This is the paper without the mathematics: a faithful, qualifier-preserving restatement. Where the paper proves something narrow, this document says so. Read the paper for the math; read this to know what the math is for.
Think about how much willingness in the world is stuck in conditional form. I’d go to the reunion if my old roommates go. I’m in for Tuesday-night soccer if we get ten regulars and at least one goalkeeper. I’ll host the block party if three neighbors split the setup. I’d commit to the weekly childcare swap if two other families from school join. I’ll play a show in your town if forty people commit to tickets first.
Economists have names for pieces of this — public goods, assurance problems, coordination games, matching. The paper argues these are subcases of one family it calls interdependent action: situations where my willingness to act depends on who else will act, in what numbers, under what terms.
The paper’s basic object is the conditional commitment: “I will, if a qualifying set of others will.” The key word is qualifying. A Kickstarter pledge is a number added to a total — a scalar. A conditional commitment can be relational: not “if 50 people sign up” but “if these people do,” “if the group includes two drivers and someone with a permit,” “if at least ten are from my building.” Who counts matters, not just how many. It’s a node with edges, not a number.
Here’s the puzzle the paper starts from: there are institutions that clear almost everything else. Stock exchanges clear orders. Kidney exchanges clear donor chains. Dating apps clear mutual interest. There is no standard institution whose job is to clear conditional commitments. All that contingent willingness just sits there, private and wasted, and the actions it would unlock never happen.
The paper’s answer: four separate barriers, all of which had to fall at once, and removing any three isn’t enough.
The paper’s historical claim is that the first and third walls (credibility, discoverability) required inference at a scale that only recently became cheap, the second falls to mechanism design, and the fourth falls to careful legal architecture. Hence: a conditional-commitment clearinghouse is now buildable. The paper models what the best one looks like.
The platform in the model chooses three design dials:
Intuition says more is better on all three: escrow proves seriousness, precise terms prevent confusion, transparency builds trust. The paper’s central result says the opposite. In the model’s main region, the welfare-maximizing clearinghouse holds nothing, fixes nothing early, and hides the granular. Each apparent weakness is doing real work:
The qualifiers, in plain terms: this triple-minimal result holds in a specific region — authentication has to be very good, and the coalition’s “integrity” (whether the conditions really interlock) has to be middling rather than extreme — and the three dials interact, so you can’t optimize them one at a time and always get the joint optimum. The paper locates these boundaries rather than hiding them.
Suppose the platform shows everyone exactly who has committed and how close the coalition is to its threshold. Two things flow through that one display, and they pull in opposite directions.
The screening channel (transparency’s friend). Watching detailed early support helps everyone tell real coalitions from illusory ones. Genuine projects attract a different texture of early support than fake ones, and disclosure lets observers read it. More disclosure → better screening of bad coalitions. The paper makes this precise with an information measure — how much does the published count actually reveal about coalition quality? — and proves a result with a punchline you can state without math: even full disclosure doesn’t perfectly screen. Real and fake support patterns overlap, so transparency’s screening benefit has a ceiling.
The protection channel (transparency’s enemy). A detailed progress display also tells each participant whether they’re pivotal. Concretely: the neighborhood park cleanup needs twenty volunteers, the page shows nineteen committed, and you realize the cleanup — whose benefits you get either way — will happen without you. So you wait. The problem is that the eighteenth and seventeenth volunteers can run the same calculation, and a coalition that displays its own slack teaches its members to free-ride. In a “contested” market (a coalition that needs most of its potential members), revelation triggers a cascade: the comfortable members free-ride, which makes the remaining members’ commitments futile, and clearing collapses. Masking blocks this: if nobody can tell whether they’re pivotal, everyone behaves as if they are, and the coalition holds. The paper proves the collapse result exactly, and proves the masking side is not an artifact of how the model picks among multiple equilibria — a previous version of the theory had a free parameter (“how rational are people?”) that flipped the result at one end, and the current version eliminates that parameter entirely.
The bundling insight — the paper’s most distinctive idea. Here’s the structural problem: one display carries both signals. You cannot show “this coalition is real” without also showing “you, specifically, are not needed.” If a designer could split those — full quality-disclosure on one dial, zero pivotality-leakage on the other — the model says she’d max out the first and zero the second. But no single progress display can do that. The two channels are bundled in one physical dial, and the optimum of the bundled dial is interior: partial masking. (The clean version of this is a one-round theorem; over longer horizons it is supported by computation rather than proof — the paper keeps that distinction explicit.) Blur the count. Show “momentum,” not the roster. That’s why the result is “hide the granular” rather than “hide everything” or “show everything.”
The paper insists its own result is conditional, and the conditions are where the policy content lives.
If authentication fails, masking flips from protective to fraud-enabling: now the blur shields manufactured commitments instead of protecting a real coalition’s resolve. If compatibility fails, there is no real coalition to protect — the masked aggregate is just noise. So the prescription “hide the granular” is only as good as the clearinghouse’s vetting. This motivates the paper’s proposed regulatory safe harbor — model-motivated design criteria, explicitly a proposal rather than a legal conclusion — which keys legal protection to four auditable features: commitments can’t be resold, the platform holds no money, authentication is real, and small-group disclosure is controlled. The theory tells you why each prong is there.
One more wrinkle, discovered when the authors’ own conjecture failed under adversarial testing: over longer time horizons, there are parameter regions where more pivotality leakage actually helps — roughly, the threat of a leakier future makes waiting less attractive, which can re-ignite a stalled coalition. The general “zero leakage is always ideal” intuition is false. The paper records this as a new open phenomenon rather than sweeping it under the rug.
The paper’s method is worth a seminar discussion on its own. The results were developed numerics-first: build the model in code, compute everything, locate the phenomena — then prove theorems about what the computation shows, with the code as ground truth. The analytical results were then attacked by three separately run adversarial verification passes — one checking logic step by step, one hunting for numerical counterexamples inside the theorems’ own assumptions (thousands of randomized parameter draws), and one auditing whether the theorems actually support the prose claims — each run without access to the others’ findings. Every first draft, including parts of the paper itself, was corrected by this process; one conjecture was outright falsified, and the falsification is reported in the paper.
So when this companion says “proven,” it means: a formal proposition with stated assumptions, surviving that gauntlet. Where the paper couldn’t close a step, it says “conjecture” and tells you exactly what’s missing — for instance, the dynamic momentum result rests on one verified-but-unproven stepping stone, and the paper says so in the proposition statement itself. There is also a live platform (ifwishlist) whose release history mirrors the theory’s four walls, but the paper is explicit that the empirical calibration hasn’t happened yet — the measurable quantities are listed, with the predictions they would discipline.
Plain-language introduction, v1.1, June 2026. Corresponds to the
working paper’s v1 (46 pp.). The full paper: main.pdf in
this directory. Nothing in this document weakens or strengthens any
claim in the paper; where they appear to differ, the paper
governs.