2.1. Validating the perceived distribution task

Figure 2a shows how participants in each of our five studies typically perceived the distribution of Democrats’ and Republicans’ attitudes on three policy issues: abortion access, border control, and gun control. Each “typical” distribution was generated by averaging the number of tokens participants collectively placed at each scale point. The solid lines represent the actual distribution of Democrats’ and Republicans’ attitudes on each policy issue, determined using a demographically representative sample of American partisans (study 1).

Figure 2. Panel a depicts the “typical” perceived distribution drawn by participants in each study. Each distribution is generated by averaging the number of tokens participants collectively placed at each scale point. The solid lines represent the actual distribution of Democrats and Republicans’ attitudes on each policy issue from study 1. In study 4, participants were randomized to draw one of two sets of non-political distributions. Some participants drew die-hard Red Sox fans’ and die-hard Yankees fans’ beliefs about the relative skill of the two baseball teams (panel b). Others drew Americans’ and Canadians’ preferences for the colors blue and pink (panel c).

As shown in each facet of Figure 2a, the perceived distributions for each issue are generally consistent across our studies. We measured this consistency by calculating the overlap between the curves of the same political party's attitudes, on the same policy issue, from every pair of samples. On average, 89 percent (SD = 0.05) of the area under the curves overlapped, indicating that our task reliably produces similar distributions across samples. Importantly, however, these “typical” distributions hide considerable variation in individual participants’ perceived distributions, as we discuss later.

To ensure that participants properly interpreted the perceived distribution task, we had participants draw straightforward, non-political distributions (study 4). Some were randomized to represent the beliefs of die-hard Red Sox and Yankees fans about the relative skill of the two baseball teams. Quite sensibly, these participants drew narrow and extreme distributions (Figure 2b). By contrast, other participants were randomized to represent Americans’ and Canadians’ preferences for the colors blue and pink, and these participants reasonably drew wide and moderate distributions (Figure 2c).Footnote ¹

We also used an existing numeracy scale (Schwartz et al., Reference Schwartz, Woloshin, Black and Welch1997) to assess whether numerate participants draw substantially more accurate perceived distributions (study 1). Compared to those at the bottom of the numeracy scale, participants at the top of the numeracy scale did not draw perceived distributions with more accurate standard deviations (b = −0.03, SE = 0.05, ${\rm p} = 0.58$). However, numerate participants did draw perceived distributions with slightly more accurate means: moving from the bottom to the top of the numeracy scale was associated with a perceived distribution mean roughly half a scale point, on an 11-point scale, closer to reality (b = −0.49, SE = 0.09, ${\rm p}< 0.001$).

In sum, participants seem to understand our perceived distribution task. However, one might worry that participants might misrepresent their perceptions of Democrats’ and Republicans’ attitudes, to make their in-party seem more open-minded or moderate than the out-party (a form of “partisan cheerleading”; Bullock and Lenz, Reference Bullock and Lenz2019). To address this concern, we randomized some participants to receive monetary incentives for drawing accurate distributions (study 2).Footnote ² As shown in our online appendix, these incentives did not affect the standard deviations of participants’ perceived distributions. They did, however, induce participants to draw distributions with less extreme means in some cases (b′s = −1.78 to −0.02). This effect is consistent with other research on how monetary incentives affect responses to political questions, including point estimates representing partisans’ policy attitudes (Bullock and Lenz, Reference Bullock and Lenz2019).

Finally, we assessed the criterion validity of our perceived distribution task and examined whether within-party attitude diversity predicts important consequences—over and above perceptions of the average partisan. Point-estimate reports of where the “average” partisan stood correlate highly with the means of participants’ perceived distributions ($r = 0.84$, ${\rm p}< 0.001$, study 5). In other words, those who report the “average” partisan to be more extreme also draw perceived distributions with more extreme means.

