| paper | Social Choice Around Decentralized Autonomous Organizations: On the Computational Social Choice of Digital Communities |
| authors | — |
| venue | AAMAS 2023 |
| filed under | voting · theory |
| judged by | gpt-5.6-luna / xhigh (triple__luna__xhigh__c2r1) |
| judge confidence | high |
| authors would recognise it | yes |
The paper contains no numbered result asserting an algorithmic or complexity property. Section 3 supports a plausible population-continuous research problem, but its objective, representation, and computational task are newly supplied by the proponent. Thus bit (a) fails under the required anchor rule.
fails bit None — no continuous question survives
There is no eligible paper result to anchor: the proposed \(L_1\) objective, type distribution \(\mu\), representation, and algorithmic task are supplied by the proponent.
fatal: True
The candidate covers only Section 3’s continuous-time ideal-trajectory proposal; it leaves constitutional evolution, multicommunal dynamics, collaboration, sampling, delegation, and markets without computational mirrors.
The paper contains no eligible anchor. It states no numbered Theorem, Lemma, Corollary, or Proposition, and gives no computational classification such as NP-hardness, membership in P, W[1]-hardness, or FPT. Its only numbered item is Remark 1, which is not a computational result. Results from cited papers cannot serve as anchors because this paper does not state them as its own named results.
The strongest positive case is therefore prospective, centred on Section 3’s explicit “continuous decision making” model. The paper already proposes voters \(v_i:[0,1]\to[0,1]\), where \(v_i(t)\) is a member’s ideal decision at time \(t\), and an aggregate trajectory \(w:[0,1]\to[0,1]\). A faithful population mirror would replace the named members by a high-multiplicity society of trajectory types.
Call the resulting problem Continuous Perpetual-Median DAO Governance. An instance consists of a finite set of complete voter types \(T=\{\theta_1,\ldots,\theta_\tau\}\), where type \(\theta_j\) has a rational piecewise-linear ideal trajectory \(v_j:[0,1]\to[0,1]\), together with rational masses \(\mu_j\ge 0\) satisfying \(\sum_j\mu_j=1\). The mass \(\mu_j\) is the fraction of DAO members of type \(\theta_j\). The decision variable is a continuous aggregate trajectory \(w:[0,1]\to[0,1]\). The task is to find \(w\) minimizing \(D_\mu(w)=\int_0^1\sum_{j=1}^{\tau}\mu_j|w(t)-v_j(t)|\,dt\), with ties resolved by choosing the smallest minimizer at each time.
This is recognisably the paper’s problem: members have ideal points changing over time, and governance must output a continuous sequence of decisions. The only additional specification is a canonical one-dimensional social-choice objective. The high-multiplicity regime could be a large DAO with millions of members but only hundreds or thousands of recurring governance types—such as users, builders, liquidity providers, grant recipients, or risk profiles sharing the same policy trajectory. Exact type equality is a modelling assumption, but it is precisely the high-multiplicity assumption rather than an objection to the mirror.
I would expect this problem to be Class A. At every time \(t\), an optimal \(w(t)\) is a weighted median of the values \(v_1(t),\ldots,v_\tau(t)\). Since the trajectories are piecewise linear, one can enumerate their breakpoints and pairwise crossings; between consecutive events their ordering is fixed, so the weighted-median type is fixed. The complete aggregate trajectory can therefore be constructed in polynomial time in the number of types, trajectory pieces, and encoding length. The discrete version with \(n_j\) members of each type is recovered by setting \(\mu_j=n_j/n\), making this a genuine high-multiplicity relaxation rather than merely “continuous time.”
This mirror covers only the paper’s Section 3 proposal. It does not claim to formalize the paper’s suggestions about constitutional evolution, liquid democracy, sampling, prediction markets, or complex collaboration. Natural follow-up questions include whether the same tractability survives dynamic masses \(\mu_j(t)\), attention or delegation constraints, conviction-style thresholds, or richer trajectory representations; those variants might produce either further Class A problems or continuum-specific hardness.
The weakest point is decisive: the authors never specify an aggregation rule, objective, input representation, or computational task. Thus this is a plausible formalization of a research direction, not a mirror of a named result in the paper. Under the programme’s strict anchor requirement, the correct verdict is consequently “no anchored case.” Under a more permissive agenda-level reading, Section 3 supplies a credible, concrete Class A mirror—but it is a proposed continuation of the paper, not a result already present in it.
The strongest negative case is procedural but decisive: this paper gives us no eligible computational result to continuize. It is a six-page blue-sky agenda. Apart from Remark 1, it contains no numbered theorem, lemma, proposition, or corollary, and it defines no computational input, output, decision problem, optimization objective, approximation guarantee, or complexity classification. Its claims are research opportunities—“what is needed,” “may be adequate,” and “no works consider”—rather than results. Under ChoCo’s anchor requirement, there is therefore no paper result whose continuous mirror can be evaluated.
Section 3 does not change that. Its actual model keeps a finite, named voter set \(V=\{v_1,\ldots,v_n\}\) and makes time continuous: each voter supplies a trajectory \(v_i:[0,1]\to[0,1]\), and an unspecified aggregation mechanism outputs \(w:[0,1]\to[0,1]\). The proponent’s distribution \(\mu\), piecewise-linear type representation, \(L_1\) objective, and tie-breaking rule are all newly invented. They produce a reasonable research problem, but not a mirror of a result in this paper.
The proposed weighted-median formulation also illustrates the underdetermination. With
\[ D_\mu(w)=\int_0^1\sum_j\mu_j|w(t)-v_j(t)|\,dt, \]
the problem separates completely across time. The solution is simply the pointwise weighted median of the trajectories. That is a legitimate high-multiplicity problem, but it removes nearly everything the paper identifies as DAO governance: proposals, status-quo change, participation, thresholds, evolving membership, delegation, attention, and path dependence. It is a continuum of independent one-shot aggregations indexed by time.
A stronger dynamic formulation could add changing masses, switching costs, conviction thresholds, delegation, or temporal regularity. But then the paper supplies no rule selecting the state variables, objective, feasibility constraints, or input representation. Such a model would be a new optimal-control or dynamic social-choice project inspired by one paragraph, not a continuization of a computational result. This is not an objection that the answer might be easy or hard; it is the more basic point that the paper never specifies the question.
The high-multiplicity story is not intrinsically implausible. Large DAOs may contain recurring cohorts with identical represented trajectories, so one could sensibly study such a model. But that establishes the possibility of future work, not an anchor in this paper. The other sections fare no better: constitutional evolution is discussed axiomatically, collaboration is described as an unmet need, and sampling, delegation, and markets are proposed as directions without computational results.
The honest limitation is that the universal substantive claim—no worthwhile continuous project could ever arise from this paper—is too strong. The weighted-median construction is a coherent Class A candidate under a permissive agenda-level reading. The defensible verdict is narrower and stronger: this paper has no anchored continuous mirror under the programme’s rules; the apparent mirror is a new formalization of an underspecified research direction.
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.