Worked Example — Impact Markets for Science

Part I · The Engine — Chapter 3

The mechanism is abstract; let's run one question all the way through it. The setting is the one the idea was born in: deciding which scientific work matters, so funding can follow.

The setting

A top-tier venue does two separable things:

• Dissemination — spreading the work. Increasingly served by other channels.
• Credentialing — the prestige of acceptance, which is the real prize. Prestige is society's signal for "high odds of future impact," used to route funding and resources.

But prestige is a retroactive, lossy proxy: things become prestigious because they turn out useful. So why not estimate the underlying quantity — future impact — directly, with the engine from the previous chapter, and keep prestige only as a fallback?

Map the roles:

One question, start to finish

Question $q$: "Will resolver $j$ judge paper X to be high-impact by 2030?" Outcome space ${\Omega }_q=\{\text{yes},\text{no}\}$.

2025 — forecasts accumulate. The crowd is skeptical; the consensus (reference) belief sits at $p^{\text{ref}}=0.30$. Three forecasters act:

• Alice has read the paper closely and thinks it's a sleeper hit. She publishes $p_{\text{Alice}}=0.80$, early.
• Bob just echoes the crowd: $p_{\text{Bob}}=0.30$.
• Carol is a reflexive contrarian and bets it flops: $p_{\text{Carol}}=0.10$.

All three forecasts are timestamped and tamper-evident, so "Alice said this in 2025" is later unforgeable.

2030 — a resolver decides. Resolver $j$, now with five years of citations, downstream results, and comparison papers, privately declares the verdict: yes, high-impact. (Had the evidence been hopelessly muddy, $j$ could have simply discarded the question and paid no one.)

Scoring. Using the log score $S(p,\omega )=\ln p(\omega )$ with outcome = yes, each forecaster's reward contribution is $S(p_i)-S(p^{\text{ref}})$:

Alice is paid handsomely for being right and different from the crowd. Bob, who only echoed consensus, earns nothing — he added no information. Carol, who was different and wrong, is penalized.

The penalty is symmetric and keeps confidence honest. Had the verdict been no, Alice's confident 0.80 would have scored $\ln (0.20)-\ln (0.70)=-1.25$ — a large loss. You are only rewarded for moving belief toward what the resolver eventually concludes.

Reputation and payout. Summed over many questions, Alice's reputation with this resolver is $R_{\text{Alice},j}={\sum }_q{\rho }_{\text{Alice},j,q}$. Resolver $j$ then splits its budget $B_j$ across forecasters in proportion to their reputation — Alice gets a large share, Bob ~none, Carol less than she started with.

Two phases, because reputation has a cold start

Before anyone has a track record, there is nothing to weight. So the system runs in two phases:

1. Bootstrap. A play-money market with tokens handed to reviewers, to seed forecasts and begin accumulating reputation before real budgets are at stake.
2. Allocation. Once reputations exist, retroactive scoring against resolvers' eventual impact verdicts converts forecaster reputation into real credentialing and funding weight.

What this example deliberately does not claim

The construction's own non-goals, stated honestly:

• It does not measure non-observable impact — only impact that is, for the targeted cases, publicly and quantitatively observable.
• It does not settle whether prestige should exist.
• It does not claim to align science with societal good.

It assumes only that impact is observable for the cases it targets, and that prestige ought to track it. That narrow scope is what makes it tractable.

The same three roles and the same scoring reappear in governance (resolvers = voters' delegated fact-finders, candidates = policies) and, more surprisingly, inside the network itself — which is where Part II goes.