population — which is the thing that we think unlikely to stay fixed, so treat it as one axis of change among several rather than a forecast.

Code

a_grid = np.geomspace(1, 100, 25)
eqA = [solve_A(a) for a in a_grid]

fig, axes = plt.subplots(1, 3, figsize=(9.5, 3), sharex=True)
axes[0].plot(a_grid, [q["tH"] for q in eqA])
axes[0].set_title("substance time $t_H$")
axes[1].plot(a_grid, [q["r"] for q in eqA])
axes[1].set_title("coverage $r$")
axes[2].plot(a_grid, [q["W"] for q in eqA],
             label="mean substance per article $W$")
axes[2].plot(a_grid, [q["thruH"] for q in eqA], ls="--",
             label="good papers per period $Q$")
axes[2].set_title("welfare")
axes[2].legend(fontsize=8)
for ax in axes:
    ax.set_xscale("log")
    ax.set_xlabel("AI capability $a$")
fig.tight_layout()
plt.show()

Optimistically, we might hope that cheap drafting frees up time, which would flow into more substance per paper. That does not happen. \(t_H\) falls as \(a\) rises, from \(0.46\) to about \(0.32\) — the first-order condition at work: cheaper drafting makes the marginal foregone manuscript cheaper, so authors choose quantity over quality. The fall is modest, though: high-quality manuscripts stay above the bar (\(s_H\) drifts from \(0.68\) down to \(0.56\) against a bar of \(0.5\)), and their authors write three of them where they used to write one. Slop output grows much faster, because a slop manuscript is nearly all drafting time: \(n_L\) rises from under \(2\) to over \(18\).

The downside is visible through the effect on the queue, albeit differently in each of the welfare metrics. Mean substance: the submission pool ends up \(93\%\) slop, slop passes a full review \(12\%\) of the time, so most of what the journal accepts is slop, and \(W\) falls by two thirds. Throughput: coverage falls from roughly \(1\) to \(0.11\), so the journal publishes about four times fewer high-quality papers — even though the high-quality authors are writing more of them than before. Most of their extra manuscripts are simply never read.

The collapse is smooth and the equilibrium is unique. The coverage rate cancels out of every author’s problem, so there is no feedback loop to amplify anything, and no tipping point. The last section describes a review technology under which there is one.

3 Policy B — Automated banning AI-drafted manuscripts

Policy B: a stylometric classifier flags AI-drafted manuscripts with recall \(\mu\) and desk-rejects them. I assume it never flags hand-drafted work—it is high-precision; a classifier with false positives would also punish the compliant—I return to that below. Desk-rejected papers consume no reviewer time—that is the point of the policy. Everyone now chooses how to draft.

For slop authors the choice reduces to comparing time costs. Their acceptance probability is the same however the manuscript was drafted, so it cancels from the comparison, and what remains is: papers per hour with AI, discounted by the survival rate \((1-\mu)\), against papers per hour by hand. They keep AI drafting while \(\mu < \mu^*(a)\), where

\[ \mu^*(a) = 1 - \frac{t_{\min} + f/a}{t_{\min} + f} \;\xrightarrow{\;a \to \infty\;}\; \frac{f}{t_{\min} + f}. \]

In this setting, the classifier’s recall is very important. The recall needed to make slop authors give up AI drafting doesn’t depend on how good review is. It depends only on the time costs of producing slop, and it rises with AI capability toward a ceiling set by how small the minimum time per paper is relative to hand-drafting time. At my parameters, the ceiling is about \(0.91\). Whether real classifiers reach that is contested: an independent test of six deployed detectors found accuracies between \(55\%\) and \(97\%\) on ordinary, non-adversarial text (Akram 2023), while the strongest commercial classifier, Pangram, reports \(99.85\%\) accuracy at a \(0.19\%\) false-positive rate, comfortably above any threshold in this model (Emi and Spero 2024), so it seems credible that Pangram is actually useful there.

