political campaign strategists

Abstract: In models of opinion dynamics, researchers typically examine how an individual's opinion on one topic is influenced by the opinions of their neighbors in a network. However, people's opinions on a topic are also influenced by their opinions and their neighbors' opinions on related topics. In an election, for example, the opinions of a voter on a variety of issues inform their opinions of electoral candidates. To consider the influence between people's opinions on multiple distinct topics, we study a multiplex extension of the traditional DeGroot consensus model. In our multiplex DeGroot model, different network layers represent distinct topics and directed interlayer edges (which are not allowed to form cycles) encode relationships between distinct topics. In our model, an individual's opinion on one topic is influenced both by the opinions of their neighbors on that topic and by their own opinions on related topics. We prove under mild conditions that our multiplex DeGroot model converges to a limit state. We also prove that strong connectedness in ``source layers'' (which represent fundamental beliefs) eventually yields a consensus opinion in each layer. In particular, we show that consensus on source layers can lead to consensus on other layers even when those layers otherwise would be polarized. By numerically simulating our multiplex DeGroot model on a two-layer network, we examine the effects on opinion dynamics of (1) different network structures and (2) different types of initial opinion data.

Abstract: Duverger's law states that plurality elections tend to concentrate support on two candidates. Pivotal-voter models typically derive this from aggregate uncertainty about votes, so that two-candidate competition emerges in the limit of large electorates. We instead propose a model for a fixed, finite population. A poll reveals the current support counts, and each voter best responds under trembling-hand beliefs, assuming that every other voter may deviate with a small probability. Starting from truthful votes, we show that a single update typically suffices for the dynamics to converge to a stable profile in which every voter supports her preferred candidate among the two poll leaders. For any number of candidates and any full-support tremble belief, a four-vote lead of the runner-up over all lower candidates suffices; for three candidates, a lead of two suffices. As a consequence, under random preferences, Duverger's law emerges after one update with probability $1-\mathcal O(N^{-1/2})$. While these results may suggest that the dynamics always settle, convergence can fail. Mild period-two cycles already arise, with a few voters swapping ballots around an otherwise stable profile. We show that substantially richer behavior is possible, even with three candidates. Period-three cycles arise with six voters changing their ballots, and no such cycle can involve fewer than four. Cycles can also alternate the plurality winner. Moreover, larger electorates support ever longer cycles: for every odd $\ell\geq3$, truthful voting can lead to a cycle whose vote counts repeat every $\ell$ rounds and whose full ballot profile repeats every $2\ell$ rounds.

Abstract: Generative Social Simulation (GSS) leverages Large Language Models (LLMs) to create sophisticated personas that define agents with demographics, emotions, and political opinions. While prior work shows that personas compress outputs into stereotypical caricatures, there is no comprehensive study of how these caricatures evolve into collective artifacts when they interact. Using a Twitter-like GSS platform with personas derived from the American National Elections Study (ANES), we ablate three layers of partisan identity: affective polarization markers, party identification, and vote choice, while retaining demographics, ideological positioning and important issues. We find that collective outcomes depend heavily on how survey responses are translated into personas. Removing a few explicitly partisan statements moves the network from near-complete segregation to cross-party ties approaching those of real Twitter networks. We argue that matching one outcome is not evidence for behavioral validity and point to salience as a possible explanation. Surveys ask for a position on every question regardless of its importance to the respondent, and persona construction turns each answer into a direct behavioral instruction. We conclude with a checklist for more comprehensive evaluation of personas in future works.

Abstract: We study a partial-participation variation of the Hotelling-Downs model. Voters each have a cost to vote, and only vote when the comparative gain from their preferred candidate exceeds the cost. Under this model the median voter theorem breaks, and we study the extent of polarization under equilibria in different voters and cost distributions. We find that the main predictor of polarization is the reverse-hazard-rate of the cost distribution, indicating that the driver of polarization under our model is the willingness of voters to respond to changes in positions of candidates. We then extend the model by adding parameters governing alienation and candidate competitiveness, showing that our results are robust even when taking into account other realistic factors.

Abstract: This paper studies resource-limited external influence in time-varying opinion networks when a controller must choose both a small set of agents and a scalar intervention at each update. We use the affine free response, which includes DeGroot and Friedkin--Johnsen dynamics, followed by a direct sparse action. Eliminating the scalar action reduces the one-step problem to a cardinality-constrained support objective whose global optimum is obtained from the largest or smallest residual components. Hence exact sparse one-step-ahead optimal control requires one sort and \(O(|\mathcal T|\log|\mathcal T|)\) operations, where \(\mathcal T\) is the support set. For periodic affine dynamics, the resulting state-dependent low-rank feedback admits cycle-based ultimate bounds and exact tracking of model-invariant targets. The DeGroot and Friedkin--Johnsen specializations expose the role of target invariance and the affine mismatch term. With several competing external players, each sparse best response retains the same sorting structure and the complete binary--continuous stage game is an exact potential game, so a pure-strategy equilibrium exists at every frozen state. Same-state welfare benchmarks separate loss due to scalar competition from the additional loss due to strategic support selection. Numerical examples validate exact support selection and illustrate switching-order effects, DeGroot/Friedkin--Johnsen tracking, resource tradeoffs, and competitive implementations.