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arxiv: 2605.15786 · v1 · pith:KTE2HNYSnew · submitted 2026-05-15 · 💻 cs.GT

An Enriched Model of Strategic Voting under Uncertainty

Henri Surugue , S\'ebastien Destercke This is my paper

Pith reviewed 2026-05-19 18:46 UTC · model grok-4.3

classification 💻 cs.GT
keywords strategic votinguncertainty representationbelief functionsprobability setsexpected utilityconvergencegame theory
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The pith

A model of strategic voting uses probability sets and lower/upper expected utility gains to represent uncertain preferences.

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

The paper builds a strategic voting model that encodes voter preferences as sets of probabilities rather than single numbers. Voters then select actions by comparing lower and upper expected utility gains under this uncertainty. When the probability sets are specialized to belief functions, the framework simultaneously recovers many earlier models that relied on precise probabilities, simple sets, or incomplete preferences. The same machinery extends several known convergence results about strategic behavior to this wider class of representations. The result is a single setting that can describe more nuanced real-world voting situations while surfacing new consistency questions.

Core claim

The authors show that probability sets together with lower and upper expected utility gains form an expressive language for strategic voting under uncertainty. Belief functions are a special case that recovers, in one stroke, models based on probabilities, sets, and incomplete preferences. Using this language, several convergence theorems previously proved only for narrower settings now hold in the broader one.

What carries the argument

Probability sets as uncertainty representations, paired with lower and upper expected utility gains to guide strategic choices.

If this is right

  • Many existing strategic voting models become special cases inside one larger framework.
  • Convergence results from the literature extend directly to belief functions and other probability-set representations.
  • Voting scenarios with partial or imprecise information become easier to encode and analyze.
  • New theoretical questions arise about consistency when uncertainty representations are combined with strategic incentives.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Researchers could now test whether convergence speed changes when moving from precise probabilities to belief functions in simulated elections.
  • The unification may let analysts translate results proved in one uncertainty language into another without re-deriving everything from scratch.
  • Practical voting systems could use this model to recommend strategies when voter information is known to be incomplete or imprecise.

Load-bearing premise

Probability sets and lower/upper expected utility calculations can represent preferences and choices consistently enough to unify prior models without creating contradictions.

What would settle it

A concrete voting profile where the new model produces a different strategic vote than one of the recovered special cases, or where convergence fails in a setting already known to converge under probabilities.

Figures

Figures reproduced from arXiv: 2605.15786 by Henri Surugue, S\'ebastien Destercke.

Figure 1
Figure 1. Figure 1: Imprecise probability (ours) Belief functions Inner measures Necessity measures Sets (Meir & Conitzer models) Probability (Myerson’s model) [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
read the original abstract

We present a new strategic voting model where we use uncertainty representation to model preferences. Specifically, we use probability sets as uncertainty representations, together with lower and upper expected utility gains to take strategic decisions. Focusing on belief functions in particular, we demonstrate that this very expressive model includes in one sweep many existing models based on probabilities, sets or incomplete preferences. Additionally, we generalize several well-known convergence results from the literature to this broader representational setting. Furthermore, we illustrate how this model can capture more realistic scenarios for practical applications but also raises theoretical challenges.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a new model of strategic voting under uncertainty that represents beliefs via probability sets and models strategic decisions using lower and upper expected utility gains. Focusing on belief functions, it claims to unify many existing models based on precise probabilities, sets, or incomplete preferences within a single expressive framework. The work additionally generalizes several well-known convergence results from the strategic voting literature to this broader setting and discusses both practical applications and theoretical challenges raised by the enriched representation.

Significance. If the embeddings of classical models into probability sets with lower/upper EU gains preserve the original best-response structure and Nash equilibria, and if the generalized convergence results are established without hidden assumptions, the paper would provide a valuable unifying framework for strategic voting under diverse uncertainty representations. This could facilitate more realistic modeling in applications while extending existing theoretical results. The unification and generalization aspects are the primary potential contributions, provided the technical preservation of strategic properties is verified.

