How voting rules impact legitimacy

Addressing complex societal challenges requires effective collective action, which hinges on the perceived legitimacy of decision-making processes. This paper focuses on how different voting methods impact the legitimacy of decisions. Legitimacy, a cornerstone of social choice theory and democratic initiatives, ensures equal treatment and allows for the expression of individual interests. Voting mechanisms vary in their capacity to elicit detailed preferences and incentivize truthful reporting. Majority voting, while commonly used, may not fully capture nuanced preferences, potentially leading to a "tyranny of the majority." Preferential voting methods, which allow for a more detailed expression of preferences, aim to mitigate this. Despite the importance of this relationship, a significant gap exists in research exploring how various voting methods influence perceived legitimacy. The study utilizes the open-source Votelab application to compare four voting methods—majority voting, combined approval voting, range voting, and the modified Borda count—in a controlled online experiment. Legitimacy is measured using a scale assessing compliance with and acceptance of results as fair, encompassing input, output, and throughput legitimacy. The study incorporates a political context (COVID-19 related questions) and a neutral context (color preferences) to investigate context-dependency.

The authors review existing literature highlighting the importance of perceived legitimacy in collective decision-making. They cite studies emphasizing the need for democratic mechanisms to enhance legitimacy and the limitations of previous research on the effects of alternative voting methods on legitimacy. They mention work that distinguishes between value-driven and self-interest-driven choices in voting. Prior research also shows that participatory processes generally lead to higher perceptions of fairness compared to representative decision-making. The study builds upon Tyler's definition of legitimacy as a belief in the appropriateness and fairness of authorities and institutions, considering input, output, and throughput legitimacy. They also acknowledge the context-dependency of legitimacy, which can be affected by factors such as issue criticality and time. Existing literature is used to justify the chosen methods and the legitimacy measurement approach.

The study employed a pre-registered online experiment using the Votelab application. Four voting methods were tested: majority voting (MV), combined approval voting (CAV), range voting (RV), and modified Borda count (MBC). These methods varied in complexity and flexibility, ranging from a simple binary choice (MV) to a ranked preference system (MBC). Participants (n=120) voted on four COVID-19-related questions and color preferences. The order of voting methods was consistent for all participants. A legitimacy rating (Likert scale 0-4) was collected for each method after each set of votes. The study defines a preference profile for each participant, question, and voting method, representing the assigned ratings. Variation in preferences was measured using standard deviation and divisiveness (a measure of polarization). A max-choice profile was created to track the highest-rated option across methods for each question. Clustering analysis was performed on preference profiles to investigate the influence of preference satisfaction on legitimacy ratings. Statistical tests (Wilcoxon signed rank test, Kruskal-Wallis test) were used to analyze the data.

The study found that different voting methods often yielded different outcomes, even for the same questions. This outcome variation was linked to the standard deviation and divisiveness of preference profiles: higher values indicated greater outcome dependency on the voting method. The 'protection' question showed the lowest standard deviation and divisiveness, explaining its lower outcome dependency. Analysis of max-choice profiles revealed that a significant portion of voters (32.8%) did not vote consistently across methods. Consistent voters tended to rate range voting and the modified Borda count as more legitimate. Legitimacy ratings were found to be context-dependent. In the COVID-19 context, range voting and the modified Borda count were perceived as more legitimate than majority voting, particularly for voters with well-defined preferences. Inconsistent voters, however, perceived less complex methods as more legitimate. Analysis of the area under the preference curve (AUC) showed that voters appreciating the flexibility of range voting, indicated by a higher AUC, rated it as more legitimate. The study also found no significant influence of participants' COVID-19 preferences on their legitimacy ratings, supporting the validity of the legitimacy framework used.

The findings highlight the importance of choosing an appropriate voting method based on the context and characteristics of voters. In highly polarized contexts, preferential voting methods offer advantages. However, the complexity of these methods can be a barrier for voters with uncertain preferences. The results confirm the context-dependency of legitimacy perceptions, with the choice of voting method having a greater impact on perceived legitimacy for more complex issues. The distinction between valence and position issues further complicates the relationship. The study demonstrates how the method's ability to accommodate nuanced preferences affects legitimacy perceptions, suggesting a need to consider voters' preference clarity when selecting a voting system. The consistent voters' tendency to favor more complex voting methods suggests a correlation between preference clarity and the preferred voting system.

This study demonstrates that the choice of voting method significantly impacts both the outcome of decisions and their perceived legitimacy. The ideal method depends on contextual factors, such as the complexity of the issue and the level of polarization among voters, as well as the degree to which voters have well-defined preferences. A phased approach, starting with simpler methods and progressing to more nuanced ones, could improve voter engagement and satisfaction. Future research should investigate the interplay between outcome favorability and perceived legitimacy, and explore the potential of allowing voters to choose their preferred voting method.

The study's limitations include the online setting, the specific voting methods used, and the focus on two specific contexts (color preferences and COVID-19 related questions). The sample size, while sufficient for statistical significance, might not be fully representative of diverse populations. The study didn't directly address the relationship between outcome favorability and perceived legitimacy, which warrants future exploration. The reliance on self-reported legitimacy ratings also introduces potential biases. Further research should explore a wider range of contexts and voting methods to enhance the generalizability of the findings.