Experiment 3: Voting

5.5.1 Experimental Design and Procedures

For Experiment 3 we considered a complex voting decision. In Cournot oligopolies the participants interacted with each other. In contrast, this study was designed in such a way that the decision task was strictly individual, because no feedback on voting outcomes was provided until the end of the experiment. We followed Forsythe et al. (1993, 1996) (see also Granić, 2017) for the design of our voting experiment. The main decision task was to cast several votes using different voting methods. The participants were split into groups of 6 and voted on four different alternatives in the voting task.

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A test concerning the difference in response times between treatments across Experi- ments also is highly significant (Experiment 1, mean difference 0.88 s; Experiment 2, mean difference 5.01 s; MWW, N = 124, z = 6.355, p < 0.0001). Tests at the group level obtain the same qualitative conclusions.

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A conservative test at the group level obtains the same conclusion.

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This one-sided test is even more significant on the group level (p = 0.0006). These tests are not significant in Experiment 1.

Within a group the participants were further divided into three different types of voters with 2 participants each. We provided a table that indicated the payoffs for each type of voter for each of the four different alternatives, i.e. a 3 × 4 payoff table. The participants then filled in their ballot according to the voting method.

The participants voted multiple times in two different voting blocks with a fixed voting method but did not receive any feedback. Therefore, all vot- ing decisions were unaffected by the previous vote because no feedback was revealed and no information of the behavior of other players in the group is revealed, ergo the task can be viewed as an individual decision task. Each voting block consisted of 8 voting decisions each using plurality voting (PV) and approval voting (AV) as voting method. In PV each participant voted for exactly one of the alternatives and the alternative with the most votes won. In AV each participant voted for as many alternatives as she approved of and the alternative with the most approvals won. In case there was a tie among the votes, a random device determined the winner of the vote. In addition there was another “voting” method which always came at the end and served as preference elicitation. For the analysis we only consider the behavior in the PV and AV blocks. At the end of the experiment one vot- ing round was randomly drawn and the winning alternative was determined according to the voting method and the votes of all members of the group.

We implemented the same cognitive load task as in Experiment 2 within subjects. They memorized a seven-digit number before entering the voting stage, voted, and then had to recall the number. In each voting block, 4 different payoff profiles were presented twice, once with cognitive Load and once with No Load. Overall, we collected voting behavior for 16 voting decisions: 4 in the Load and 4 in the No Load treatment for AV and 4 in the Load and 4 in the No Load treatment for PV. At the end of the experiment 1 of the 8 rounds with cognitive load was randomly drawn. If the participants correctly recalled the number they earned additional points.11

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For a correct recall the participants earned 40 points while the earnings from the voting decision ranged between 43 and 93 points.

Since only one randomly drawn round was paid we will not use the payoff as an performance measure in this experiment. We will measure performance as the number of sincere votes and in AV the number of votes cast. A sincere vote is defined as a vote which is in agreement with the subjects preferences and does not include any strategic voting. With respect to cognitive load a possible directional hypothesis could be that cognitive load reduces strate- gic behavior because less cognitive resources are available. The decrease in strategic behavior could be manifested by an increase in sincere votes for both voting methods. A change in behavior could also be exhibited by a change in the number of votes cast under approval voting.

60 participants (38 female; age range 18–32 years, mean 23.1 years) par- ticipated in exchange for performance-based payment plus a show-up fee. Students with a major in Psychology and who already participated in sim- ilar voting experiments were excluded from the participants pool. The par- ticipants earned on average 18.29 Euro (ranging from 12.00 to 22.20 Euro including the show-up fee of 4.00 Euro) and a session lasted about 1 hour and 15 minutes. The data was collected in two sessions with each 30 participants at the University of Cologne.

5.5.2 Results

The cognitive load task was the same as in Experiment 2 except that there were only a total of 8 rounds with cognitive load compared to a total of 24 rounds in Experiment 2. The mean error rate is 9.58% (SD= 12.47, ranging from 0% to 50.00%) and significantly smaller compared to Experiment 2 (recall, mean 13.26%, MWW, z = 2.591, p = 0.0096).

The participants voted for only one alternative in plurality voting and may approve of multiple alternatives in approval voting. By design the voting decision in approval voting might potentially take longer and we decided to split the response time analysis by voting method. Figure 5.3 shows the average response time of all decisions in the No Load and Load treatments for plurality voting (left-hand side) and approval voting (right-hand side). In the case of plurality voting, the average response time is 21.77 s in the No

*** *** 0 5 10 15 20 25 30 35

Average Response Times in s

Plurality Voting Approval Voting

No Load Load

Figure 5.3: Experiment 3, Average response times of voting decisions.

Notes. ⋆⋆⋆ _{p < 0.01, WSR test.}

Load treatment and 15.32 s in the Load treatment. As expected, a WSR test confirms our prediction and shows that decisions are significantly faster in the cognitive Load treatment (N = 60, z = 5.683, p < 0.0001). For approval voting, the average response time is 22.01 s in the No Load treatment and 15.25 s in the Load treatment. Again, a WSR test confirms that response times are significantly shorter in the Load treatment compared to the No Load treatment (N = 60, z = 5.897, p < 0.0001).

Figure 5.4 shows the relative frequency of sincere votes for both voting methods and the number of votes under approval voting for the No Load and Load treatments. As performance measure we find significant differences between the amount of sincere votes between No Load and Load treatment for both voting methods. Under plurality voting, the participants voted on average 55.42% sincere in the No Load rounds and 64.17% sincere in the Load rounds. This difference is significant according to a WSR test (N = 60, z = −2.260, p = 0.0119). Under approval voting, the participants voted on average 82.92% sincere in the No Load rounds and 87.50% sincere in the Load

** ** ** 0 .5 1 1.5 2 2.5 Number of Votes 0 .2 .4 .6 .8 1

Relative Frequency of Sincere Votes

Plurality Voting Approval Voting Approval Voting No Load Load

Figure 5.4: Experiment 3, Relative frequency of sincere votes and number of votes.

Notes. ⋆⋆ _{p < 0.05,}⋆⋆⋆ _{p < 0.01, WSR test.}

rounds. This difference is less pronounced but still significant according to a WSR test (N = 60, z = −1.683, p = 0.0462). Another indicator of change in behavior in approval voting is the number of votes cast which significantly increased between treatments. The average number of votes cast is 1.75 votes in the No Load treatment and 1.875 votes in the Load treatment. According to a two-sided WSR test, this difference is significant (N = 60, z = −2.522, p = 0.0117).