---
abstract: |
  Journals cannot referee every paper they receive. When submissions outrun the time reviewers can give, an editor must decide what to do with the papers no one reads: reject them, or check them with a faster but less accurate tool, of the kind artificial intelligence now supplies. A paper the tool passes carries the same public stamp as one an expert approved, and readers cannot tell a screened paper from a reviewed one. This paper asks which choice makes the stamp more valuable. Rejecting the unread papers keeps the approved pool cleaner, because the faster tool sometimes passes weak work. Yet rejection can make the stamp worth less: good papers turned away unread join the pool of unstamped papers and raise the quality against which a stamped paper is judged. Which effect wins depends on how common good work is, and the model gives the exact switching point when there is one. The choice also shifts how much a strong affiliation is worth; and once authors can run the screening tool themselves, wherever some game it and some do not, the stamp’s value is set by what getting past the screen costs, not by what the screen detects, while expert judgment allows no such gaming.
author:
- Johan Fourie[^1]
bibliography: references.bib
reference-section-title: References
title: The Value of Peer Review and the Reward to Reputation[^2]
---

> Figures and typeset tables are omitted from this Markdown version.
> The complete paper, with all figures, is in JF_ValueOfPeer_v5.pdf.


**Keywords:** certification; peer review; pedigree; expert judgment; artificial intelligence

**JEL codes:** D82; D83; I23; L15; O33

# Introduction

Some research tasks can be written down as rules, and some cannot. Recent work on AI divides jobs along this line: codifiable work, which follows rules a machine can now carry out at scale, and messy work, which still needs a person’s judgment (Garicano et al. 2026). Generative artificial intelligence keeps widening the set of research tasks that rules can handle. Writing a plausible manuscript is now largely rule-based (Fourie 2026b); judging one is not. Expert judgment has not become cheaper, and economists who study AI in science treat it as the input that stays scarce (Agrawal et al. 2026). The change has now reached evaluation itself: the technical checks a referee once ran by hand can be written as rules, and journals have begun to adopt the tools that run them. This paper works out what that second change does to the value of certification, the worth of the stamp a journal puts on a paper. The two changes share one feature: whatever part of writing can be reduced to rules, anyone can produce, and whatever part of evaluation can be reduced to rules, anyone can pass.

Journals were crowded before either change. Yearly submissions to the top five economics journals nearly doubled between 1990 and 2012 while those journals published fewer articles, so acceptance rates fell from about 15 per cent to about 6 per cent (Card and DellaVigna 2013). What limits a journal is referee time, and that time comes at a price which does not clear the market (Engers and Gans 1998). That time is also shared very unevenly: across the biomedical literature a small share of researchers carry most of the reviewing (Kovanis et al. 2016). AI has now added volume on top of the shortage: after ChatGPT appeared, submissions to *Organization Science* rose sharply while measured writing quality fell, both in the submissions and in the reviews (Gartenberg et al. 2026). The crowding extends beyond journals as well: in weeks when more working papers are released, each one receives fewer downloads and less attention, and is later published and cited less (Lusher et al. 2023). A journal that cannot read every submission must decide what to do with the papers its referees do not reach: reject them unread, or check them with a faster but less accurate tool, of the kind AI now supplies. This paper asks one main question. Which choice keeps the journal’s stamp more valuable? The natural guess is that rejecting the unread papers protects the stamp, because it withholds approval from everything the journal has not checked. That guess can be wrong. A stamp is valued by comparison: a reader prices a stamped paper against the papers that have no stamp, so anything that raises the quality of the unstamped papers lowers what the stamp is worth. Good papers rejected only because no referee reached them are papers of exactly this kind. Turned away unread, they join the unstamped papers and raise their average quality, and the stamp that excluded them is then worth less.

Two further questions follow from the same choice, and the paper answers them too. What does each rule do to the worth of an author’s pedigree, the track record readers can see? And what is the fast tool’s verdict worth once authors can run the tool themselves? Existing work on certification studies certifiers who choose what to reveal about the work they have examined. A crowded certifier faces an earlier choice, what to examine at all, and that work has treated the screening tool behind the choice as fixed equipment, not as something the screened authors also hold. Those are the two gaps this paper fills. Fourie (2026a) applies the codifiable–messy division to certification and argues that a journal’s stamp survives only if the journal commits to rejecting what it cannot read. The model below shows that this commitment is not always the right one.

I answer all three questions in a deliberately small model. There is a fixed batch of papers, each either high or low quality, where high quality means the paper would pass a careful expert review. The journal’s expert reviewers reach only a random fraction of submissions, say one in four; this intensive review, when it happens, judges quality without error. The journal chooses what happens to the papers it does not reach. Under *strict verification* it rejects them. Under *scalable evaluation* it hands them to an imperfect tool that passes a high-quality paper with probability $\alpha$, say three in four, and a low-quality paper with probability $\beta$, say one in five. The two tools mirror the two kinds of work. Intensive review is the messy input, the judgment that does not scale; the scalable screen is the part of evaluation that has been reduced to rules. Both routes end in the same public stamp, so readers see that a paper is approved but not how. A competitive market pays each paper what it is worth on average given what the market can see, which is the quality a rational reader infers from the presence or absence of the stamp. The value of the stamp is the premium: the gap between the price of a stamped paper and the price of an unstamped one, and also the most an author would pay to display it. Last, I let authors fall into two visible pedigree groups, one likelier than the other to produce high-quality work. Review stays blind to the group, but readers see both the stamp and which group the author is in.

The precise answer is a single crossing. Suppose the screen lets some bad work through ($\beta>0$) and still tells good work from bad to some degree ($\alpha>\beta$). Then, as good papers become a larger share of the batch, the two stamps’ values cross at most once, and the crossing point has a formula. When that crossing lies strictly between zero and one, strict verification gives the more valuable stamp while good work is scarce, and scalable evaluation gives it once good work is common. The screen can also be too weak for any crossing to occur: if it passes too few good papers relative to the bad ones it lets through, strict verification wins at every share. With the running numbers, one paper in four reviewed and the screen passing three good papers in four and one bad paper in five, the crossing is at a good-work share of 0.410. At every share, though, strict verification leaves the higher average quality among stamped papers. A cleaner stamp and a more valuable stamp can therefore point to opposite rules. That gap is the paper’s central finding.

The second question, about pedigree, has its own threshold. Here the comparison turns on one summary of the two groups: a midpoint between how likely each group is to produce good work, defined precisely in Section 5. When that midpoint lies below the threshold, strict verification produces the wider gap between the two groups’ prices among unstamped papers; when it lies above, scalable evaluation produces the wider gap. Because the two thresholds are separate numbers, a pair of groups can fall on one side of the first and the other side of the second. And when the two groups lie on opposite sides of the value crossing, they value the stamp more under opposite rules: no single rule gives both groups their more valuable stamp.

The third question makes the screen’s error rates something the model determines. Section 6 gives authors the same tool the journal screens with, so an author can pay to fix the rule-checkable flaws the screen would catch. Fixing them changes what the screen sees, not what the paper actually contributes, so strict verification is untouched: expert judgment still reads the quality that no fix reaches. Under scalable evaluation, in every equilibrium where some flagged authors pay to fix their papers and some do not, the value of the stamp is pinned down: it equals the fee an author pays to show the stamp plus the cost of fixing divided by the chance $1-p$ of being sent to the screen. The stamp is then priced by what getting past the screen costs, not by what the screen can detect. And if fixing is cheap enough, every paper the screen reads passes, and the comparison reduces to a simple benchmark: strict verification gives the more valuable stamp exactly when good papers are fewer than half.

The same comparison explains the pedigree result. An unstamped paper is weaker evidence of low quality under strict verification, which leaves the overflow unread, than under scalable evaluation, which screens it. So a missing stamp lowers an author’s price by more under screening, and it does so for both groups. What this does to the gap between the groups depends on where they start. When both groups are unlikely to produce good work, the extra bad news lowers both prices towards zero and narrows the gap between them; when both are likely to, it widens the gap. A single threshold separates the two cases. This is a statement about prices, not a claim that either rule changes how much a group’s pedigree tells a reader about quality.

The paper contributes to three literatures: the economics of science, the theory of certification, and the economics of AI and the division of labour.