Moreover, perceived distribution means correlate with previously documented consequences of misperception. We estimate the associational “effects” of perceived diversity after controlling for extremity perceptions (and vice versa). We compile the data across our five studies and regress (1) warmth toward the out-party, (2) comfort socializing with the out-party, and (3) perceptions of the out-party's support for violating democratic norms on the means and standard deviations of participants’ perceived distributions. Perceived out-party support for democratic norms is measured by asking participants whether most out-partisans would support ignoring court rulings, reducing voting stations, or using violence for political gain. As a point of comparison, we also include partisan identity strength as an independent variable. We use covariates that control for study, policy issues, participant demographics (including partisanship), and participants’ own policy attitudes.

Figure 3 visualizes the results of these regressions. As expected, the more stereotypically extreme a participant perceives out-partisans to be, the less they like the out-party (d = −0.17, ${\rm p}< 0.001$) and the less comfortable they feel socializing with the out-party (d = −0.10, ${\rm p}< 0.05$). Also consistent with previous research, perceiving out-partisans as stereotypically extreme is associated with greater concern that the out-party supports violating democratic norms (d = 0.19, ${\rm p}< 0.001$).

Figure 3. This figure visualizes standardized regression coefficients describing the relationship between previously documented consequences of partisan misperceptions and the perceived diversity of out-partisans’ attitudes (i.e., the standard deviation of participants’ perceived distributions), the perceived extremity of the average out-partisan (i.e., the mean of participants’ perceived distributions), and participants’ partisan identity strength.

Yet, even after controlling for perceptions of extremity, perceived within-party attitude diversity also predicts these outcomes. The more diverse the out-party's attitudes are perceived to be, the more participants like the out-party (d = 0.14, ${\rm p}< 0.001$) and feel comfortable socializing with the out-party (d = 0.15, ${\rm p}< 0.001$). Additionally, perceiving the out-party as having more diverse attitudes is associated with lesser concern that the out-party supports violating democratic norms (d = −0.16, ${\rm p}< 0.001$).

In sum, our evidence suggests that the perceived distribution task is a reliable and valid way of measuring American partisans’ perceptions of other partisans’ attitudes about policy issues. Moreover, it shows that perceived diversity can explain variation in downstream consequences that perceived extremity cannot. Indeed, perceived diversity has a comparable associational “effect” on downstream consequences after controlling for perceived extremity. How accurate, then, are these perceptions?

2.2. Accuracy of participants’ perceptions

Perceptions of within-party diversity. One might think that Figure 2a—which visualizes the perceived distributions typically drawn by participants across our five studies—suggests that American partisans have generally accurate perceptions of other partisans’ policy attitudes. However, these “typical” distributions are drawn by averaging the number of tokens participants collectively placed at each scale point. As such, these distributions benefit from the “miracle of aggregation” (Page and Shapiro, Reference Page and Shapiro1992). That is, highly inaccurate estimates from individuals, when averaged, can produce highly accurate aggregate estimates, so long as individuals’ errors are uncorrelated.

To more usefully characterize the accuracy of American partisans’ perceptions, we turn to our demographically representative sample (study 1). Figure 4a shows the distribution of standard deviations as calculated from each participant's perceived distributions. The solid lines represent the actual standard deviation of each party's attitudes, and the dotted lines represent the average standard deviation of perceived distributions drawn by participants.

Figure 4. Panel a depicts study 1 participants’ perceptions of within-party diversity in policy attitudes—i.e., the standard deviation of participants’ perceived distributions—by policy issue and participant partisanship. Solid lines depict the actual standard deviation of partisans’ attitudes. Dotted lines depict the average standard deviation of participants’ perceived distributions. Panel b depicts study 1 participants’ perceptions of the average Republican's and Democrat's policy attitude—i.e., the average of participants’ perceived distributions—by policy issue and participant partisanship. Solid lines depict the actual attitude of the average partisan. Dotted lines depict the average of participants’ perceived distribution averages.