On the other hand, we might wish to leaven our enthusiasm with caution: the model needs recall sustained against slop authors who are actively rewriting to evade detection, because once a detector cuts into their earnings, defeating it becomes worth their effort. The arms race is outside the model, but the recall it must sustain is not. And the bar itself moves: because \(\mu^*(a)\) rises with capability, a ban that deters slop today can fail open with no visible policy change — hold \(\mu\) fixed, let \(a\) grow, and the journal slides backward through the regimes of the next figure, from deterring slop, to taxing only the compliant, to doing nothing. Running a ban means re-winning that race continuously, in a world where both the detectors and the models they detect are improving.

The high-quality authors have a different behaviour threshold. Write \(V(d)\) for the best value per unit time an author can get at drafting cost \(d\). High-quality authors abandon AI drafting once \((1-\mu)\,V(\delta)\) falls below \(V(f)\), that is at

\[ \mu_H(a) = 1 - \frac{V(f)}{V(\delta)}. \]

The two thresholds are strictly ordered: \(\mu_H(a) < \mu^*(a)\), always. To see this, we evaluate the hand-drafting value at the AI-drafting optimum \(t^*_\delta\), which gives \(V(f) \ge V(\delta)\,\frac{t^*_\delta + \delta}{t^*_\delta + f}\), and the ratio \(\frac{t + \delta}{t + f}\) increases in \(t\). In words: the more substance time we invest in a manuscript, the smaller the share of its cost that AI drafting saves, so the less detection risk an author will accept to keep using it. A detector therefore stops high-quality authors from using AI strictly before it stops slop authors. Neither type is ever deterred from submitting: at worst, slop authors revert to hand-drafting, which restores the pre-AI spam rate, never less. Being flagged costs a high-quality author a manuscript full of work; it costs a slop author almost nothing.

Bauer (2026) prove a general version of this problem for markets in expert services, where consultants sell reports to clients who cannot judge their quality. Suppose a consultant can pay a third party to certify that their report is human-written. The certificate costs a competent consultant the same That it costs an incompetent one, so it is worth buying for both or for neither; everyone shows up certified either way, and the client learns nothing. A signal separates types only when it costs the types different amounts; a provenance test can only distinguish types whose provenance choices differ. That is approximately why our classifier works when it does: hand-drafting costs the two types very different amounts relative to what AI saves them, so between the thresholds, the drafting technology an author chooses reveals which type they are. And it is why the ban does nothing below \(\mu_H\): once both types draft the same way, provenance carries no information about quality at all.

Code

mus = np.linspace(0.02, 0.98, 120)
W_pre = solve_A(1.0)["W"]

fig, ax = plt.subplots(figsize=(6.5, 3.5))
for a, col in zip((2, 5, 15, 100),
                  ("#b5541c", "#7f4c94", "#2d6e8e", "#3a7d44")):
    ax.plot(mus, [solve_B(a, mu)["W"] for mu in mus],
            color=col, label=f"$a = {a}$")
    ax.axvline(mu_sub(a), color=col, ls="--", lw=0.8)
    ax.axvline(mu_star(a), color=col, ls="-", lw=0.8, alpha=0.5)
ax.axhline(W_pre, color="#555555", ls=":", lw=1)
ax.set_xlabel(r"classifier recall $\mu$")
ax.set_ylabel("mean substance per article $W$")
ax.legend()
plt.show()

The two thresholds cut the recall axis into three regimes. Below \(\mu_H\), the ban deters nobody and changes nothing. It throttles both types in the same proportion, so the mean substance of what gets accepted is untouched, and the review slots freed by desk rejection offset the good papers rejected at the desk: both metrics remain at their free-for-all values. Between \(\mu_H\) and \(\mu^*\), the ban’s only behavioural effect is on the wrong people. High-quality authors have gone back to hand-drafting, writing one manuscript where they could have drafted three; slop authors still submit at full rate and merely lose a fraction \(\mu\) at the desk. Welfare rises across this range of recall only because \((1-\mu)\) shrinks the surviving spam, not because anyone has stopped. Above \(\mu^*(a)\), everyone hand-drafts and the pre-AI equilibrium reappears exactly — same coverage, same substance time, same welfare.