The first contribution connects certification to how attention and status are shared out in science. Hanson et al. (2024) show that the number of indexed articles has outrun the researchers available to vet them, and warn that the resulting strain can blur what a journal’s name signals. I take that shortage as given and work out how the rule for the overflow changes two things at once: what the signal is worth, and what a strong reputation is worth. Science studies has long found that how a paper is judged depends in part on who wrote it (Lee et al. 2013): an author’s prominence sways peer assessments in a controlled experiment (Huber et al. 2022), editors give more weight to reports from heavily published referees (Card and DellaVigna 2020), and reputation even shifts how credit is split between teams that reach near-identical results (Hill and Stein 2025b). Publishing in a handful of top journals strongly predicts tenure in economics, and the standing of the department where an author trained predicts where they are hired (Heckman and Moktan 2020; Clauset et al. 2015), so what the stamp is worth, and who can earn it, are questions about careers as much as prices. A second kind of sorting runs through money: authors at less-resourced institutions and in poorer countries cluster in lower-fee journals, while better-resourced institutions publish where the charges are higher (Oldford et al. 2023; Klebel and Ross-Hellauer 2023). The sorting studied here needs no money at all. It survives even when submitting is free and review is blind. Journals have already used blindness as a lever: the *American Economic Review* ran a double-blind experiment and found that hiding the author’s name lowered acceptance rates for some groups (Blank 1991). Even so, blindness does not settle the matter. When the evaluator never sees who wrote a paper, the rule for the papers it cannot reach still changes the market reward to reputation, because it changes what a missing stamp implies. Experiments with AI evaluations of economics papers show that the tool itself reacts to affiliation, prominence and gender (Pataranutaporn et al. 2025); the blind-screen case here isolates a separate, indirect route that works even when the evaluator is not told who the author is.

The second contribution is to the economics of certification. The closest predecessor is Farhi et al. (2013), where a rejection from a choosy certifier is itself bad news: every rejected paper was read and found wanting, so rejection lowers the standing of those turned away and worsens the pool of the rejected. Rationing by capacity turns this around. A paper rejected only because the journal ran out of reviewers is not bad news about the paper, because no one read it. Rejection without reading produces mistakes that carry no stigma, and it can raise rather than lower the quality of the unstamped pool. That reversal is what lets a cleaner stamp be worth less, and it cannot happen when every rejection is informative. The paper adds a second result of the same kind: the tool a certifier screens with is itself shaped by behaviour. Once the authors being screened hold that tool, its price shapes the screen’s error rates, and where some game the screen and some do not, the stamp’s value is pinned by the cost of passing it rather than by anything the certifier chose.

A broad literature studies certifiers that choose what to tell the market: what to disclose, what to charge, how open to be, and how many grades to give (Lizzeri 1999; Stahl and Strausz 2017; Zapechelnyuk 2020; Pollrich and Strausz 2024). Work on grading makes a related point: any one grade is read against the other grades the same scheme hands out (Dranove and Jin 2010; Daley and Green 2014; Harbaugh and Rasmusen 2018). In another line of work the standard itself is set by behaviour, either as a norm about what referees demand that shifts slowly over time (Ellison 2002), or as a journal’s best response to its own aims, which can make deliberately lax review worthwhile (Zollman et al. 2024). A further line asks how an editor should choose among referees and combine their reports (Bayar and Chemmanur 2021). I study a different margin. When review capacity is spread too thin, what happens to the papers that get no report, and how does that choice change the price the market puts on a shared stamp? A separate literature studies authors who game a fixed scoring rule, and the blurred information that results (Frankel and Kartik 2019; Ball 2025); there the question is the score itself and how the designer should answer the gaming. Here both tools are held fixed, there is a single public stamp, and I do not model the journal’s aims; Section 6 then lets authors game the screen, and that gaming changes which rule gives the more valuable stamp. What is new here is the cost that rationing imposes on a stamp’s standing: the model sets the two rules against each other for the same shortage of expert time, and finds the exact share of good work at which the more valuable stamp switches from one rule to the other.

The third contribution is to the economics of AI and the division of labour. There the codifiable–messy split sorts tasks: rule-based work is now done by machines at scale, and messy work is still done by people (Garicano et al. 2026). The first of the two changes is already documented. Employers on a large freelancing platform stopped paying extra for well-written applications once large language models arrived, because good writing no longer told strong applicants from weak ones (Galdin and Silbert 2025), and scientific output now grows fastest among the authors who used to pay the highest price for language, those writing outside their first language (Kusumegi et al. 2025). This paper asks what the same split does to the institutions that certify the work. Turning an evaluation task into rules changes more than who does it. A check a journal can run by rule at scale is a check an author can pass by rule at will, so the very step that lets a journal screen its overflow lets the screened authors pass the screen. The line between rule-based and messy work therefore shows up in prices. When some authors game a rule-based screen and others do not, the value of the stamp it grants is set by what getting past the screen costs; the premium of a stamp built on judgment answers to no such cost, because judgment stays messy. In the division-of-labour literature the messy remainder is the work machines leave to people. Here it also decides what sets a stamp’s value once everyone owns the tools: the value of a stamp built on rule-based checks comes to depend on how authors respond to the tool rather than on what the tool detects, while a stamp built on judgment keeps the value the fundamentals give it. So the line does a second job: it sorts tasks by who does them, and it sorts stamps by what fixes their value once the tools are in every author’s hands.

All three results inform a live debate about what AI does to the making of knowledge. Algorithms are expected to reorganise scientific work, not just speed it up (Mullainathan and Rambachan 2025), and formal models show that when machine output stands in for human effort, the shared store of knowledge can shrink even as each person’s decisions improve (Acemoglu et al. 2026). Two findings from nearby settings strengthen the concern. Competition lowers measured quality when the evaluation is rough (Hill and Stein 2025a), and applicants who can use generative AI are harder for employers and investors to judge (Cowgill et al. 2026). Editorial discretion, by contrast, changes what gets published less than is often assumed (Krieger et al. 2025). The debate has so far said little about certification itself, which is how science turns private judgment into a public signal. The results below show that a crowded certifier choosing between the two rules faces a trade-off with no clear winner: the rule it picks sets both how much a stamp is worth and how much an author’s affiliation is worth to those without one. Recent models of AI and publishing study richer problems, including submission volume, review costs, capacity and fees (Atasu 2026; Lopez-Lira and Seyfi 2026), and how to redesign review when authors and reviewers both use AI (Hakobyan 2026). This paper isolates one piece those problems can build on: the price the market puts on a shared stamp, and what that price becomes once authors hold the screening tool themselves.

The rest of the paper runs as follows. Section 2 sets out the model. Section 3 works out the value of a stamp and shows that it equals what an author would pay for one. Section 4 compares the two rules and states the main result. Section 5 asks whose prices the choice of rule falls on, across pedigree groups. Section 6 puts the screen itself in play, letting authors hold the tool it is built from, and maps artificial intelligence onto the model’s inputs. Section 7 concludes. Appendix A gathers the proofs; Appendix B extends the model to two noisy screens, targeted expert review, a continuous measure of quality, and authors who choose whether to submit.

# The model

There is a fixed batch of completed papers, treated as a unit mass. Each paper $i$ has a hidden quality $q_i\in\{0,1\}$ that matters for certification. Quality one means the paper would pass a careful expert review; quality zero means it would not. Write
$$
\pi=\mathop{\mathrm{Pr}}(q_i=1)\in(0,1)
$$
for the share of high-quality papers.

The model takes as given whatever a reader can already see. It holds fixed the visible features of a manuscript, such as its topic or how polished the prose is. So $q$ is the part of quality that only evaluation can reveal: the soundness or importance not already obvious to the market that will read it. Among papers that look the same, the journal cannot rank them before evaluating. Sections 2–4 stay inside one such group of look-alike papers; Section 5 compares two groups that differ in the author’s publicly visible pedigree.

The journal announces one of two rules. Under either rule, a paper gets intensive review with probability $p\in(0,1)$; intensive review passes a high-quality paper and rejects a low-quality one. How much review there is, $p$, is taken as given. A journal could in principle buy more, but referees are paid little or nothing and give their time for reasons a fee does not easily change, so the amount of intensive review barely responds to what a journal is willing to spend (Engers and Gans 1998). Prices are nowhere near the level at which that would even be tested. Among the 600 highest-ranked economics journals, only 118 charge a submission fee at all, and the median charge among those is 125 dollars. Posted fees come to about one per cent of a central estimate of what an acceptance is worth to an author, and the fee that would clear the queue, along with the referee pay it would fund, sits well above anything charged today (Fourie and Macdonald 2026). Review is therefore rationed, not priced. That companion paper prices entry to the queue; this one prices what the queue produces, the stamp itself. The interesting case is a $p$ below the level that would clear the queue, and it is the only case in which the two rules differ at all: at $p=1$ every paper is examined and the choice disappears. The rules differ in what they do with the overflow, the papers intensive review does not reach. Under *strict verification*, a paper that misses intensive review is rejected. Under *scalable evaluation*, a paper that misses intensive review is passed with probabilities
$$
\alpha=\mathop{\mathrm{Pr}}(C\mid q=1,\text{ scalable}),\qquad
 \beta=\mathop{\mathrm{Pr}}(C\mid q=0,\text{ scalable}),
 \qquad 1\geq\alpha\geq\beta\geq0.
$$
Here $\alpha$ is the true-positive rate, the chance a good paper passes the screen, and $\beta$ is the false-positive rate, the chance a bad one does. The running example has $p=0.25$, $\alpha=0.75$ and $\beta=0.20$: reviewers reach one paper in four, and the screen passes three good papers in four and one bad paper in five. The figures use these numbers throughout.

