Figure 1. Example stimuli for Who Won the Election Task (WWET). In the WWET, participants were asked to imagine that they worked for a company deciding to hire a new employee from three candidates. Each member of the hiring committee voted on whether they wanted a candidate who excelled technically or in terms of leadership on a -100 to +100 scale, and each candidate was assessed through the hiring process at a specific number on the same scale. The graph provided to participants represented the preferences of the hiring committee members (vertical black lines) and the candidates preferences (vertical blue lines and letters). Participants were asked, “Based on the preferences of the hiring committee members in the graph above, which job candidate do you think should be hired?”

From the figures in the WWET, it is possible to determine which candidate should be hired according to plurality, RCV, and cardinal voting. In this example, Candidate N wins according to plurality voting, because 4 committee members are closest to N, whereas 3 are closest to W and 2 are closest to L. Candidate W wins according to RCV. Since Candidate N had 4 out of 9 votes in the first round, which is less than 50%, an instant-runoff would occur. Candidate L would be eliminated in the instant-runoff because L has the least number of votes. The two voters in the middle of the scale are closer to W than N, so W would win the election with 5 out of 9 votes. Candidate L wins according to cardinal voting because L has a lower average distance to all 9 committee members (63.00) than N (71.90) or W (78.70).

Figure 2. Screenshots of applet for “center squeeze phenomenon” (A), “majority criterion violation” (B), and “spoiler effect” (C). These applets were created in JavaScript and piped into Qualtrics. They created an interactive display were participants could change aspects of the scenario in order to discovery important truths about how the different voting systems work.

Figure 3. Percent of choices in WWET in support of each voting system and declared voting system preferences and 95% CIs. Note: Some choices in the WWET support two voting systems, so the bars add up to over 100%. For studies in which the tasks were performed more than once, the first is shown. Declared voting systems refers to the preferred voting system when directly asked, whereas WWET choices are choices from viewing data in the Who Won the Election Task. We typically found that participants stated preferring ranked-choice voting but made choices from data that were consistent with plurity voting.

Figure 4. Comprehension scores for the three voting by preferred voting system. In general, participants had an excellent understanding of how plurality voting works, but struggled to understand how ranked-choice voting works.

Figure 5. Belief Change in Fairness Ratings Across Teaching Intervention (left panel) & Mean (95% CI) Change in Comprehension Scores by Teaching Intervention in Study 2 (right panel). Here we see that participants changed how fair they felt each voting system was in response to all three teaching intervention strategies (retrieval practice, re-study, and discovery learning)--even just viewing the election figures a second time after learning about the voting systems had an impact on their ratings (control condition). Lastly, we see in the second panel that retrieval practice was the msot effective intervention for increasing comprehension of how the voting systems work.