Upgrading Democracies with Fairer Voting Methods

TL;DR

The paper tests fair voting methods—cumulative voting for input and the method of equal shares for aggregation—in Aarau's City Idea participatory budgeting to address distortions from majoritarian rules. It demonstrates that these methods produce more winning projects, improve geographic and preference representation, and enhance perceived legitimacy, with representation gains observed across other PB processes in Europe and Poland. A causal-analysis framework links shifts toward proportional voting to democratic values such as altruism and compromise. The study provides a practical, scalable blueprint for upgrading democracies, supported by open-source digital tools and careful consideration of governance and AI implications. Overall, the work argues for a shift from sole focus on majoritarian efficiency to fairer, more inclusive decision-making that preserves legitimacy and social cohesion.

Abstract

Voting methods are instrumental design elements of democracies. Citizens use them to express and aggregate their preferences to reach a collective decision. However, voting outcomes can be as sensitive to voting rules as they are to people's voting choices. Despite significance and interdisciplinary scientific progress, several democracies keep relying on outdated voting methods that do not fit modern, pluralistic societies well, while lacking social innovation. Here, we demonstrate how one can upgrade real-world democracies, namely by using alternative preferential voting methods such as cumulative voting and the method of equal shares designed for a proportional representation of voters' preferences. We rigorously evaluate the striking voting outcomes of these fair voting methods in a new participatory budgeting approach applied in the city of Aarau, Switzerland, including past and follow-up evidence. Results show more winning projects with the same budget. They also show broader geographic and preference representation of citizens by the elected projects, in particular for voters who used to be under-represented. We provide causal evidence showing that citizens prefer proportional voting methods, which possess strong legitimacy without the need of very specialized technical explanations. We also reveal strong underlying democratic values exhibited by citizens who support fair voting methods such as altruism and compromise. These findings come with the momentum to unleash a new and long-awaited participation blueprint of how to upgrade democracies globally.

Figures (4)

• Figure 1: Compared to the utilitarian greedy ("Standard") method, which is majoritarian in nature, the number of winning projects resulting from the method of equal shares (see column "Equal Shares") increases dramatically, with more than half of the proposed projects winning, while the citizens' proposed project ideas are better represented geographically. (A) Equal shares (s)elects 17 winning projects as compared to 7 with the majoritarian standard method. The project 'Wild bees' paradise', requiring 40% of the total budget, is popular winner under the standard method, but a loser under equal shares. This allows more low-cost projects to win, which, in combination, represent the voter preferences better. (B) Under equal shares, five districts receive more winning projects as compared to the standard majoritarian method, thereby strengthening the periphery of the city. (C) Spatial fairness increases by 44% under equal shares. This is measured by the relative reduction in the index of dispersion for the number of winning projects relative to the proposed ones for each district.
• Figure 2: Compared to earlier participatory budgeting experiences based on the standard utilitarian greedy method, the method of equal shares improves the representation of voter preferences and project categories, both in the project ideation and the project selection phase. (A) 27.8 % more voters on average get any minimum representation level using the method of equal shares as compared to earlier participatory budgeting processes based on the standard utilitarian greedy method. (B) The projects proposed for voting under equal shares promote project categories that have traditionally been under-represented, such as welfare and health, while projects that usually come with high costs, such as public transit, lose appeal. (C) When using the method of equal shares, some otherwise under-represented projects are winning. On average, project categories show a 3% higher representation.
• Figure 3: In the exit survey after voting, the method of equal shares was found to be more preferred and fairer than the standard majoritarian ballot aggregation method. Strikingly, before voting and adopting equal shares, there was no clear preference for any of the two methods, while the standard method was found fairer. The voting outcomes themselves were sufficient for individuals to determine equal shares as their preferred and fairer ballot aggregation method. (The explanation of the methods does not significantly contribute to shifting the choice to equal shares.) Furthermore, the legitimacy of equal shares was assessed based on (A) the voters' preference and (B) their perceived fairness of equal shares over the standard method. The x-axis determines the difference (gain) of the voters proportion between those choosing equal shares and those choosing the standard method. Legitimacy is assessed based on 24 combinations of winners/losers and satisfied/unsatisfied voters that are grouped into (i) satisfied winners, (ii) unsatisfied losers and (iii) mixed. Winners/losers are determined in three different ways: 1st and 2nd quartile of representation score for the winning projects that are (i) non-exclusive and (ii) exclusive between the two ballot aggregation methods. (iii) Non-supporters and supporters of the top popular losing project. Satisfied/unsatisfied voters are determined by three post-voting survey questions that assess: (i) satisfaction, (ii) acceptance of the outcome and (iii) accurate representation of will.
• Figure 4: The shift to equal shares as the preferred method after voting is explained by distinguishing human traits that reflect the promotion of strong democratic values such as being altruistic, compromisers, and supporting more expressive, inclusive ballots. In contrast, shifting to the standard majoritarian method is found among voters showing mistrust, under-representation, dissatisfaction, and self-interest. These voters also support the popular costly loser project. A classification model (with 85.92% accuracy) is designed with four classes representing the preferred ballot aggregation method before and after voting (with explanation of methods). The independent variables are human traits of voters that explain the observed transitions. (A) Distinguishing human traits of voters who shift to the standard method and equal shares after voting. These are prominently associated with democratic backsliding on the one hand, and promotion of democratic values on the other hand. (B) Summary of distinguishing qualities for those who prefer the method of equal shares over the standard majoritarian method after voting. Altruism, support of expressive, inclusive ballots and opposition to the popular, costly loser project of equal shares are qualities with the highest prominence for those voters preferring equal shares. (C) Human traits (features) that explain the preference of each voter before and after voting, in particular the transitions from the standard majoritarian method to equal shares and from equal shares to the standard method (see Figure \ref{['fig:legitimacy']}). The '*' indicates that a feature is statistically significant (p<0.05) in explaining the voters' choice of the method before and after voting.