The journal issues one common public stamp: readers see that a paper is certified, not which route certified it. This pooling is essential to everything that follows. If the journal revealed the route, readers would price intensively reviewed and screened papers separately, and the single-stamp comparison below would not apply.

Submissions and rejections are private. The market sees whether a paper has the stamp, not whether it applied and was turned down. A competitive market pays a paper its expected quality given what the market sees: the chance the paper is high quality, conditional on the stamp being present or absent. An author who has earned the stamp may display it by paying a fixed, stamp-only price $f\geq0$, set outside the model. This price is a measuring device for willingness to pay; it is not a claim that journals should charge for acceptance. Submitting a finished paper costs nothing in the baseline. The order of events is: the journal announces its rule and $f$; authors submit; the journal evaluates; authors who qualify decide whether to display the stamp; and the market pays each paper its expected quality.

A little notation finishes the setup. For either rule, write
$$
x_H=\mathop{\mathrm{Pr}}(C\mid q=1),\qquad x_L=\mathop{\mathrm{Pr}}(C\mid q=0),
$$
for the overall chances that a high- and a low-quality paper end up certified, and let the certified share be
$$
m=\pi x_H+(1-\pi)x_L.
$$
Write the two market prices as
$$
P_C=\mathop{\mathrm{\mathbb E}}[q\mid C],\qquad P_N=\mathop{\mathrm{\mathbb E}}[q\mid N],
$$
where $N$ is the pool of papers the public sees without a stamp. The premium is $\Pi=P_C-P_N$, the gain in reputation from holding the stamp. The uncertified pool $N$ is terminal: the model has a single certification stage, so a paper the journal rejects for want of capacity stays in $N$ and earns no other publicly observed stamp. This is what lets a rejected good paper raise $P_N$, the mechanism behind the results.

# The value of a certificate

Bayes’ rule reduces the value of a stamp to one expression.

**Lemma 1** (Certification premium). *For any $0<m<1$,
$$
\begin{equation}
 \Pi(x_H,x_L)=
 \frac{\pi(1-\pi)(x_H-x_L)}{m(1-m)}.
 \label{eq:premium}
\end{equation}
$$*

Each part of equation [\[eq:premium\]](#eq:premium) does a job. The numerator is the prior variance of quality, $\pi(1-\pi)$, times how sharply the rule separates good papers from bad, $x_H-x_L$. The prior variance is only one factor: the same $\pi$ also enters the denominator, so a more uncertain prior does not by itself make the stamp worth more. What the numerator isolates is the rule’s separation, which raises the premium whenever it improves. The denominator captures how the rule splits the papers between the two pools, stamped and unstamped. This is where the result comes from. A rule that certifies more papers leaves fewer in the unstamped pool it is judged against, and it is that change in the comparison pool, not the cleanliness of the stamp, that can raise or lower the premium. Every paper the rule does not stamp falls into that comparison pool.

The premium is not just a statistical gap; it is also what an author would pay for the stamp. Authors know more about their own papers than the market does. Let author $i$ privately put the chance her paper is high quality at $\theta_i\in(0,1)$, with these beliefs averaging out to $\mathop{\mathrm{\mathbb E}}[\theta_i]=\pi$. Her chance of ending up eligible for the stamp is
$$
s(\theta_i)=x_L+(x_H-x_L)\theta_i.
$$
The argument has two steps: first work out the premium assuming every author submits, then check that submitting is indeed what every author wants. The order matters: the premium is computed under a guess about behaviour, and the lemma then shows the guess was right.

**Lemma 2** (Private demand). *Fix a regime and calculate $\Pi$ in the all-submission outcome. For every $f\in[0,\Pi)$, all authors strictly submit and every eligible author strictly displays the stamp. The supremum price consistent with strict participation and display is $\Pi$.*

An author who earns the stamp gains $P_C-f-P_N=\Pi-f$ from showing it, and she reaches that point with probability $s(\theta_i)$, so submitting has expected gain $s(\theta_i)(\Pi-f)>0$. The display price is a measuring device: it turns the premium into demand for the stamp without our having to model the journal’s own aims. Whichever rule gives the larger premium is the rule whose stamp authors value more.

# Strict versus scalable evaluation

Section 3 turned the value of the stamp into one formula. That formula now answers the main question: when a journal cannot read everything, does rejecting the overflow or screening it keep the stamp more valuable? We compute the two premiums and compare them. Throughout, a superscript $R$ marks strict verification, which rejects the overflow, and a superscript $S$ marks scalable evaluation, which screens it. Under strict verification a good paper is certified only if intensive review reaches it, and no bad paper is ever certified, so $x_H^R=p$ and $x_L^R=0$. Hence
$$
\begin{equation}
 \Pi_R=\frac{1-\pi}{1-\pi p}.
 \label{eq:strict}
\end{equation}
$$
For scalable evaluation define
$$
c=(1-p)\beta,\qquad
 d=p+(1-p)(\alpha-\beta),
$$
where $c$ is a bad paper’s overall chance of being certified and $d$ is how much higher a good paper’s chance is. Then $x_L^S=c$, $x_H^S=c+d$, and
$$
\begin{equation}
 \Pi_S=
 \frac{\pi(1-\pi)d}
 {(c+\pi d)(1-c-\pi d)}.
 \label{eq:scale}
\end{equation}
$$

The main result says when each rule gives the more valuable stamp. Its one condition, interior pools, asks only that both pools, stamped and unstamped, contain some papers, so that both prices are well defined.

**Proposition 1** (The value of strictness). *For interior certified and uncertified pools,
$$
\begin{equation}
 \operatorname{sign}(\Pi_R-\Pi_S)
 =\operatorname{sign}K(\pi;p,\alpha,\beta),
 \label{eq:sign}
\end{equation}
$$
where
$$
\begin{equation}
 K(\pi;p,\alpha,\beta)
 =c(1-c)-2cd\pi-d(d-p)\pi^2.
 \label{eq:K}
\end{equation}
$$
If $\beta>0$ and $\alpha>\beta$, $K$ is strictly decreasing in $\pi$, so the premiums cross at most once. If the positive root is interior, it is
$$
\begin{equation}
 \pi^*=\frac{c(1-c)}
 {\sqrt{c^2d^2+d(d-p)c(1-c)}+cd}.
 \label{eq:root}
\end{equation}
$$
Strict verification has the larger premium below $\pi^*$; scalable evaluation has the larger premium above it. If $\beta=0<\alpha$, scalable evaluation has the larger premium for every $\pi\in(0,1)$.*

In plain terms: which rule wins depends only on the sign of a quadratic in the share of good work, and that quadratic falls as good work becomes more common. When its root sits inside the unit interval, strict verification wins while good work is scarce (low $\pi$), scalable evaluation wins once it is common (high $\pi$), and the switch happens exactly once, at $\pi^*$. The running example puts numbers on the switch. The crossing is at $\pi^*=0.410$. When one paper in five is good, the strict premium is 0.842 and the scalable premium 0.523. At the crossing the two are equal, at 0.657. When three papers in five are good, the strict premium is 0.471 and the scalable premium 0.642.

Even when $\beta>0$ and $\alpha>\beta$, the crossing may lie outside the range. Because $K(0)>0$ and $K$ falls, the positive root is below one exactly when
$$
\begin{equation}
 \alpha[p+(1-p)\alpha]>(1-p)\beta.
 \label{eq:attainability}
\end{equation}
$$
If this fails, strict verification has the larger premium at every share of good work.

The case with no false positives has a clean interpretation from information theory. One tool is said to Blackwell-dominate another when it is more informative for every user who might rely on it, whatever the decision. When $\beta=0<\alpha$, the screen certifies no bad paper, just as strict verification does, and certifies more good ones, so it Blackwell-dominates strict review: it is better on every count. When $\beta>0$ and $\alpha>\beta$, neither tool wins outright: strict review is better at keeping bad papers out, while the screen is better at letting good ones in. Since neither is more informative for every user, the two are not ranked by Blackwell’s criterion, and the share of good work can reverse the ranking.

