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A belief systems analysis of fraud beliefs following the 2020 US election

Abstract

Beliefs that the US 2020 Presidential election was fraudulent are prevalent despite substantial contradictory evidence. Why are such beliefs often resistant to counter-evidence? Is this resistance rational, and thus subject to evidence-based arguments, or fundamentally irrational? Here we surveyed 1,642 Americans during the 2020 vote count, testing fraud belief updates given hypothetical election outcomes. Participants’ fraud beliefs increased when their preferred candidate lost and decreased when he won, and both effects scaled with partisan preferences, demonstrating partisan asymmetry (desirability effects). A Bayesian model of rational updating of a system of beliefs—beliefs in the true vote winner, fraud prevalence and beneficiary of fraud—accurately accounted for this partisan asymmetry, outperforming alternative models of irrational, motivated updating and models lacking the full belief system. Partisan asymmetries may not reflect motivated reasoning, but rather rational attributions over multiple potential causes of evidence. Changing such beliefs may require targeting multiple key beliefs simultaneously rather than direct debunking attempts.

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Fig. 1: Empirical fraud belief update given hypothetical election outcome maps.
Fig. 2: Bayesian model, priors and predictions.
Fig. 3: Predicted fraud belief update as a function of preference strength across models.

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Data availability

Data are publicly shared at https://doi.org/10.5281/zenodo.5730630, release version 5.0.0.

Code availability

Code is publicly shared (along with the data) at https://doi.org/10.5281/zenodo.5730630, release version 5.0.0. All analyses were performed with R version 3.6.3 (https://www.r-project.org). For reproducibility, we used the checkpoint package, which installs all needed R packages as they were on a specific date. We set the date to June 30, 2021.

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Acknowledgements

We thank J. M. Carey, R. Muirhead and B. J. Nyhan for providing comments on a previous version of this manuscript. R.B.-N. is an Awardee of the Weizmann Institute of Science—Israel National Postdoctoral Award Program for Advancing Women in Science. M.J. was supported by a National Science Foundation (NSF) grant (2020906). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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Authors and Affiliations

Authors

Contributions

Study design: R.B.-N. and T.D.W. Data collection: R.B.-N. Data analysis: R.B.-N. Supervision, expertize and feedback: M.J. and T.D.W. Bayesian model formulation: M.J. Conceptual framework development: R.B.-N., M.J. and T.D.W. Writing: R.B.-N., M.J. and T.D.W.

Corresponding authors

Correspondence to Rotem Botvinik-Nezer, Matt Jones or Tor D. Wager.

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Competing interests

This research was conducted in part while M.J. was a Visiting Faculty Researcher at Google Research, Brain Team (Mountain View, CA, USA). This work was not part of a commercial project. The other authors declare no competing interests.

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Nature Human Behaviour thanks Eric Groenendyk and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data

Extended Data Fig. 1 Demographic and partisan affiliation of participants.

(a) Number of participants for each combination of preferred candidate (x axis) and political affiliation (color). (b) Number of participants from each state who preferred each candidate (color). (c) Kernel density plot of participants’ age as a function of the preferred candidate (color). Preferred candidate: Dem = Biden; Rep = Trump; Affiliation: Dem = Democrat; Rep = Republican; Ind = Independent; Other.

Extended Data Fig. 2 Preference and prior belief data.

Kernel density plots of: (a) preference strength; (b) prior subjective probability of win by the preferred candidate; and (c) prior fraud belief. (d) Scatterplot for prior fraud belief as a function of prior subjective probability of win by the preferred candidate. Gray area represents 95% confidence interval; each point represents a single participant (with 30% opacity). Color represents the preferred candidate: Rep = Trump (red); Dem = Biden (blue). (e) Fraud belief update as a function of the scenario (loss or win according to the hypothetical map) and the preference strength (categorized into three ordered categories). Points represent single participants, and error bars represent standard error of the mean across participants.

Extended Data Fig. 3 Simulations of predicted fraud update across the prior belief space for all models.

Predictions are shown for each of the four models: (a) The original Bayesian model (note that the plot for the Bayesian model is also the plot for the Hypothesis Desirability model, because fitting the latter to the data yields \(\alpha = 0\)); (b) the Outcome Desirability model, with predictions based on the mean preference strength in the sample (u = .95) and the strength of bias that best fits the data (α = .3); (c) the Fraud-Only model; and (d) the Random Beneficiary model.

Extended Data Fig. 4 Update of true vote belief.

Simulations of predicted true vote belief update across the prior belief space for the Bayesian model and the Outcome Desirability model. Outcome Desirability model predictions assume the strength of bias that best fits the data (α = .3) and are shown for the mean preference strength in the sample (u = .95) as well as a lower value (u = .55) for comparison.

Extended Data Fig. 5 Empirical and predicted fraud belief updates across models.

Empirical fraud belief updates as a function of the predicted fraud belief updates from each model (based on empirically measured priors). Each point represents a single participant. The 95% confidence regions are for the linear approximation of the regression of empirical upon predicted fraud belief updates (the lines have slopes less than unity in part because of regression effects). Note that the plot for the Bayesian model is also the plot for the Hypothesis Desirability model, because fitting the latter to the data yields \(\alpha = 0\).

Extended Data Fig. 6 Predicted posterior fraud belief for each scenario across models.

Paralleling the empirical results from Fig. 1c, the model-based predictions of the posterior fraud belief for each participant (N = 828) are presented as a function of the map scenario (hypothetical winner), for each of the four models: (a) The original Bayesian model (note that the plot for the Bayesian model is also the plot for the Hypothesis Desirability model, because fitting the latter to the data yields \(\alpha = 0\)); (b) the Outcome Desirability model; (c) the Fraud-Only model; and (d) the Random Beneficiary model. In all panels, the prior values are based on the empirically obtained prior fraud beliefs from the original survey, only for participants who completed the follow-up survey. Points represent single participants, and error bars represent standard error of the mean across participants.

Extended Data Fig. 7 Empirically measured priors from the follow-up survey.

(a-b) Heat maps for the proportion of participants with each combination of v (probability of the preferred candidate winning the true votes) and c (probability of fraud, if present, favoring the preferred candidate), based on the follow-up sample, for (a) Democratic participants and (b) Republican participants. (c-d) Heat map of the mean preference strength of participants for each combination of v and c, for (c) Democratic participants and (d) Republican participants. For panels C and D, mean preference is shown only for cells with >1% of participants.

Extended Data Fig. 8 Predicted fraud belief update as a function of prior win belief across models.

Paralleling the empirical results from Fig. 1e, the model-based predictions of the fraud belief update for each participant are presented as a function of the empirically measured prior probability of the preferred candidate’s win. Dashed lines show linear fits to models’ predictions, with 95% confidence regions. For comparison, solid lines show the linear fits to the observed empirical patterns (Fig. 1e). Note that the plot for the Bayesian model is also the plot for the Hypothesis Desirability model, because fitting the latter to the data yields \(\alpha = 0\).

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Botvinik-Nezer, R., Jones, M. & Wager, T.D. A belief systems analysis of fraud beliefs following the 2020 US election. Nat Hum Behav 7, 1106–1119 (2023). https://doi.org/10.1038/s41562-023-01570-4

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