American partisans under-estimate—by more than a factor of two—the diversity of each party's attitudes. To begin, Democrats and Republicans perceive each other's policy attitudes to be far more homogenous than they are in reality. Across policies, Democrats under-estimated the standard deviation of Republicans’ attitudes by 1.46 points (SE = 0.03). Similarly, Republicans under-estimated the standard deviation of Democrats’ attitudes by 1.59 points (SE = 0.04). Perhaps more surprisingly, American partisans homogenize their own party's attitudes to a similar extent. Democrats under-estimate the standard deviation of their own party's policy attitudes by 1.37 points (SE = 0.03). Likewise, Republicans under-estimate the standard deviation of other Republicans’ policy attitudes by 1.55 points (SE = 0.04).

Perceptions of the “average” partisan. Our perceived distribution task also enables us to re-examine the scholarly consensus about perceived polarization, which has traditionally been estimated using point estimates representing the “average” Democrat and Republican. Figure 4b depicts the distribution of Americans’ perceptions of the average member of each party. Once again, solid lines represent reality: the actual attitude of the average member of each party. The dotted lines represent the result of averaging across Americans’ perceptions of the average Republican or Democrat.

Counter past evidence using point-estimate questions, American partisans do not consistently over-estimate how extreme the policy attitudes of the average Republican or Democrat are. When using the distribution task, Americans over- and under-estimate the extremity of average partisans to a roughly equal extent: Looking across policy issues, Democrats did not over-estimate the extremity of Republicans ($\bar {x} = -0.07$, SE = 0.07) or other Democrats ($\bar {x} = -0.07$, SE = 0.06). Similarly, Republicans did not over-estimate the extremity of Democrats ($\bar {x} = 0.02$, SE = 0.11). However, Republicans did slightly over-estimate the extremity of other Republicans by about a quarter of a scale point on an 11-point scale ($\bar {x} = 0.24$, SE = 0.08, p < .01).

Question-wise differences in estimates of perceived polarization. This lack of perceived polarization is initially surprising, given existing findings that partisans do over-estimate polarization (Fernbach and Van Boven, Reference Fernbach and Van Boven2022). To verify that our unique results were a function of the perceived distribution task, not arbitrary differences in sample composition or study timing, we conducted another experiment (study 2).Footnote ³ We randomized participants to draw perceived distributions or to indicate the stances of “most” Democrats and Republicans using point estimates, consistent with previous research on perceived polarization. In our online appendix, we show that referring to “most” out-partisans versus the “average” out-partisan does not affect the extremity of responses to the point-estimate question.

As shown in Figure 5a, the point-estimate question produces larger estimates of perceived polarization. When asked to provide point estimates, partisans report a 5.7–6.4 point gap between the policy attitudes of the “average” Democrat and Republican on an 11-point scale (SEs = 0.16 − 0.17). By contrast, when asked to draw a distribution, this gap collapses to 4.8–5.2 points (SEs = 0.15–0.17). Thus, perceived polarization in policy attitudes appears far more extreme when partisans are asked to provide a point estimate representing the “average” partisan's view. The estimates derived from our perceived distribution task are more consistent with reality: actual polarization on our three policy issues, as represented by solid vertical lines, ranged from 3.0 to 3.7 points.

Figure 5. Panel a depicts estimates of perceived polarization derived from a point-estimate question that is typical of existing research versus our perceived distribution task. Panel b depicts generalized additive model (GAM) lines of the relationship between when a participant placed a token in our perceived distribution task and the extremity of that token (in the direction of the party stereotype). For example, if a participant, when representing the attitudes of Democrats, placed a token close to the far-left position on an issue, that token would be considered “extreme.”

Why might our perceived distribution task yield more modest estimates of perceived polarization? When asked to represent partisans’ policy attitudes, Americans likely “sample” partisan exemplars from memory (Zaller and Feldman, Reference Zaller and Feldman1992; Ahler and Sood, Reference Ahler and Sood2023), and policy extremists may be more accessible in memory (Levendusky and Malhotra, Reference Levendusky and Malhotra2016). Because they are quick to answer, point-estimate questions likely over-represent extreme and accessible exemplars (i.e., stereotypes). Indeed, Figure 5b shows that participants tended to place extreme tokens (exemplars) first when completing our perceived distribution task (studies 4–5). This is true regardless of whether the participant is depicting the attitudes of in-partisans or out-partisans.