The result is easiest to see from the two pools. Strict verification never certifies a bad paper, so the stamped pool is pure, $P_C^R=1$. But a good paper that misses expert review joins the unstamped pool. When good papers are common, this raises the unstamped price $P_N^R$ by enough to reduce the premium $\Pi_R$. Scalable evaluation lets some bad papers through, which lowers the stamped price $P_C^S$, yet it can certify enough good papers that the unstamped price $P_N^S$ falls by more than $P_C^S$ does. The scalable stamp is then noisier but worth more.

How the crossing changes with the screen’s quality follows the same logic.

**Corollary 1** (Performance of scalable evaluation). *Suppose $\pi^*$ is interior. Holding $p$ and $\beta$ fixed, $\partial\pi^*/\partial\alpha<0$. Holding $p$ and $\alpha$ fixed, $\partial\pi^*/\partial\beta>0$.*

A better hit rate on good papers widens the range of shares over which scalable evaluation gives the larger premium; more false positives narrows it. The reason is general: for a fixed $\pi$,
$$
\begin{align}
 \frac{\partial\Pi}{\partial x_H}
 &=\pi(1-\pi)\left\{\frac{x_L}{m^2}
 +\frac{1-x_L}{(1-m)^2}\right\}>0, \label{eq:dxh}\\
 \frac{\partial\Pi}{\partial x_L}
 &=-\pi(1-\pi)\left\{\frac{x_H}{m^2}
 +\frac{1-x_H}{(1-m)^2}\right\}<0. \label{eq:dxl}
\end{align}
$$
Any premium rises when good papers are certified more often and falls when bad papers are. The crossing changes in the stated directions because $x_H^S=p+(1-p)\alpha$, $x_L^S=(1-p)\beta$, and $\Pi_R-\Pi_S$ crosses zero from above.

*[Figure not reproduced here — see JF_ValueOfPeer_v5.pdf]*
A cleaner stamp need not be a more valuable one. Panel (a) plots the premium, the value of holding the stamp, under strict and scalable evaluation against the share of high-quality papers. Panel (b) plots the average quality of stamped papers. The parameters are $p=0.25$, $\alpha=0.75$ and $\beta=0.20$, giving $\pi^*=0.410$. The parameter values are illustrative, not calibrated.

Figure [1](#fig:wedge) shows the gap between how clean a stamp is and how much it is worth. Strict verification gives the cleaner stamped pool at every share: $P_C^R=1>P_C^S$. Yet above the crossing scalable evaluation gives the larger premium. The point is not that the noisier screen yields the cleaner pool; it is that cleanliness alone does not settle how much a common stamp is worth to the author who holds it.

One special case makes the threshold easy to see. Suppose the journal certifies every overflow paper without reading it, so $\alpha=\beta=1$. Equation [\[eq:K\]](#eq:K) then reduces to
$$
\begin{equation}
 \operatorname{sign}(\Pi_R-\Pi_S)=\operatorname{sign}(1-2\pi).
 \label{eq:half}
\end{equation}
$$
Strict verification is more valuable exactly when fewer than half of all papers are good. This benchmark is worth stating on its own. A journal that stamps its overflow unread is doing the least selective thing it can, and even then rejecting wins only while good papers are the minority. Where the line sits for a screen that does sort papers is not fixed by this case. It is fixed by Corollary [1](#cor:performance): a higher hit rate on good papers lowers the crossing and more false positives raises it, so the threshold can sit on either side of one half, depending on how good the screen is.

Two clarifications mark the limits of the result. First, $\Pi$ is a difference in prices, the private gain from holding the stamp. It is not welfare, not the amount of information produced, not average stamped quality, and not the certifier’s running costs; the model does not treat maximising the premium as the journal’s goal. Nor is the premium the journal’s income. Push the display fee up towards its ceiling $\Pi$; every certified author pays it, so revenue tends to $m\Pi$. Write $m_R$ and $m_S$ for the certified shares under the two rules. Scalable evaluation certifies at least as large a share of both types, so $m_S\geq m_R$, and it sorts the types at least as sharply, so $d\geq p$. By equation [\[eq:premium\]](#eq:premium) the product $m\Pi$ equals $\pi(1-\pi)(x_H-x_L)/(1-m)$, which is at least as large under scalable evaluation on both counts: the larger certified share shrinks the denominator, and the sharper sorting raises the numerator. So its potential revenue is at least strict review’s at every share. The crossing is about the value of one certificate, not total fees. Second, the proposition compares the two rules for a fixed batch of completed papers. Once submitting costs something and the net premium is fixed, strict review draws a stronger set of authors, because weaker authors are less willing to try. Near the crossing this change in who submits can reverse the ranking. Appendix [9](#app:extensions) works this out.

# Pedigree and the incidence of certification

Section 4 answered the value question for one pool of look-alike papers. The same model answers a second question: which authors gain or lose from the rule. Let the market now see something about the author as well as the journal’s stamp. Suppose authors fall into two visible pedigree groups $b\in\{B,0\}$, where a share $\pi_0$ of one group and a larger share $\pi_B$ of the other produce high-quality work, $0<\pi_0<\pi_B<1$. Pedigree might be the author’s institution, membership of a research network, or an established name. Posting in a prominent working paper series is the clearest example, and crowding within such a series measurably cuts the attention each paper gets (Lusher et al. 2023). The difference between the groups is a statistical link with quality, not a taste for or against anyone. The question is one of incidence, in the sense the word has in the study of taxes: on whose prices does the choice of rule fall? Review is blind: how often intensive review reaches a paper, and the screen’s error rates, do not depend on the group $b$. Some journals have adopted and tested such blindness (Blank 1991), and the results below show what it does not achieve. Because the market does see the group, every earlier price formula applies group by group, with $\pi$ replaced by the group’s own share $\pi_g$.

What review does to an unstamped paper is captured by a likelihood ratio $\ell$, how likely a good paper is to go unstamped relative to a bad one,
$$
\begin{equation}
 \ell=\frac{\mathop{\mathrm{Pr}}(N\mid q=1)}{\mathop{\mathrm{Pr}}(N\mid q=0)}
 =\frac{1-x_H}{1-x_L}.
 \label{eq:ell}
\end{equation}
$$
For a group with share $\pi$, the market price of an unstamped paper is
$$
\begin{equation}
 U(\pi;\ell)=\mathop{\mathrm{\mathbb E}}[q\mid N;\pi]
 =\frac{\ell\pi}{1-\pi+\ell\pi}.
 \label{eq:unstamped}
\end{equation}
$$
The two rules give
$$
\begin{equation}
 \ell_R=1-p,
 \qquad
 \ell_S=\frac{(1-p)(1-\alpha)}{1-(1-p)\beta}.
 \label{eq:ells}
\end{equation}
$$
When $0\leq\beta<\alpha<1$, $0<\ell_S<\ell_R<1$. A smaller likelihood ratio means that having no stamp points more strongly to low quality, so a missing stamp is worse news under scalable evaluation than under strict verification. The reason is that the screen looks at every overflow paper, while strict verification leaves the papers it cannot reach unexamined.

Define the pedigree gap among unstamped papers under rule $r\in\{R,S\}$ as the difference in the two groups’ unstamped prices,
$$
W_r=U(\pi_B;\ell_r)-U(\pi_0;\ell_r).
$$
Because the two groups need not be close together, the comparison leans on one summary of the pair: the logit midpoint, the group share whose odds are the geometric mean of the two groups’ odds, so that its log-odds sit exactly halfway between the two groups’ log-odds,
$$
\widetilde\pi=
 \operatorname{logit}^{-1}\left\{
 \frac{\operatorname{logit}\pi_0+\operatorname{logit}\pi_B}{2}
 \right\}.
$$

**Proposition 2** (Pedigree and uncertified work). *Under blind review with $0<\pi_0<\pi_B<1$ and $0\leq\beta<\alpha<1$,
$$
\begin{equation}
 \operatorname{sign}(W_R-W_S)
 =\operatorname{sign}(\widehat\pi-\widetilde\pi),
 \label{eq:pedigreesign}
\end{equation}
$$
where
$$
\begin{equation}
 \widehat\pi=
 \frac{1}{1+\sqrt{\ell_R\ell_S}}
 =\frac{1}{1+(1-p)
 \sqrt{(1-\alpha)/[1-(1-p)\beta]}}\in(1/2,1).
 \label{eq:pedigreethreshold}
\end{equation}
$$
Strict verification produces the larger pedigree-related price gap among uncertified papers exactly when $\widetilde\pi<\widehat\pi$. Moreover,
$$
\begin{equation}
 \frac{\partial\widehat\pi}{\partial\alpha}>0,
 \qquad
 \frac{\partial\widehat\pi}{\partial\beta}<0,
 \qquad
 \frac{\partial\widehat\pi}{\partial p}>0.
 \label{eq:pedigreecomparative}
\end{equation}
$$*

The proposition stops just short of $\alpha=1$, and that boundary case runs in strict verification’s favour. At $\alpha=1$ the screen passes every good overflow paper, so under scalable evaluation an unstamped paper is known to be bad, both groups’ unstamped prices are zero, and strict verification opens the larger gap for every pair. This is the limit of the stated result, since $\widehat\pi\to1$ as $\alpha\to1$.