The standard objection to a ban is that it removes the time savings of AI drafting from the compliant. Our model seems to support this. In the free-for-all, we waste those savings: we invest them in extra manuscripts that mostly go unread. On the other hand, the pay-to-play Policy C regime below turns the same savings into a rising flow of published good papers. So what the ban destroys is not what the savings are worth today, but what they would be worth under a better policy.

The assumed zero false-positive rate matters more than it looks. A classifier that sometimes flags hand-drafted prose punishes compliance directly, and small changes near \(\mu^*\) move the outcome significantly. I intend to extend the model with a false-positive rate to see how much that changes things.

4 Policy C — submission fees

Charge \(P\) per submission, allow anything, triage and review as always. To be clear: this is not on the table for the Alignment Journal, but is included as a baseline.

Fees as screening devices are not a novelty of the AI era: submission fees and refereeing delay are substitute prices on the same margin, and a journal chooses a mix of them whether it admits to pricing or not (Cotton 2013).

Recall that a submission’s expected private return is \(b\) times its acceptance probability: \(r\,b\,\Lambda_L\) for slop, and roughly \(r\,b\,\Lambda_H\) — much larger — for a high-quality paper. Any fee between those two numbers is separating: submitting slop now loses money, while submitting good work still pays. Nobody is forced back to hand-drafting, because the fee does not care how the paper was written — which is as it should be, since drafting provenance was never the harm.

An underpriced fee fails in a specific way. Below the excluding level, slop authors keep entering until the fee equals the expected return, \(r\,b\,\Lambda_L = P\). That pins the coverage rate at \(r = P/(b\,\Lambda_L)\): slop fills every review slot that good work does not claim. Raising \(P\) buys back coverage one-for-one, but the accepted set stays diluted until the fee crosses the slop authors’ break-even.

Full exclusion has a definite price. A slop author facing an uncongested queue (\(r = 1\)) expects \(b\,\Lambda_L\) per submission, so the fee that keeps slop out entirely is

\[ P^* \;=\; b\,\Lambda\big(h\,(s_L - \bar{s})\big), \]

about an eighth of the private value of an acceptance at my parameters. \(P^*\) does not depend on \(a\): review depth is fixed, so slop’s acceptance odds remain the same no matter how large the flood. In a world where \(a\) keeps rising, that flatness is a policy property rather than a curiosity: the fee is the one instrument in this menu whose calibration survives capability growth, where the ban must be re-verified against a rising \(\mu^*\) forever. Review depth never becomes more selective as the queue grows, so the fee must do all the deterring by itself. The exclusion at \(P^*\) is total and abrupt because all slop authors share one break-even; a spread of their costs or payoffs would smooth the cliff into a taper.

Code

fig, (ax, axt) = plt.subplots(1, 2, figsize=(9.5, 3.4))
eqC = [solve_C(a) for a in a_grid]
for ax_, key in ((ax, "W"), (axt, "thruH")):
    ax_.plot(a_grid, [q[key] for q in eqA], color="#b5541c",
             label="A: free-for-all")
    for mu, ls in ((0.6, "--"), (0.95, "-")):
        ax_.plot(a_grid, [solve_B(a, mu)[key] for a in a_grid], ls,
                 color="#2d6e8e", label=f"B: classifier, $\\mu={mu}$")
    ax_.plot(a_grid, [q[key] for q in eqC], color="#3a7d44", label="C: fee")
    ax_.set_xscale("log")
    ax_.set_xlabel("AI capability $a$")
ax.set_ylabel("mean substance per article $W$")
axt.set_ylabel("good papers per period $Q$")
ax.legend(fontsize=8)
fig.tight_layout()
plt.show()

Interestingly, with the fee, more AI capability is simply good. High-quality authors keep all the time AI saves them and spend it writing more manuscripts; the journal, its queue protected, has the capacity to review and publish them; and the flow of good papers into print more than doubles across the plotted range. Under the other regimes, that saved time is thrown away — by the ban, which forces hand-drafting, or by the free-for-all, which converts it into unread submissions. The figure charges the full \(P^*\), and that matters: it is what makes the accepted set pure substance, whereas an underpriced fee would leave slop filling the residual capacity, as above.