major comments (2)
  1. [Abstract and §3] Abstract and §3: The central unification claim—that the model 'includes in one sweep many existing models based on probabilities, sets or incomplete preferences'—requires explicit verification that the strategic best-response correspondence induced by lower/upper EU gains coincides with the classical one when the belief function reduces to a precise probability (Dirac measure). Because lower and upper expectations are non-additive, the best responses and resulting Nash equilibria may differ even in this special case; without a direct comparison of equilibria or convergence paths for the embedded models, the 'includes in one sweep' statement does not follow from representational inclusion alone.
  2. [§5] §5: The generalization of convergence results to belief functions must confirm that the proofs do not rely on additivity or other properties lost under the general lower/upper expectation operators. If the original results depend on precise probabilities and the extension introduces additional conditions or fails for some belief functions, the generalization claim would need substantial qualification or counterexample analysis.
minor comments (2)
  1. [Notation] Ensure all notation for lower and upper expected utility gains is defined consistently and introduced before its first use in strategic decision sections.
  2. [Discussion] Add a brief discussion or reference to potential inconsistencies that could arise from non-additivity when applying the model to incomplete preferences.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on the unification and generalization claims. We address each major comment point by point below, providing the strongest honest defense of the manuscript while indicating where revisions will strengthen the technical details.

read point-by-point responses

  1. Referee: [Abstract and §3] The central unification claim—that the model 'includes in one sweep many existing models based on probabilities, sets or incomplete preferences'—requires explicit verification that the strategic best-response correspondence induced by lower/upper EU gains coincides with the classical one when the belief function reduces to a precise probability (Dirac measure). Because lower and upper expectations are non-additive, the best responses and resulting Nash equilibria may differ even in this special case; without a direct comparison of equilibria or convergence paths for the embedded models, the 'includes in one sweep' statement does not follow from representational inclusion alone.

    Authors: We agree that representational inclusion alone is insufficient and that explicit verification of the induced strategic properties is required. When the belief function reduces to a Dirac measure, the lower and upper expected utility gains coincide exactly with the standard expected utility gain. As a result, the best-response correspondence, Nash equilibria, and convergence behavior are identical to the classical probabilistic model. To make this fully explicit and address the non-additivity concern in the special case, we will add a new proposition in §3 that formally proves the equivalence of best responses and equilibria for the embedded Dirac case, along with a short discussion of the resulting convergence paths. revision: yes

  2. Referee: [§5] The generalization of convergence results to belief functions must confirm that the proofs do not rely on additivity or other properties lost under the general lower/upper expectation operators. If the original results depend on precise probabilities and the extension introduces additional conditions or fails for some belief functions, the generalization claim would need substantial qualification or counterexample analysis.

    Authors: The proofs in §5 rely only on monotonicity and continuity of the lower and upper expectation operators with respect to the belief function; these properties are preserved without requiring additivity. No additional conditions are imposed beyond those in the original results, and the arguments extend directly. We will revise §5 to add an explicit remark identifying the key preserved properties and confirming their sufficiency for the generalized convergence results. We have not found belief functions where the results fail, but we would welcome specific examples from the referee for further analysis if needed. revision: partial

Circularity Check

0 steps flagged

No circularity: unification and generalization rest on explicit embeddings and external results

full rationale

The paper defines a new strategic voting model via probability sets paired with lower/upper expected-utility gains, then demonstrates that classical probability, set-based, and incomplete-preference models arise as special cases of this representation. Convergence results are generalized by direct extension of the same decision rule to the richer uncertainty class. No equation reduces a claimed prediction to a fitted parameter by construction, no load-bearing premise rests solely on self-citation, and no ansatz is smuggled in via prior work by the same authors. The derivation therefore remains self-contained against the cited external literature and does not collapse to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions from decision theory and uncertainty modeling; no free parameters or new invented entities are evident from the abstract.

axioms (2)
  • domain assumption Preferences under uncertainty can be represented using probability sets and belief functions.
    The model focuses on these representations to model preferences and derive strategic decisions.
  • domain assumption Lower and upper expected utility gains are appropriate measures for strategic voting choices.
    Used to take strategic decisions within the model.

pith-pipeline@v0.9.0 · 5610 in / 1221 out tokens · 35376 ms · 2026-05-19T18:46:48.079559+00:00 · methodology

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Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages

  1. [1]

    In: Proceedings of the 19th Interna- tional Conference on Autonomous Agents and Multiagent Systems (AA- MAS 2020)

    Baumeister, D., Selker, A.K., Wilczynski, A.: Manipulation of opinion polls to influence iterative elections. In: Proceedings of the 19th Interna- tional Conference on Autonomous Agents and Multiagent Systems (AA- MAS 2020). pp. 132–140 (2020)

    work page 2020

  2. [2]

    Cambridge University Press (1958)

    Black, D.: The theory of committees and elections. Cambridge University Press (1958)

    work page 1958

  3. [3]