The threshold lies above one half for every allowed set of parameters, which fixes the direction of the result whenever the two groups’ quality shares are low. Suppose the two shares add to less than one. Then the product of their odds is below one, the logit midpoint is below one half, and one half is below the threshold. So strict verification produces the wider gap. The condition is that the two group-specific shares sum below one, not that good papers are a minority of the whole population, which would also turn on how many authors sit in each group. A crowded certifier whose two groups meet it therefore cannot avoid the following combination: rejecting what it cannot examine keeps its stamped pool clean and, at the same time, raises what an author’s affiliation is worth among the papers it turned away. Scalable evaluation reverses the comparison only when both groups are strong enough to raise their midpoint above the threshold.

The result compares market rewards, not how much pedigree actually tells a reader about quality. In odds terms pedigree is worth exactly the same under both rules, because a blind stamp multiplies both groups’ starting odds by the same likelihood ratio:
$$
\begin{equation}
 \frac{\operatorname{odds}(q=1\mid N,B)}
 {\operatorname{odds}(q=1\mid N,0)}
 =\frac{\pi_B/(1-\pi_B)}{\pi_0/(1-\pi_0)}
 \label{eq:oddsinvariance}
\end{equation}
$$
under either rule. The gap in log-odds does not change. The rule also leaves each group’s average price untouched: by the law of iterated expectations a group’s stamped and unstamped prices average back to its prior $\pi_g$. What the rule moves is the spread between those two prices, and with it the gap $W_r$ among unstamped papers, not any group’s expected reward. Prices are a different matter, because the market pays expected quality in levels, and going from odds to levels is not a straight-line step. A smaller $\ell$ makes an unstamped paper stronger evidence of low quality. For two weak groups, that evidence is close to decisive for both, so both prices are near zero and nearly equal, and the gap between them is small. For two strong groups, the same evidence makes each price react sharply to the group’s exact share, so a small difference in share produces a large difference in price, and the gap is wide. The formula behind this is the slope of the unstamped price as the group’s share rises, $\ell/[1-(1-\ell)\pi]^2$: a smaller $\ell$ makes it flatter where shares are low and steeper where they are high. The threshold $\widehat\pi$ is the share at which the two slopes are equal.

*[Figure not reproduced here — see JF_ValueOfPeer_v5.pdf]*
On whose prices the choice of rule falls. Panel (a) plots the price of an unstamped paper against a group’s share of good work under the two rules, at the parameters of Figure [1](#fig:wedge). The marked pairs are groups at $(0.20,0.30)$ and $(0.80,0.90)$; the line joining each pair is the gap between their prices. Panel (b) shades, for every pair of group shares with $\pi_B>\pi_0$, the rule that produces the larger gap. The solid curve is the boundary $\widetilde\pi=\widehat\pi$, the dashed lines mark the premium crossing $\pi^*$ of Proposition [1](#prop:strictness), and the gold point is the pair $(0.50,0.60)$ discussed below. The parameter values are illustrative, not calibrated.

Figure [2](#fig:incidence) draws both halves of the result. In panel (a) the scalable price line lies below the strict line everywhere, flatter where shares are low and steeper where they are high, and their order reverses at $\widehat\pi=0.711$. The groups at shares 0.20 and 0.30 are separated by 0.085 under strict verification and by 0.034 under scalable evaluation. The groups at 0.80 and 0.90 are separated by 0.121 under strict verification and by 0.196 under scalable evaluation. Panel (b) covers every possible pair of group shares. Over most of the square strict verification produces the larger gap, which follows from $\widehat\pi>1/2$.

Pedigree is also priced differently among stamped papers. Under strict review $\mathop{\mathrm{\mathbb E}}[q\mid C,b]=1$ for both groups, so among stamped papers the two groups fetch the same price and the gap is zero. Under scalable evaluation the gap is positive exactly when $\beta>0$. The zero gap under strict review comes from taking intensive review to be perfect; it need not survive if intensive review is itself noisy.

The premium crossing of Section 4 has one more consequence for who pays what.

**Corollary 2** (Regime disagreement). *Suppose the crossing $\pi^*$ in Proposition [1](#prop:strictness) is interior. If $\pi_0<\pi^*<\pi_B$, then
$$
\begin{equation}
 \Pi_R(\pi_0)>\Pi_S(\pi_0),
 \qquad
 \Pi_S(\pi_B)>\Pi_R(\pi_B).
 \label{eq:groupdisagreement}
\end{equation}
$$*

An author from the weaker group will pay more for the stamp under strict verification; an author from the stronger group will pay more under scalable evaluation. This ranks what each group would pay to hold the stamp, the willingness to pay of Lemma [2](#lem:demand); it is not a ranking of which rule each group would choose overall. An author’s expected gain from submitting is her premium times her chance of being certified, and strict verification, by rejecting the overflow, lowers that chance. A weaker author can therefore value the stamp more under strict review yet be better off overall under scalable evaluation, which certifies her more often. At the running parameters, an author in a group where good work is one paper in five, who privately rates her own chance at that same one in five, expects 0.042 from submitting under strict review but 0.148 under scalable evaluation, though the strict premium of 0.842 is larger than the scalable one of 0.523. If a single display fee applies to both groups, every author still submits as long as the fee is below the smaller of the two groups’ premiums.

The two thresholds answer different questions, and the rankings they induce need not agree. The premium crossing $\pi^*$ is compared with one group’s share and ranks what the stamp is worth to that group. The pedigree threshold $\widehat\pi$ is compared with the logit midpoint of a pair of groups and ranks the gap between their prices among unstamped papers. The two rankings agree at the two ends. Suppose both groups’ shares lie below $\pi^*$ and the pair’s midpoint lies below $\widehat\pi$. Then strict verification gives both groups the more valuable stamp and also produces the wider gap between them among unstamped papers. For an author in the weaker group this is the high-stakes rule: it raises what she gains by being stamped and what she loses by not being. When instead both shares lie above $\pi^*$ and the midpoint lies above $\widehat\pi$, scalable evaluation gives both groups the more valuable stamp and the wider gap, so it is then the high-stakes rule and strict verification shrinks both differences. In between, the two rankings can point different ways.

Neither condition implies the other. The gold pair in Figure [2](#fig:incidence), with shares 0.50 and 0.60, has its logit midpoint at 0.55, below $\widehat\pi=0.711$, so strict verification produces the wider pedigree gap; yet both shares exceed $\pi^*=0.410$, so scalable evaluation gives the more valuable stamp to both groups. Which threshold is larger depends on the parameters, and nothing in the model forces the two comparisons to agree. All of this is about prices; none of it is a ranking of welfare.

# The codified screen in equilibrium

The scalable screen is no longer hypothetical. In August 2026, Refine, an AI referee built by economists to run scalable technical checks (Golub 2026), announced partnerships with two leading publishers in economics. Where such a tool sits in the process decides which part of the model it touches. Run after acceptance, as a final technical audit, it only checks papers expert judgment has already chosen; it arrives after the stamp is given and changes nothing above. Run on the overflow, it is exactly the scalable screen of this model. This section asks the third question: what is the screen’s verdict worth once the authors it screens can run the tool themselves?

Let the screen read a rule-checkable mark on each manuscript, the result of the checks it can run by rule. A high-quality paper has a passing mark with probability $\alpha$ and a low-quality paper with probability $\beta$, and the screen certifies an unreviewed paper exactly when its mark passes. These are the same rates as before, now with a story behind them. Suppose the tool that runs the screen is also in the authors’ hands before they submit: an author can read the paper’s mark from the tool’s report and pay a cost $\kappa>0$ to fix the rule-checkable flaws the screen would catch. Fixing changes the mark, not the quality, because quality is the messy part no rule reads. The market sees neither the mark nor the fixing, only the stamp, and prices using how authors actually behave. Two assumptions keep this honest: the screen is not already useless (it does not pass everything), and the mark is a feature of the manuscript alone, learned only from the report and, once quality is held fixed, unrelated to anything else the author knows.

