We study majority correctness when voting is preceded by sustained social interaction on a social network. Motivated by the Condorcet Jury Theorem, we consider a binary choice with an objectively correct alternative, where uninformed voters revise their vote intentions through repeated interaction in the presence of competing committed leaders (zealots). In this zealot--contrarian voter model, voters may either imitate or oppose the views they encounter. For fully mixed electorates, we characterize the long-run distribution of votes and the correlation structure induced among voters, and we show that Erd\H{o}s--R\'enyi networks exhibit the same majority-correctness behavior after an appropriate rescaling of leader influence. Building on these results, we establish a finite-electorate Condorcet-type guarantee: when post-deliberation individual correctness exceeds random choice, a strict majority is more likely to select the correct alternative than a randomly chosen voter. At the same time, we identify an aggregation failure: social interaction can reduce majority accuracy relative to a no-deliberation benchmark in which voters respond only to zealots. As the electorate size tends to infinity, this finite-electorate advantage disappears unless social updating is purely conformist, revealing a tipping point at full conformity: any persistent contrarian updating drives both individual and majority correctness to the random choice level of one half. Simulations on scale-free, ring, and small-world networks further show that topology matters because it shapes the vote correlations generated by social influence: hub-dominated structures generate stronger positive correlations and lower majority accuracy, whereas spatially structured networks generate weaker correlations, preserve a larger effective number of independent judgments, and improve majority accuracy.
Voters in multiparty systems often fail to coordinate on majority-preferred parties. Using constituency-level election data linked to party-ideology measures across 96 countries, we show that in 20–30% of multiparty elections since 1940 the Condorcet winner does not win, and in roughly 10% the winner is the Condorcet loser. Failures are most common under plurality rule and in fragmented, volatile party systems, and systematically disadvantage opposition and culturally liberal parties while benefiting organizationally strong ones. Can information fix this? In four pre-registered experiments around Indian elections (N > 4,000), constituency-level polls shift voting intentions by at most 2 percentage points, a precisely estimated null, despite modest belief updating, though undecided voters become 7 points more likely to support a viable party. A model with expressive motives rationalizes both results: polls refine beliefs but lack the leverage to overcome entrenched attachments, identifying boundary conditions on polls as coordination devices.
F. Capozza, Ruben Durante, S. George· CESifo working papers· 0 citations
Online communities often treat large support margins in public elections as strong mandates. We argue that such margins can overstate the independent scrutiny behind a decision. Using 198,275 free-text rationales from Wikipedia admin elections, we introduce vote-text divergence, a measure that flags a decisive vote paired with a thin, deferential rationale. Divergence rises as voters arrive later, even after controlling for voter and election fixed effects. The pattern is consistent with information saturation: once prior text is accounted for, arrival order no longer predicts divergence, while accumulated prior evidence does. The effect is strongest among peripheral voters in the co-voting network. Yet divergence does not predict worse post-promotion outcomes, such as administrative activity or survival. Public tallies can therefore weaken the scrutiny signal even while selecting capable administrators: a margin may appear to reflect more consensus and support than it actually contains.
Liquid democracy permits voters to vote directly or delegate their votes to others. Existing algorithmic analyses assign each voter a single scalar parameter, interpreted as an independent probability of voting for the ground truth. This representation is inadequate when delegation is fixed before public information changes different voters'reliability in different ways. In this work, we study a minimal common-signal model of this phenomenon. Delegation occurs before a public binary signal is realised, while voting occurs afterwards. Conditional on the signal, sink votes are independent, and each voter has a signal-specific competence; marginally, correctness events are correlated through the common signal. We show that delegation based on average competence is not a safe scalarisation: it can violate do-no-harm, and a beneficial delegation rule may send votes to voters with lower average competence. We present and analyse three novel delegation mechanisms for this setting. The first is a conservative intersection mechanism that delegates only to neighbours whose competence exceeds the delegator's by a prescribed margin in every signal state; the conservative intersection mechanism inherits all the guarantees of delegation in the scalar competence setting. The next mechanism is a confounded-set mechanism that enable the delegation to neighbours who are favoured in one state and worse by at most a prescribed tolerance in the other. For this mechanism, we prove expected-margin bounds, and identify the weight-dispersion and mechanism-concentration conditions needed to obtain majority-correctness guarantees. Finally, on bounded-in-degree graphs, a multi-round certified-path mechanism propagates nonnegative two-dimensional path certificates; it is acyclic, yields statewise terminal competence improvement, and gives uniform bounds on path length and terminal voting weight.
Seth Gilbert, Stefan Schmid, Santiago Schnell et al.· 0 citations
Voting is a core element of social choice theory and a subarea of computational social choice. The goal is to rank (or rate) candidates according to voters’ preferences, and to eventually select the winner(s) of the election. In multiwinner voting, the same applies to sets of candidates and winning committee(s). The intuition is therefore quite similar to centrality in networks, where the goal is to rate (or rank) nodes—or groups of nodes—according to their structural positions. We establish correspondences between these two research fields by deriving preference rankings from network relations, and adapting single- and multiwinner voting rules to identify the most central (groups of) nodes. The transfer of reasonable and desirable properties and axioms from social choice theory to network science opens up the possibility to study novel aspects of centrality, and leads to the definition of voting-based centrality measures.
Christian Laußmann, Katharina Volz, Ulrik Brandes et al.· Computational and mathematic...· 0 citations
Confidence in the conduct and results of American elections has declined and polarized along party lines in recent years. Can a nonpartisan public information campaign featuring election officials enhance trust in elections when delivered to skeptical voters during a contentious political contest? We analyze a preregistered, randomized field experiment conducted during the 2024 US presidential election in which conservative voters were randomly assigned to a control condition or to receive a multimodal messaging campaign designed by political professionals explaining protections on election integrity. In contrast to the large positive effects of informational messages found in recent survey experiments, we observed primarily null effects with respect to turnout (n = 147,488), general confidence in elections (n = 4740 to 4868), and perceptions of the frequency of fraud (n = 4925). We observed one hypothesized effect: an increase in trust in the vote-by-mail process (n = 6438). This study provides rigorous evidence from a real public information campaign on election integrity, yielding effect sizes in the field that are much smaller than those observed in prior survey settings.
We study the peer selection problem in which a group of peers must select a fixed-size committee from among themselves. To this end, we introduce a class of approval-based preference profiles, inspired by delegation graphs in liquid democracy and the transitivity of trust therein, which we call ``liquid profiles''. Under this new domain restriction, each voter designates a single trusted agent and, in turn, approves all those trusted by that individual. After establishing relationships to standard restricted preference profiles and examining computational properties of liquid profiles, we focus on understanding how novel and established proportionality axioms behave in this domain and how they relate to one another. Then, we study their satisfaction under various voting rules, including new ones that are directly inspired by the structure of liquid profiles. Our findings reveal that particularly strong proportionality guarantees are attainable in this new domain, showing promise for applications to real-world peer selection problems via transitive delegations.
Davide Grossi, Grzegorz Lisowski, Georgios Papasotiropoulos· 1 citation
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