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The No-show Paradox in Single Transferable Vote under One-dimensional Preferences

T0 review · 0 major / 2 minor · reviewed 2026-06-27 · grok-4.3

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Pith's one-line read Single Transferable Vote is vulnerable to the group no-show paradox under one-dimensional voter preferences, unlike Condorcet rules.

desk verdict STV shows clear vulnerability to group no-show under 1D preferences via new sufficient conditions, while Condorcet rules stay immune. read the letter →

arxiv 2606.12785 v1 pith:HA5MHFBN submitted 2026-06-11 cs.GT

Farhad Mohsin This is my paper · ORCID
classification cs.GT
keywords groupno-showparadoxsingletransferablevoteone-dimensionalpreferencessingle-peakedsingle-crossingvotingparadoxescomputationalsocialchoice
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper shows that under preferences that are one-dimensional, such as single-peaked or single-crossing, groups of voters can benefit from not showing up to an STV election. This happens because the elimination order in STV can shift favorably when certain voters abstain. Sufficient conditions for this to occur are identified and shown to be prevalent in these models. Simulations indicate the effect strengthens with more candidates and is driven by voters at the ends of the spectrum. Condorcet methods avoid this issue completely in the same preference domains.

What carries the argument

Sufficient conditions for the group no-show paradox in STV based on the structure of one-dimensional preferences and the sequential elimination process.

What would settle it

A synthetic or real preference profile that is single-peaked but shows no occurrence of GNSP for STV under the identified conditions.

Watch

Extended reading notes

Core claim

Under 1D-Euclidean, single-peaked, and single-crossing preferences, STV admits the group no-show paradox under tractable sufficient conditions that become more likely as the number of alternatives increases, with voters at the extremes particularly prone to causing it through abstention.

Load-bearing premise

One-dimensional preference models accurately represent the settings where GNSP vulnerability should be evaluated.

Editorial extensions

If this is right

  • STV elections in spatial or linear preference settings are susceptible to strategic abstention by groups.
  • The vulnerability grows with the number of candidates.
  • Extreme voters are the key actors in triggering the paradox.
  • Condorcet-consistent voting rules remain immune to GNSP in these domains.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Designers of voting systems for one-dimensional issues might prefer Condorcet rules over STV to avoid this form of abstention paradox.
  • Empirical studies could check how closely real preference data matches the sufficient conditions identified.
  • Similar vulnerabilities may exist in other sequential elimination rules under restricted preferences.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 2 minor

Summary. The paper claims that under one-dimensional preference models (1D-Euclidean, single-peaked, single-crossing), STV is highly vulnerable to the group no-show paradox (GNSP). It theoretically identifies tractable sufficient conditions for GNSP under STV in these domains (in contrast to the impossibility result for Condorcet rules), and uses synthetic experiments to show that the conditions are prevalent, with voters at the extremes particularly likely to trigger GNSP by abstaining and with likelihood increasing in the number of alternatives.

Significance. If the sufficient conditions and prevalence results hold, the finding is significant for social choice theory: it shows that STV remains susceptible to GNSP even inside the structured domains routinely used to model preferences, while Condorcet rules are immune. The work supplies concrete, checkable conditions and demonstrates their frequency via synthetics drawn from the same classes, advancing the literature on when paradoxes arise under domain restrictions. Credit is given to the prior impossibility results for Condorcet rules.

minor comments (2)
  1. [Abstract and §1] The abstract and introduction use 'highly vulnerable' without an explicit quantitative benchmark; a short definition or threshold (e.g., frequency above X% in the reported experiments) would improve precision.
  2. [Experiments section] The generation process for the synthetic 1D-Euclidean, single-peaked, and single-crossing profiles (including any distribution parameters or sampling method) is referenced but not fully detailed; expanding this in the experimental section would aid reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No major comments were raised in the report.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity detected

full rationale

The paper's central results consist of theoretical identification of sufficient conditions for GNSP under STV within the mathematically defined classes of 1D-Euclidean, single-peaked, and single-crossing preferences, plus synthetic experiments drawn from those same classes. The contrast with Condorcet rules is explicitly attributed to prior literature rather than re-derived internally. No equations, definitions, or experimental protocols reduce a claimed prediction or uniqueness result to a fitted parameter, self-citation chain, or renaming of the input domain. The derivation chain is therefore self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities. The central claim implicitly rests on the modeling choice that one-dimensional preference structures are the appropriate test domain and that the synthetic generation process faithfully samples from those structures.

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Cite this review

Pith. "Pith review of The No-show Paradox in Single Transferable Vote under One-dimensional Preferences." pith.science (2026). https://pith.science/paper/HA5MHFBN

@misc{pith2026260612785,
  author       = {Pith},
  title        = {Pith review of: The No-show Paradox in Single Transferable Vote under One-dimensional Preferences},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HA5MHFBN}},
  note         = {Machine review of arXiv:2606.12785}
}
read the original abstract

The group no-show paradox (GNSP) occurs when a group of agents abstaining from voting can make the new winner more preferred to them. Previous work has suggested that even for voting rules susceptible to this paradox, it is a rare occurrence in real elections and under various assumptions. However, we find that under one-dimensional preference models such as 1D-Euclidean, single-peaked, or single-crossing preferences, Single Transferable Vote (STV), a popular runoff rule, is highly vulnerable to GNSP. This is in stark contrast to Condorcet rules, another family of rules susceptible to GNSP, where the paradox cannot occur under these one-dimensional preferences. We theoretically identify tractable and prevalent sufficient conditions for GNSP to occur for STV under one-dimensional preference models. Through our theoretical results and experiments with synthetic preference profiles from these domains, we demonstrate that voters at the extremes of the 1D spectrum are particularly likely to cause GNSP by abstaining. Furthermore, the likelihood of occurrence increases substantially as the number of alternatives grows.

Figures

Figures reproduced from arXiv: 2606.12785 by the authors.

Figure 1
Figure 1. Illustration of STV rounds with contiguous voting regions for each alter [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Showing the top-preference interval for each alternative and the thresholds [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Likelihood of GNSP for STV for increasing number of alternatives (a) [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Likelihood heatmap of winner transitions caused by GNSP for STV. (a) [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: Likelihood heatmap of winner transitions caused by GNSP for STV for [PITH_FULL_IMAGE:figures/full_fig_p021_5.png]
Figure 6
Figure 6. Figure 6: STV winner empirical distribution for single-peaked preferences (Walsh [PITH_FULL_IMAGE:figures/full_fig_p022_6.png]
Figure 7
Figure 7. Figure 7: STV winner empirical distribution for single-peaked preferences (Walsh [PITH_FULL_IMAGE:figures/full_fig_p022_7.png]
Figure 8
Figure 8. Figure 8: Likelihood heatmap of winner transitions caused by GNSP for STV for [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Reviewed June 27, 2026 · model on record in the stance chip above.