Under strict verification, fixing is worthless. An unreviewed paper is rejected whatever its mark, and a reviewed paper is judged on quality, which fixing does not change. Under scalable evaluation, a fixed paper is certified in the overflow instead of rejected, so every author whose mark fails gains the same amount from fixing: the premium minus the fee $f$ to display the stamp, when that difference is positive and nothing otherwise, times the chance $1-p$ of being sent to the screen. That the gain is the same for good and bad papers is the crux: being indifferent about fixing does not sort good papers from bad.

**Proposition 3** (Erosion of the codified screen). *Under scalable evaluation with repair cost $\kappa>0$:*

1.  *The strict-verification premium is unaffected at every $\kappa$.*

2.  *In every equilibrium in which a positive mass of failing-mark papers is repaired and a positive mass is not, the scalable premium equals
    $$
    \Pi_S=f+\frac{\kappa}{1-p}.
    ```*

3.  *Let $\Pi^{\min}$ be the premium when repair reaches every failing-mark low-quality paper and no high-quality one, given in closed form in the appendix. If $\kappa<(1-p)\bigl(\Pi^{\min}-f\bigr)$, the unique equilibrium is full repair: the screen passes everything it reads, scalable evaluation certifies the overflow unfiltered, and $\operatorname{sign}(\Pi_R-\Pi_S)=\operatorname{sign}(1-2\pi)$.*

Part (ii) pins the premium, in every partial-fixing equilibrium, at the display fee plus the cost of fixing divided by $1-p$. Fixing pays off only in the fraction $1-p$ of papers that reach the screen, so its cost is spread over that fraction and enters divided by $1-p$. The logic is a no-arbitrage argument. If the stamp were worth more than that sum, every flagged author would fix; if it were worth less, none would; a premium at which some flagged authors fix and some do not must equal it exactly. Which authors fix is not pinned down. When authors have some private read on their own quality, fixing can concentrate on exactly the papers the screen would have caught, and the screen’s real error rates can converge until it separates nothing at all, while the premium stays exactly at the pinned level. Equilibrium disciplines the price of the stamp, not who ends up behind it.

Across the repair cost the equilibrium shifts from one regime to another: a high cost leaves the screen intact and no one repairs, an intermediate cost gives the partial-repair equilibria whose premium part (ii) pins, and a low cost brings on full repair, which is the unique equilibrium when the screen’s floor is positive and one equilibrium among several otherwise. The pinning identity rests on every flagged author facing the same repair cost, which is what stops repair from sorting good papers from bad. If the cost fell unevenly by quality, repair would carry information about quality and the identity need not hold exactly; whether the screen then separates more or less depends on which papers are cheaper to fix.

Part (iii) is the limit the introduction promised. When fixing is cheap enough, the screen certifies everything it reads, and the choice between the two rules reduces to the clean benchmark of Section 4, equation [\[eq:half\]](#eq:half): strict verification gives the more valuable stamp exactly when fewer than half the papers are good. Full repair is an equilibrium whenever repairing pays for itself at full participation, that is when $\kappa$ is at most $(1-p)$ times the full-repair premium net of the fee. For full repair to be the *only* equilibrium, the screen’s worst-case premium $\Pi^{\min}$ must be positive, which at a display fee of zero requires coverage $p$ to exceed $(1-p)(1-\alpha)$, the share of good papers that sit in the overflow and fail the screen; at the running parameters, one quarter exceeds three sixteenths. Where that floor is not positive, full repair can still occur, but alongside other equilibria.

Erosion does not always lower the premium. When good work is common, the intact screen does harm of its own: it wrongly rejects good overflow papers and so raises the quality of the unstamped pool, and dissolving the screen stops this. Whether full fixing lowers the premium is therefore a single-crossing question: the premium when the overflow is passed unfiltered is $\pi/[1-p(1-\pi)]$, and when the quadratic recorded in the appendix changes sign inside the unit interval, this unfiltered premium is larger than the intact screen’s above a third threshold $\pi^{u}$. At the running parameters $\pi^{u}=0.580$. Below it the intact screen has the higher premium, so erosion lowers the premium: at a good-work share of 0.20 it falls from 0.523 to 0.250. Above it, for the reason just given, erosion raises the premium: at 0.60 it rises from 0.642 to 0.667. The paper’s three thresholds run in the order $\pi^*=0.410$, then $\pi^u=0.580$, then $\widehat\pi=0.711$ at these parameters, and the order depends on the parameters.

The same tool can instead be sold per manuscript, so that an author buys the report and the fix together without first seeing the mark. Then, when the stamp is worth displaying and the screen still separates at all, the authors willing to pay most are the ones least sure of their work, because their papers are the likeliest to fail the screen. So the authors who buy are those least sure, everyone below a confidence cutoff, and their buying raises the false-positive rate by at least as much as the true-positive rate, so any interior cutoff erodes the screen’s separation. This is the pattern experiments already find: applicants who can use generative AI are harder for employers and investors to judge (Cowgill et al. 2026). None of this denies that fixing genuinely improves a manuscript on the things a rule can check; the model says nothing about that value. What full fixing removes is information: a pass mark everyone can obtain separates no one, while the messy quality underneath is unchanged.

Fourie (2026a) reaches the one-half benchmark a different way, through a flood of submissions while the journal stamps its overflow unread. The erosion limit reaches the same boundary for a fixed batch of papers, by dissolving the filter instead. When the publisher partnerships were announced, Garicano noted that authors will run the tool before submitting, so that in equilibrium papers “will have passed by it beforehand and the AI referee will find nothing new” (Garicano 2026). In the model this is exactly right in the full-fixing equilibrium; short of that, authors’ indifference pins the premium instead.

