| paper | Control in Computational Social Choice |
| authors | Jiehua Chen, Joanna Kaczmarek, Paul Nüsken, Jörg Rothe, Ildikó Schlotter, Tessa Seeger |
| venue | IJCAI 2025 |
| filed under | voting · bribery-control |
| judged by | gpt-5.6-luna / xhigh (triple__luna__xhigh__c2r1) |
| judge confidence | high |
| authors would recognise it | yes |
The proposed Borda–CCAV mass-addition problem is a direct, plausible continuous mirror, and the authors would likely recognise it. However, the paper contains no numbered theorem, lemma, corollary, or proposition asserting a computational result; its complexity claims appear in tables, prose, and challenges. Therefore bit (a) fails under the explicit screening rule.
fails bit a — no named computational result to mirror
The proposed mirror covers only Borda CCAV, leaving the survey's other voting, allocation, cooperative-game, matching, group-identification, budgeting, judgment-aggregation, and opinion-diffusion results untreated.
Strictly under your anchoring rule, this paper supplies no eligible anchor. It contains no numbered Theorem, Lemma, Corollary, or Proposition asserting a complexity result. Its claims appear in tables, prose, and numbered Challenges. For example, Table 1 marks Borda CCAV as resistant, \(R^{\S}\), attributing the result to Russel [2007], but that is not a numbered theorem proved in this paper. Thus I cannot honestly present a compliant anchored case from this text.
That is a limitation of the paper’s format, not evidence against a mirror. The strongest latent positive case would lead with the Table 1 Borda-CCAV entry.
A natural continuous version is Borda Continuous Control by Adding Voter Mass. An instance consists of candidates \(C\), explicit ranking types \(T\subseteq S_C\), current masses \(\mu_t\), available unregistered masses \(\nu_t\), a preferred candidate \(c^\star\), and a rational budget \(\kappa\). Choose \(x_t\) satisfying \(0\le x_t\le\nu_t\) and minimize \(\sum_t x_t\), subject to \(\sum_t x_t\le\kappa\) and \(\mathrm{sc}_{\mu+x}(c^\star)\ge \mathrm{sc}_{\mu+x}(d)\) for every \(d\in C\). The normalized post-addition society is \((\mu+x)/(1+\sum_t x_t)\), but normalization does not affect the Borda winner.
This is recognisably the paper’s CCAV problem: the candidates, complete rankings, Borda rule, preferred winner, and voter-addition control action are unchanged. Only the high-multiplicity regime changes the unit of action from selecting named voters to adding mass of interchangeable voter types. A national election with millions of voters, a small candidate set, and ballots concentrated among a moderate number of recurring rankings is a credible regime; \(\mu_t\) and \(\nu_t\) represent fractions of current and persuadable populations.
For explicitly represented types, the problem is a linear program and is therefore expected to be tractable. The discrete NP-hardness can disappear because the \(0/1\) subset-selection difficulty is replaced by divisible mass allocation. With an implicit type space, the remaining issue is a pricing problem over rankings; for Borda, the relevant score-difference optimization is structurally simple. This would be a Class A mirror, not a claim that the paper’s original NP-hardness was erroneous.
Its weakest point is fidelity to the cited hardness result: CCAV’s reductions may exploit individually selectable voters with distinct roles, whereas the continuous mirror permits fractional selection among repeated types. The mirror is convincing only as a high-multiplicity version of CCAV, not as a relaxation preserving every finite-instance feature. Since the survey never states the result as a numbered theorem, however, this remains a useful candidate mirror rather than a valid anchored answer under the rules given.
The decisive negative point is source discipline, not the mathematics. This is a survey, and it contains no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational-complexity result. The Borda–CCAV entry \(R^\S\) in Table 1 is a literature summary attributed to Russel [2007], not a result established by this paper; the numbered Challenges are open questions, not results. Thus the proponent has not supplied an eligible anchor at all. Under the stated screening rule, no continuous mirror can count as a mirror of a named computational result of this paper.
The proposed Borda mirror is nevertheless substantively strong. With current masses \(\mu_t\), available masses \(\nu_t\), and added mass \(x_t\), the winner constraints are linear:
\[
\sum_t (\mu_t+x_t)\bigl(s(t,c^\star)-s(t,d)\bigr)\ge 0
\]
for every opponent \(d\), with \(0\le x_t\le \nu_t\) and \(\sum_t x_t\le\kappa\). Clearing denominators recovers elections with repeated ballots, so this is a faithful high-multiplicity formulation. National elections with recurring ballot types provide a credible regime, and fractional mass is precisely the intended continuization—not a defect.
Consequently, I cannot honestly claim that Borda–CCAV has no worthwhile continuous mirror in any modelling scenario. The strongest defensible negative case is narrower but decisive: the mirror is of an externally cited table entry, not of a named computational result in this paper. If the source gate is relaxed, this paper should probably be rejected as a negative example, because the proposed mirror is a plausible Class A candidate.
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.