| paper | d4-journals-jet-2015-0063 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | medium |
| authors would recognise it | no |
Proposition 2's backward recursion supplies a computable optimal stopping policy, making it the strongest computational anchor even without a stated complexity bound. In a society represented by known masses of preference and cost types, aggregate preferences are fixed, so consultation no longer reveals the finite random vote margin; atomless voters also cannot affect the outcome individually. This changes the paper's information and incentive problem, so the proposed continuum version does not preserve an anchor.
fails bit b-changes — the continuum limit changes the question
The proposed extension targets Proposition 2's stopping policy and Proposition 3's incentive compatibility, but no result has a surviving continuous-population mirror; it leaves the other propositions and the second-best problem in Section 6 without a counterpart.
I don’t see a qualifying computational anchor in this paper. Its numbered results are economic and mechanism-design results, not claims that a computational problem is in P, NP-hard, or belongs to another complexity class.
The closest candidate is Proposition 2, proved in the paper: when \(p=1/2\) and participation costs decrease in the consultation order, there is a first-best procedure that consults voters in increasing order of cost and stops when \(|m(h)|\geq\mu(r(h))\), for a weakly increasing threshold \(\mu\) determined by the costs of the remaining voters. Proposition 3, also proved here, says that every canonical first-best procedure is incentive compatible in that case, and that a minimal one has a unique sequential equilibrium. These are substantive results, but neither asserts a computational complexity bound for optimizing the procedure. The recursion in Proposition 2’s proof does not by itself make it a named “in P” result.
A high-multiplicity setting is imaginable: a large referendum population grouped by preference and participation-cost types, with the planner choosing a sequential participation policy to maximize expected welfare. But that would be a proposed extension. The paper’s voters remain finite and individually ordered, and its results do not establish the computational question that a continuous mirror would need to anchor. So I would give no per-anchor continuous problem or predicted complexity class for this paper.
The strongest negative case is that this paper has no named computational result to mirror. Propositions 1–4 characterize first-best procedures and their incentives; Section 6 offers a conjecture about the second-best problem. Proposition 2 comes closest to an algorithmic anchor: it gives a recursive stopping rule over the discrete state \((r,m)\). But the result is a structural characterization, not a complexity claim about a computational problem.
The proposed large-referendum mirror runs into a more basic problem. If the society is a known distribution over preference and cost types, then the aggregate preference shares are already known. With independent private preferences, a continuum fixes those shares at their probabilities. The finite model’s random vote margin—the information that makes sequential consultation valuable—disappears. A positive mass of voters reveals its known composition; an individual of zero mass cannot change the aggregate decision. For \(p>1/2\), the planner can choose \(A\) immediately; for \(p=1/2\), consultation cannot improve aggregate welfare and still incurs costs. Either way, Proposition 2’s stopping problem collapses.
Proposition 3’s incentive result also depends on finite voters having a chance to affect the outcome. In an atomless society, a single voter’s action has zero effect, so a positive-cost voter has no individual incentive to participate. Treating a whole cohort as one decision-maker restores influence only by changing the strategic unit; that is no longer the paper’s individual incentive-compatibility question.
A latent common state, as in the paper’s correlated-types discussion, is the most plausible rescue. But with deterministic continuum shares conditional on the state, consulting any positive mass can reveal the state perfectly. The planner can then shrink that mass toward zero, making information effectively free and potentially leaving no optimal positive consultation mass. Adding sampling noise, indivisible cohorts, or a scaling limit could prevent that collapse, but each adds a new source of uncertainty or discreteness. Such a model might merit study on its own; it does not supply a continuous-population mirror of the paper’s named results. The negative case is strongest for these anchors, though it cannot rule out every worthwhile extension of costly voting.
The adversarial triple: the proponent anchors on up to three named results; the opponent sees that case and must defeat every anchor; the judge decides which case convinced it. These are the pipeline’s own outputs, generated by tools/triple_run.py — no human edited them. The paper’s own text is not reproduced here beyond the quoted statement above.