The other links from AI to the model give a map, not a forecast, because none of them has a sign that holds unconditionally. Let AI capability be $a$, the volume of completed papers $n(a)$, and intensive-review capacity $A(a)$. Under random rationing,
$$ math
p(a)=\min\{1,A(a)/n(a)\},
```
where at $p=1$ every paper gets intensive review, the two rules coincide, and there is nothing to compare. AI may also change the share of good work $\pi(a)$ and the screen’s performance $(\alpha(a),\beta(a))$. The dividing line for policy is simply
$$
K\bigl(\pi(a);p(a),\alpha(a),\beta(a)\bigr)=0.
$$
This setup allows both a flood of AI-written submissions, which lowers $p$, and AI-assisted review, which raises $A$ or improves $(\alpha,\beta)$. The introduction’s split between rule-based and messy work organises these links. A tool raises $\alpha$ without raising $\beta$ when it turns more of the evaluation task into rules, as verification-first proposals aim to (You et al. 2026), and the proposition above gives the terms on which that gain survives once authors hold the same tool. It raises $A$ when it saves referees time on the rule-based parts of their work. The messy core, the judgment itself, stays the scarce input. The one term with no settled sign is the share of good work $\pi(a)$: the same tools that make submissions harder to screen can also let authors finish projects whose ideas were sound but whose execution was held back, and these two effects have opposite signs. Whether a given tool helps or hurts is an empirical question; the model points to the quantities that settle the answer rather than guessing it.

Blindness is itself a choice the journal makes. If the screen sees who the author is and reacts to affiliation or prominence, as recent AI experiments suggest (Pataranutaporn et al. 2025), its error rates have to be tracked group by group, $(\alpha_g,\beta_g)$. Section 5 instead isolates the indirect price effect that survives when the journal hides pedigree from both expert and scalable review. Direct bias in the evaluator would be a further channel on top of it.

# Conclusion

Does a journal that cannot review everything protect the value of its stamp by rejecting what it cannot examine? Not always. Strict verification keeps the stamped pool clean at every share of good work. Yet when the screen sorts well enough, and once good work is common enough, the strict stamp is worth less than the noisier scalable one. The line between the two cases is a single crossing in the share of good work, which the model gives in closed form, and the model also says when the screen is too weak for that line to be reached at all. Nor is the screen a fixed alternative. Because scalable evaluation certifies by rule, authors who hold the same rule can pass it, and in every equilibrium where some pay to do so and some do not, the scalable premium equals the display fee plus the cost of fixing, made larger because fixing pays off only in the papers that reach the screen. When fixing is cheap enough, the screen certifies everything it reads and the comparison reduces to the clean benchmark: strict verification gives the more valuable stamp exactly when fewer than half the papers are good.

The three thresholds are separate quantities. At the illustrative parameters used throughout, review reaching one paper in four and a screen passing three good papers in four and one bad in five, they fall in a strict order: the premium crossing at a good-work share of 0.410, the erosion threshold at 0.580, the pedigree threshold at 0.711. A journal can then give the more valuable stamp under scalable evaluation, see that premium cut by authors fixing their papers, and still be the rule that narrows the pedigree gap, all at once. The order depends on the parameters; the point is that the three comparisons need not line up.

The rule also sets how the market rewards pedigree. Even when review is blind, the two rules create different unstamped pools. A second closed-form threshold says when strict verification produces the wider pedigree gap among unstamped papers and when scalable evaluation does. And two groups on opposite sides of the premium crossing value the stamp more under opposite rules. So rationing expert attention falls on some authors more than others, even when no one is treated differently on purpose.

The results revise three beliefs. A journal that keeps its stamp scarce by rejecting what it cannot read is not thereby protecting the stamp’s value; wherever the crossing lies inside the range, there are shares of good work at which it is lowering it. Blind review does not settle what pedigree is worth; the rule for the overflow does. And a journal that adopts a well-tested screen has not bought a tool with fixed error rates; it has entered an equilibrium in which its own authors’ choices set those rates, and in which, whenever some authors game the screen and others do not, its verdict is worth exactly what getting past it costs. The third belief matters most for the debate about adopting these tools: the accuracy a screening tool shows in trials need not be the accuracy, or the value, it keeps once everyone can use it.

Taken together, the results separate three properties of a certifier. The purity of its stamped pool, the chance a stamped paper is good, depends on that pool alone. The value of its stamp compares the stamped and unstamped pools. The market reward to pedigree compares visible author groups within those pools. A review rule changes all three, and they need not rank institutions the same way. The scarce input throughout is the messy one. Expert judgment is the resource the journal cannot scale, and it is also the one form of evaluation an author cannot pass in advance: when some authors game a rule-based screen and others do not, its stamp is priced by the cost of the gaming, and no gaming cost exists for judgment. The three thresholds say how institutions divide the consequences of that scarcity.

That separation is why the argument reaches beyond journals, to any institution built the same way: one pooled public stamp, a comparison pool of those it turns away, and expert attention too scarce to reach everyone. Grant panels, hiring committees, accreditation bodies and rating agencies often share that structure, and each rations the expert attention behind the stamp. Each has the same two options for the applications it cannot reach, and each is judged in public by how clean its approvals look. The model says that this standard can misrank them, because the pool an evaluator turns away is priced too; that any check an institution can run by rule, applicants can in time pass by rule, so the price of a certificate built on rule-based checks can equal the cost of passing them rather than the quality of what passes; and that a certifier can examine every applicant blind to who they are and still change what an applicant’s affiliation is worth. Rationing expert attention is therefore not a back-office decision that leaves the market untouched. It sets what a credential is worth, and what an author’s affiliation is worth to those who do not hold one.

The results hold for a fixed batch of completed papers, one public stamp, and competitive pricing on what the market can infer. The pedigree result also needs review that is blind to the author’s group. If the journal reveals which route a paper took, readers price the two routes separately and the pooling the results depend on is gone. If submitting is costly, the two rules attract different sets of authors, and near the crossing that change in who submits can reverse the ranking. If the evaluator reacts to pedigree directly, group-specific error rates add a separate channel. The results also treat the uncertified pool as terminal: a paper rejected for capacity stays in the comparison pool rather than moving on to certification elsewhere, and where it is recertified at another venue the outside pool that prices the stamp is different and the institutional reach of the results narrows. None of these price comparisons is a ranking of welfare or fairness.

What would settle where real institutions stand relative to the crossing is a paired-assessment study. The same manuscripts would be run through both a scalable screen and an independent expert review; treating that expert review as the gold standard, the pairs pin down $(\pi_g,\alpha,\beta)$ within each pedigree group, and editors’ own records fix the coverage $p$. RePEc could supply a population of economics papers to draw from. Publication outcomes on their own will not do, because a paper rejected for lack of capacity need not reveal how an expert would have judged it. Such a study would pin down $(\pi_g,\alpha,\beta)$ and the coverage $p$, but not how rejected papers come to populate the market’s comparison pool, the engine of the main result; tracking where capacity-rejected papers end up is a separate empirical step. Until that evidence exists, the model’s message is conditional but exact: to judge a crowded certifier, one has to price both the pools its rule creates and the groups that fill them.

# Proofs

*Proof of Lemma [1](#lem:premium).* Bayes’ rule gives
$$
P_C=\frac{\pi x_H}{m},\qquad
 P_N=\frac{\pi(1-x_H)}{1-m}.
$$
Subtracting and using $m=\pi x_H+(1-\pi)x_L$ yields equation [\[eq:premium\]](#eq:premium). ◻

*Proof of Lemma [2](#lem:demand).* A stamp-eligible author earns $P_C-f$ by displaying and $P_N$ by declining, so she strictly displays when $f<\Pi$. Not submitting also yields $P_N$ because applications are private. Submission followed by optimal display has expected gain $s(\theta_i)(\Pi-f)>0$. Under strict review $s(\theta_i)=p\theta_i>0$; under scalable evaluation it is weakly larger. At $f=\Pi$, the relevant choices are weak, making $\Pi$ the supremum strictly sustainable price. ◻