The size of the fee’s lead in the left panel has a simple decomposition: \(W\) is the share of published articles that are high-quality, times the substance \(s_H\) of a high-quality one. The ban’s ceiling is the pre-AI equilibrium, and at these parameters the pre-AI journal published only about \(58\%\) high-quality articles — slop authors predate AI, submit at hand-drafting rates, and fool full review \(12\%\) of the time, and a drafting-provenance detector cannot touch hand-drafted slop even in principle. The fee acts on being slop rather than on using AI, so it empties the queue of slop entirely and its high-quality share is \(100\%\). That is the whole gap: roughly \(0.58 \times 0.68\) against \(1.00 \times 0.65\).

An entailment of that calibration is that the journal was hypothetically going to be about \(40\%\) bullshit in the absence of AI drafting. That number follows from parameter choices we made (\(\lambda\), \(s_L\), \(h\)). Readers who believe their journal is cleaner than that should raise \(\lambda\) or \(h\) and watch the fee’s lead over the ban shrink accordingly — the fee’s advantage on this metric arises from the amount of pre-AI slop share it eliminates, so the dirtier we think journals already are, the stronger the case for pricing submission over policing provenance.

Of course, many journals cannot charge submission fees for reasons of custom and equity, and the Alignment Journal is one such. In such cases, the deadweight losses of dealing with spam is still imposed on someone, and the mechanism by which journals impose it instead is queue time: with money fees near zero, first-response delay is the de facto submission price (Azar 2005). So Policy C stands as the benchmark: it prices the congestion directly rather than through shadow instruments, and its gap over the best feasible policy measures is something like the platonic ideal of efficiency.

If a journal did wish to explore this route, it would need to be done carefully and transparently. For instance, Journals like the Alignment journal, which pay their reviewers, could consider using fee revenue to enlarge the review budget, so the fee would partly fund its own capacity; the classifier, by contrast, only costs money.

Another interesting option might be a rejection-contingent fee — refunded on acceptance — charges bad papers more than good ones in expectation. This might have attractive equity properties, because it would penalize authors who submit good paper less.

5 Future work

On this analysis, the classifier ban is a stand-in for a price on an externality. It is imperfect: as its recall improves, it starts hurting the compliant at \(\mu_H\) and only starts working at \(\mu^*\). Whether the Alignment Journal, or any journal, should adopt it depends crucially on some concrete parameters that we have only guessed here:

• The recall a detector can sustain against motivated rewriting, compared against a \(\mu^*\) we could estimate from the time costs of producing slop; and
• how many good AI-drafted papers we would tolerate losing in the recall range between the two thresholds.

The review technology deserves its own caveat, because it decides what kind of failure the flood produces. Holding depth fixed and rationing coverage, as here, congestion worsens outcomes but never changes incentives. The failure is correspondingly tame: the equilibrium is unique, welfare falls continuously in \(a\), and a marginal improvement — a little more budget, a slightly better classifier — buys a proportionate marginal repair.

The opposite assumption is that the journal absorbs a growing queue by reviewing all of it less carefully: coverage stays at \(r = 1\), and each manuscript gets \(e = R/N\) reviewer-hours instead of the fixed \(h\). That puts congestion inside the incentives: the return to substance is now scaled by the per-manuscript attention \(e\), so as review thins, even high-quality authors stop investing in their manuscripts, which frees more time for volume, which thins review further. That feedback loop changes the failure from quantitative to qualitative, and we can compute where.

