| paper | d4-conf-ecai-2016-0361 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The paper's named results compare manipulability across rules and characterize which rules can attain certain properties. A mass-based version of those comparisons is conceivable, but it would be a new structural question rather than a mirror of a computational result in this paper.
fails bit a — no named computational result to mirror
No result has a computational mirror; the nearest continuous analogue would extend the structural comparisons in Theorems 1–3 and Corollary 1 to mass distributions.
I don’t find a qualifying computational anchor in this paper. Theorem 1, Theorem 2, Corollary 1, and Theorem 3 are named results, but they establish structural claims about inclusion between sets of manipulable profiles and about which voting rules can be considered. None classifies a computational problem as tractable, hard, or otherwise.
There is a plausible population-level question nearby: represent complete preference types by masses \(\mu_t\), and ask whether some coalition can transfer mass to new ballots so that the winner changes in the coalition’s favor. A large electorate with relatively few ballot types is a credible regime. Theorem 2 could motivate asking whether its strict reduction in manipulable profiles survives for such mass distributions. But that would be a new structural theorem, not a mirror of a computational result in this paper; the paper supplies no algorithmic problem or complexity result to anchor it. Under the stated criteria, there is no continuous problem per eligible anchor, and no sound basis here for assigning it to classes A, B, or C.
The proponent’s own concession is decisive: this paper has no computational result to mirror. Theorem 2 is its strongest candidate, but \(M_{f^*}\subsetneq M_f\) is a structural comparison between sets of manipulable profiles. Theorem 1, Theorem 3, and the optimality corollary make similar claims about voting rules. None gives an algorithm, a complexity bound, or a computational problem whose input and output could be continuized.
The best version of the proposed mirror would represent rankings by types with masses and ask whether a coalition can shift enough mass to change the winner in its favor, or whether Condorcification still shrinks the set of manipulable societies. Those are coherent questions; fractional coalitions need not make them meaningless. But they remain new structural questions. The paper’s results quantify over voting rules and profiles as whole domains; they do not take an encoded society as input and ask for a computational answer. Turning one into a problem such as “is this rational mass distribution manipulable under rule \(f\)?” requires choosing a rule representation and an input model the paper never studies. That could start a separate complexity project, but it would not be a continuous mirror of Theorem 2.
So the negative case is strongest on scope, not on whether mass-based manipulation can be modelled. A continuous population version may be mathematically sensible, and this paper does not show that such a version is already known. It simply offers no named computational result for ChoCo’s continuization programme to extend.
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.