    In: Proceedings of the 25th AAAI conference on artifi- cial intelligence (AAAI 2011)

    Conitzer, V., Walsh, T., Xia, L.: Dominating manipulations in voting with partial information. In: Proceedings of the 25th AAAI conference on artifi- cial intelligence (AAAI 2011). vol. 25, pp. 638–643 (2011)

    work page 2011

  4. [4]

    Decision processes3, 159–165 (1954)

    Debreu, G., et al.: Representation of a preference ordering by a numerical function. Decision processes3, 159–165 (1954)

    work page 1954

  5. [5]

    Denneberg, D.: Non-additive measure and integral, vol. 27. Springer Science & Business Media (2013)

    work page 2013

  6. [6]

    International Journal of Ap- proximate Reasoning124, 194–216 (2020)

    Denoeux, T., Shenoy, P.P.: An interval-valued utility theory for decision making with dempster-shafer belief functions. International Journal of Ap- proximate Reasoning124, 194–216 (2020)

    work page 2020

  7. [7]

    Introduction to Imprecise Proba- bilities (chapter 4), 79–91 (2014)

    Destercke, S., Dubois, D.: Special cases. Introduction to Imprecise Proba- bilities (chapter 4), 79–91 (2014)

    work page 2014

  8. [8]

    Theoretical Computer Science726, 78–99 (2018)

    Dey, P., Misra, N., Narahari, Y.: Complexity of manipulation with partial information in voting. Theoretical Computer Science726, 78–99 (2018)

    work page 2018

  9. [9]

    AAAI Press/International Joint Confer- ences on Artificial Intelligence (2016)

    Endriss, U., Obraztsova, S., Polukarov, M., Rosenschein, J.S.: Strategic vot- ing with incomplete information. AAAI Press/International Joint Confer- ences on Artificial Intelligence (2016)

    work page 2016

  10. [10]

    Journal of mathematical economics18(2), 141–153 (1989)

    Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. Journal of mathematical economics18(2), 141–153 (1989)

    work page 1989

  11. [11]

    In: Set Functions, Games and Capacities in Decision Making, pp

    Grabisch, M.: Decision under risk and uncertainty. In: Set Functions, Games and Capacities in Decision Making, pp. 281–323. Springer (2016)

    work page 2016

  12. [12]

    Artificial Intelligence189, 1–18 (2012)

    Hazon, N., Aumann, Y., Kraus, S., Wooldridge, M.: On the evaluation of election outcomes under uncertainty. Artificial Intelligence189, 1–18 (2012)

    work page 2012

  13. [13]

    Hurwicz, L.: Optimality criteria for decision making under ignorance. Tech. rep., Cowles Commission discussion paper, statistics (1951)

    work page 1951

  14. [14]

    Proceedings of the 35th Conference on Neural Information Processing Systems (NeurIPS 2021)34, 19021–19032 (2021)

    Kavner, J., Xia, L.: Strategic behavior is bliss: iterative voting improves social welfare. Proceedings of the 35th Conference on Neural Information Processing Systems (NeurIPS 2021)34, 19021–19032 (2021)

    work page 2021

  15. [15]

    In: Proceedings of the Multidisciplinary Workshop on Advances in Preference Handling (IJCAI 2005)

    Konczak, K., Lang, J.: Voting procedures with incomplete preferences. In: Proceedings of the Multidisciplinary Workshop on Advances in Preference Handling (IJCAI 2005). vol. 20, p. 12 (2005)

    work page 2005

  16. [16]

    In: Proceedings of the 14th International Conference of Scalable Uncertainty Management (SUM 2020)

    Kreiss, D., Augustin, T.: Undecided voters as set-valued information– towards forecasts under epistemic imprecision. In: Proceedings of the 14th International Conference of Scalable Uncertainty Management (SUM 2020). pp. 242–250. Springer (2020) 16 H. Surugue and S. Destercke

    work page 2020

  17. [17]

    In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI 2019)

    Lev, O., Meir, R., Obraztsova, S., Polukarov, M.: Heuristic voting as ordi- nal dominance strategies. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI 2019). vol. 33, pp. 2077–2084 (2019)

    work page 2019

  18. [18]

    In: Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI 2015)

    Meir, R.: Plurality voting under uncertainty. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI 2015). vol. 29 (2015)

    work page 2015

  19. [19]