*Proof of Proposition [1](#prop:strictness).* Substitute equations [\[eq:strict\]](#eq:strict) and [\[eq:scale\]](#eq:scale), multiply by their positive denominators, and collect terms. The sign of the difference is the sign of $K$. If $\alpha>\beta$, then $d>p$, and
$$
K_\pi=-2cd-2d(d-p)\pi<0
$$
when $\beta>0$. Solving the quadratic and rationalising its positive root gives equation [\[eq:root\]](#eq:root). If $\beta=0$, then $c=0$ and $K=-d(d-p)\pi^2<0$. For attainability, observe that $K(0)=c(1-c)>0$ and
$$
K(1)=(1-p)\{(1-p)\beta-\alpha[p+(1-p)\alpha]\}.
$$
The decreasing function therefore crosses inside $(0,1)$ exactly when equation [\[eq:attainability\]](#eq:attainability) holds. ◻

*Proof of Corollary [1](#cor:performance).* Equations [\[eq:dxh\]](#eq:dxh) and [\[eq:dxl\]](#eq:dxl) follow by differentiating the two posterior means. Increasing $\alpha$ raises $x_H^S$ and therefore $\Pi_S$ at every prior; increasing $\beta$ raises $x_L^S$ and lowers $\Pi_S$. At an interior crossing, Proposition [1](#prop:strictness) implies that $\Pi_R-\Pi_S$ crosses zero from above. The implicit-function theorem gives the two signs. ◻

*Proof of Proposition [2](#prop:pedigree).* Blind review implies $\mathop{\mathrm{Pr}}(C\mid q,b)=\mathop{\mathrm{Pr}}(C\mid q)$, so Bayes’ rule applies separately within each pedigree cell. Equation [\[eq:unstamped\]](#eq:unstamped) gives
$$
U(\pi_B;\ell)-U(\pi_0;\ell)
 =\frac{\ell(\pi_B-\pi_0)}
 {[1-(1-\ell)\pi_0][1-(1-\ell)\pi_B]}.
$$
Multiplying $W_R-W_S$ by its positive denominators leaves the sign of
$$
(\ell_R-\ell_S)
 \{(1-\pi_0)(1-\pi_B)-\ell_R\ell_S\pi_0\pi_B\}.
$$
Because $\ell_R>\ell_S$, the expression is positive exactly when
$$
\sqrt{\frac{\pi_0}{1-\pi_0}
             \frac{\pi_B}{1-\pi_B}}
 <\frac{1}{\sqrt{\ell_R\ell_S}}.
$$
Applying the increasing logistic transformation gives equations [\[eq:pedigreesign\]](#eq:pedigreesign) and [\[eq:pedigreethreshold\]](#eq:pedigreethreshold). The denominator of $\widehat\pi$ is one plus a positive term. Increasing $\alpha$ reduces that term, while increasing $\beta$ raises it. For $p$, set $u=1-p$. The same term becomes $u\sqrt{(1-\alpha)/(1-u\beta)}$, which is strictly increasing in $u$ and therefore strictly decreasing in $p$. This proves equation [\[eq:pedigreecomparative\]](#eq:pedigreecomparative). ◻

*Proof of Corollary [2](#cor:groupdisagreement).* Proposition [1](#prop:strictness) states that $\Pi_R(\pi)>\Pi_S(\pi)$ below an interior $\pi^*$ and that the inequality reverses above it. Evaluating the two group-specific premiums at $\pi_0<\pi^*<\pi_B$ gives equation [\[eq:groupdisagreement\]](#eq:groupdisagreement). ◻

*Proof of Proposition [3](#prop:erosion).* Describe repair behaviour by the pattern $(r_H,r_L)\in[0,1]^2$, the shares of failing-mark high- and low-quality papers repaired. The certification rates are
$$
x_H=p+(1-p)\bigl[\alpha+(1-\alpha)r_H\bigr],\qquad
 x_L=(1-p)\bigl[\beta+(1-\beta)r_L\bigr],
$$
and Lemma [1](#lem:premium) gives the premium $\Pi(r_H,r_L)$. (i) Strict verification rejects every unreviewed paper at every mark, and a reviewed paper is judged on its quality, which repair does not change. (ii) In such an equilibrium some failing-mark author weakly prefers repairing and some weakly prefers not. The gain from repair, $(1-p)\max\{\Pi-f,0\}$, is common to all failing-mark authors, so both weak preferences hold for every one of them: indifference, $\kappa=(1-p)(\Pi-f)$, which rearranges to the identity displayed in part (ii). Reallocations of repair across indifferent authors that hold the premium at this level preserve equilibrium, so which authors repair is not identified, while the premium is. (iii) By equations [\[eq:dxh\]](#eq:dxh) and [\[eq:dxl\]](#eq:dxl), $\Pi$ is strictly increasing in $x_H$ and strictly decreasing in $x_L$, so its minimum over patterns is at $(r_H,r_L)=(0,1)$:
$$
\Pi^{\min}=\frac{\pi(1-\pi)\,d_w}{m_w(1-m_w)},\qquad
 d_w=p-(1-p)(1-\alpha),\qquad
 m_w=\pi\bigl[p+(1-p)\alpha\bigr]+(1-\pi)(1-p).
$$
Suppose $\kappa<(1-p)(\Pi^{\min}-f)$. A no-repair equilibrium requires $\kappa\geq(1-p)[\Pi(0,0)-f]$ and a partial-repair equilibrium requires $\kappa=(1-p)[\Pi(r_H,r_L)-f]$; both right-hand sides are at least $(1-p)(\Pi^{\min}-f)$, which exceeds $\kappa$, a contradiction. Full repair is an equilibrium because $(1-p)[\Pi(1,1)-f]\geq(1-p)(\Pi^{\min}-f)>\kappa$. At full repair every overflow paper is certified, which is the transparent benchmark of Section 4, equation [\[eq:half\]](#eq:half). ◻

The threshold $\pi^u$ of Section 6 compares the intact screen with unfiltered overflow. Applying the argument of Proposition [1](#prop:strictness) to this pair of technologies and dividing the resulting expression by the positive constant $p$ leaves the sign of
$$
J(\pi)=d(1-p)-c(1-c)+2d(c-1+p)\,\pi+d(d-p)\,\pi^2,
$$
whose derivative $2d(1-p)[(\alpha-\beta)\pi-(1-\beta)]$ is strictly negative on $(0,1)$ when the screen is not trivial. Full repair lowers the premium exactly while $J(\pi)>0$. When $J(0)>0>J(1)$, the threshold $\pi^u$ is the unique root of $J$ in $(0,1)$, the smaller root of the quadratic when $\alpha>\beta$; at $p=0.25$, $\alpha=0.75$ and $\beta=0.20$ it equals $0.580$.

# Robustness and boundaries

## Two noisy classifiers

Perfect intensive review is useful for the single-crossing result, but the posterior representation does not require it. For regime $j\in\{R,S\}$ write $c_j=x_{Lj}$ and $d_j=x_{Hj}-x_{Lj}>0$. Then
$$
\begin{align}
 \operatorname{sign}(\Pi_R-\Pi_S)=\operatorname{sign}\{&
 d_Rc_S(1-c_S)-d_Sc_R(1-c_R) \notag\\
 &+2d_Rd_S(c_R-c_S)\pi
 +d_Rd_S(d_R-d_S)\pi^2\}. \label{eq:arbitrary}
\end{align}
$$
To obtain this expression, apply Lemma [1](#lem:premium) with $m_j=c_j+\pi d_j$ and expand $d_Rm_S(1-m_S)-d_Sm_R(1-m_R)$. Two arbitrary binary classifiers can generate at most two isolated interior crossings unless their premiums coincide. The assumption that intensive review is perfect sharpens this to at most one isolated crossing.

## Targeted intensive review

Suppose a pre-review signal assigns intensive review with probabilities $r_H$ and $r_L$ for high- and low-quality papers. Strict verification has $(x_H^R,x_L^R)=(r_H,0)$, whereas scalable evaluation has
$$
x_H^S=r_H+(1-r_H)\alpha,\qquad
 x_L^S=(1-r_L)\beta.
$$
Define $c=(1-r_L)\beta$ and $d=x_H^S-x_L^S$. Direct substitution gives
$$
\begin{equation}
 \operatorname{sign}(\Pi_R-\Pi_S)=\operatorname{sign}
 \{c(1-c)-2cd\pi+d(r_H-d)\pi^2\}. \label{eq:targeted}
\end{equation}
$$
If
$$
(1-r_H)\alpha\geq(1-r_L)\beta,
$$
then $d\geq r_H$ and the expression in braces is weakly decreasing in $\pi$. Unless the two regimes coincide, the one-crossing result survives. If the condition fails, a global one-crossing claim is false in general.

## Continuous quality

Let $q$ have any integrable distribution and let $x(q)=\mathop{\mathrm{Pr}}(C\mid q)$, with $m=\mathop{\mathrm{\mathbb E}}[x(q)]\in(0,1)$. Then
$$
\begin{equation}
 \mathop{\mathrm{\mathbb E}}[q\mid C]-\mathop{\mathrm{\mathbb E}}[q\mid N]
 =\frac{\mathop{\mathrm{Cov}}(q,x(q))}{m(1-m)}. \label{eq:covariance}
\end{equation}
$$
Indeed, the difference between $\mathop{\mathrm{\mathbb E}}[qx(q)]/m$ and $\{\mathop{\mathrm{\mathbb E}}[q]-\mathop{\mathrm{\mathbb E}}[qx(q)]\}/(1-m)$ equals the right-hand side. The binary model is therefore the pass–fail version of a general covariance identity.

## Selective entry

Let submitting cost $k>0$ and private assessments have distribution $F$. For a candidate cutoff $t$, authors with $\theta\geq t$ submit. Define
$$
M_C(t)=\int_t^1s(\theta)\,dF(\theta),\qquad
 Q_C(t)=x_H\int_t^1\theta\,dF(\theta),\qquad
 \bar\theta=\int_0^1\theta\,dF(\theta).
$$
The premium is
$$
\begin{equation}
 \Pi(t)=\frac{Q_C(t)}{M_C(t)}
 -\frac{\bar\theta-Q_C(t)}{1-M_C(t)}, \label{eq:entrypremium}
\end{equation}
$$
and an interior cutoff satisfies
$$
\begin{equation}
 s(t)[\Pi(t)-f]=k. \label{eq:entrycutoff}
\end{equation}
$$
With fixed intensive-review capacity $A$, coverage becomes $p(t)=\min\{1,A/[1-F(t)]\}$. Holding the net premium fixed, strict verification gives low-assessment authors a smaller chance of certification and therefore induces stronger positive selection. This composition effect coexists with the baseline outside-pool effect and may reverse its ranking near the zero-cost crossing. The main proposition should consequently be read as the direct certification effect for a fixed completed-paper cohort, not as an unconditional ranking of optimal journal policies.

# Data availability

This article is a theoretical contribution and uses no empirical data. The computational scripts that verify the analytical results and generate the two figures recompute every reported quantity from the closed-form expressions in the text. They are openly available in a public repository; a persistent identifier will be added before publication.

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[^1]: Department of Economics, Stellenbosch University. Email: <johanf@sun.ac.za>.

[^2]: Many conversations have informed this paper. I particularly appreciate thoughtful discussions with Rulof Burger, Helanya Fourie, Willem Fourie, Jesse Naidoo, Matthew Olckers, Melt van Schoor and Marisa von Fintel, and the many reader comments on ourlongwalk.com on this and related issues. I chose the question, assumptions and argument. Anthropic’s Claude Code and OpenAI’s Codex assisted with derivations, drafting, literature search, computational verification and adversarial review. I reviewed every claim and remain responsible for all errors. Cite this paper as: Fourie, Johan. 2026. “The Value of Peer Review and the Reward to Reputation.” Working Paper, Department of Economics, Stellenbosch University. Earlier versions circulated as “When Cleaner Certification Is Worth Less: Peer Review and Pedigree” and “Messy Review: Certification Value and the Return to Pedigree.”