Code

T2 = np.geomspace(P["t_min"], 25.0, 600)

def tH_dilute(e, delta, p=P):
    """H's optimal substance time when acceptance depends on attention e."""
    obj = logistic(e * (p["theta"] * np.sqrt(T2) - p["sbar"])) / (T2 + delta)
    return T2[int(np.argmax(obj))]

def dilution_equilibria(a, p, n=600):
    """All fixed points of e * N(e) = R in the dilution variant."""
    delta = p["f"] / a
    nL = p["T"] / (p["t_min"] + delta)
    def load(e):
        tH = tH_dilute(e, delta, p)
        return p["lam"] * p["T"] / (tH + delta) + (1 - p["lam"]) * nL
    es = np.geomspace(0.1, 50.0, n)
    g = np.array([e * load(e) - p["R"] for e in es])
    roots = []
    for i in range(n - 1):
        if (g[i] < 0) != (g[i + 1] < 0):
            lo, hi = es[i], es[i + 1]
            for _ in range(40):
                mid = np.sqrt(lo * hi)
                if ((mid * load(mid) - p["R"]) < 0) == (g[i] < 0):
                    lo = mid
                else:
                    hi = mid
            roots.append(np.sqrt(lo * hi))
    return roots

fold_a = np.concatenate([np.linspace(1.5, 3.1, 20),
                         np.linspace(3.1, 3.7, 45),
                         np.linspace(3.7, 8.0, 20)])
fig, axes = plt.subplots(1, 2, figsize=(9.5, 3.4), sharey=True)
for ax, lam in zip(axes, (0.25, 0.75)):
    p2 = dict(P, lam=lam)
    for a in fold_a:
        for e in dilution_equilibria(a, p2):
            ax.plot(a, e, "o", ms=3, color="#7f4c94")
    ax.set_xlabel("AI capability $a$")
    ax.set_title(f"$\\lambda = {lam}$")
axes[0].set_ylabel("equilibrium attention $e$")
fig.tight_layout()
plt.show()

The computation confirms both halves of the claim. At our baseline author mix, \(\lambda = 0.25\), the dilution variant also declines smoothly: one equilibrium at every \(a\). At \(\lambda = 0.75\) there is a narrow range of capability values, around \(a \approx 3.4\), in which three equilibria exist at once; the middle one is unstable, so in practice the journal is in one of two self-consistent states: careful review with restrained submission, or cursory review with a flood. Which state it ends up in depends on its history. Suppose the journal is in the careful state and \(a\) rises through this range. The journal stays careful, changing only a little — until, at the top of the range, the careful state stops being self-sustaining at all, and the journal falls to the flooded state in one step. The fall does not reverse: lower \(a\) back into the range and the journal stays flooded, because the flooded state is self-sustaining there too. Recovery means pushing \(a\) well below the point of collapse — raising the cost of slop past where the fall began, to where the flooded state itself stops existing. Bartolucci and Vivo (2026) works this margin out properly in a queueing model: under load, reviewers rationally raise the risk threshold for checking AI output, cutting scrutiny when it matters most. Which margin a real overloaded journal degrades on first — how carefully it reads, or whether it reads — is an empirical question I have not seen answered, and it decides whether the collapse is a slope or a cliff.

Several other exclusions would change the answer if relaxed. Slop’s apparent substance \(s_L\) is fixed here; the realistic case has it rising with \(a\), and as \(s_L \to \bar{s}\) the fee’s separating band closes — at which point the journal’s problem stops being mechanism design and becomes epistemology. More broadly, everything here describes the world as it stands: the premise that AI can write a paper but not do the science behind it is a statement about current capability, and the measured trend is that the boundary moves; none of these results survive the regime where it fails. The high-quality authors’ half of the wedge is assumed away artificially: apparent and delivered substance coincide for them by assumption, so nobody can oversell. If AI drafting also made real but modest work read as better than it is, the high-quality authors would gain an inflation margin of their own.

Accepted slop is harmless here; if it instead poisons training corpora (Shumailov et al. 2023) or locks in error (Qiu et al. 2025), its value is negative and everything above understates the case for keeping it out. The payoff \(b\) is the same for everyone; a paper mill with a much larger \(b\) would shrug off any plausible fee. If publishing slop were reputationally harmful, the return to slop would change and the amount of spam might also be moderated.

And there is, in this model, only one journal; with many journals, the slop flood routes around the strict one and there is a race-to-the-bottom, which is a different and worse game.

6 References