    In: Endriss, U

    Meir, R.: Iterative voting. In: Endriss, U. (ed.) Trends in Computational Social Choice, chap. 4, pp. 69–86. AI Access (2017)

    work page 2017

  20. [20]

    Synthesis lectures on artificial intelligence and machine learning13(1), 1–167 (2018)

    Meir, R.: Strategic voting. Synthesis lectures on artificial intelligence and machine learning13(1), 1–167 (2018)

    work page 2018

  21. [21]

    Springer Nature (2022)

    Meir, R.: Strategic voting. Springer Nature (2022)

    work page 2022

  22. [22]

    In: Proceedings of the fifteenth ACM conference on Economics and computation (ACM 2014)

    Meir, R., Lev, O., Rosenschein, J.S.: A local-dominance theory of voting equilibria. In: Proceedings of the fifteenth ACM conference on Economics and computation (ACM 2014). pp. 313–330 (2014)

    work page 2014

  23. [23]

    In: Proceedings of the 24th AAAI conference on artificial intelligence (AAAI 2010)

    Meir, R., Polukarov, M., Rosenschein, J., Jennings, N.: Convergence to equi- libria in plurality voting. In: Proceedings of the 24th AAAI conference on artificial intelligence (AAAI 2010). vol. 24, pp. 823–828 (2010)

    work page 2010

  24. [24]

    Journal of Mathematical Psychology64, 44–57 (2015)

    Miranda, E., Destercke, S.: Extreme points of the credal sets generated by comparative probabilities. Journal of Mathematical Psychology64, 44–57 (2015)

    work page 2015

  25. [25]

    Mousseau,V.,Surugue,H.,Wilczynski,A.:Dowecareaboutpollmanipula- tion in political elections? In: Proceedings of the 27th European Conference on Artificial Intelligence (ECAI 2024) (2024)

    work page 2024

  26. [26]

    American Polit- ical science review87(1), 102–114 (1993)

    Myerson, R.B., Weber, R.J.: A theory of voting equilibria. American Polit- ical science review87(1), 102–114 (1993)

    work page 1993

  27. [27]

    In: Proceedings of the 29th AAAI conference on artificial intelligence (AAAI 2015)

    Rabinovich,Z.,Obraztsova,S.,Lev,O.,Markakis,E.,Rosenschein,J.:Anal- ysis of equilibria in iterative voting schemes. In: Proceedings of the 29th AAAI conference on artificial intelligence (AAAI 2015). vol. 29 (2015)

    work page 2015

  28. [28]

    In: Proceeding of the 4th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2012)

    Reijngoud, A., Endriss, U.: Voter response to iterated poll information. In: Proceeding of the 4th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2012). vol. 4, p. 8 (2012)

    work page 2012

  29. [29]

    Journal of economic theory10(2), 187–217 (1975)

    Satterthwaite, M.A.: Strategy-proofness and arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare func- tions. Journal of economic theory10(2), 187–217 (1975)

    work page 1975

  30. [30]

    In: Proceedings of the Information Processing and Management of Uncertainty (IPMU 1992)

    Smets, P., Kennes, R.: The concept of distinct evidence. In: Proceedings of the Information Processing and Management of Uncertainty (IPMU 1992). pp. 789–794 (1992)

    work page 1992

  31. [31]

    Artificial Intelligence332, 104133 (2024)

    Terzopoulou, Z., Terzopoulos, P., Endriss, U.: Iterative voting with partial preferences. Artificial Intelligence332, 104133 (2024)

    work page 2024

  32. [32]

    Troffaes, M.C.: Decision making under uncertainty using imprecise proba- bilities. International journal of approximate reasoning45(1), 17–29 (2007) An Enriched Model of Strategic Voting 17 Technical Appendix A Complete proofs Proposition 1.With a uniform pignistic criterion on a neighborhood of scores of size 1 (with respect to theℓ1 distance), convergen...

    work page 2007

  33. [33]

    Proof.We know that the weightsβ i k of our belief functions defined as∀i∈ N,∀k⩾1,M i(Sk) =β i k are decreasing

    will converge to an equilibrium. Proof.We know that the weightsβ i k of our belief functions defined as∀i∈ N,∀k⩾1,M i(Sk) =β i k are decreasing. We consider a feasible movea i →a i′. Using the fact that the lower (an upper) expectation is positive homogeneous, i.e.,αE(f) =E (αf), we get α·E M(ui(a′ i|ai, s)) + (1−α)· EM((ui(a′ i|ai, s)) = riX i=1 M(Si)[αi...

    work page