Fair Voting Outcomes with Impact and Novelty Compromises? Unraveling Biases in Electing Participatory Budgeting Winners

Abstract

Participatory budgeting, as a paradigm for democratic innovations, engages citizens in the distribution of a public budget to projects, which they propose and vote for implementation. So far, voting algorithms have been proposed and studied in social choice literature to elect projects that are popular, while others prioritize on a proportional representation of voters' preferences, for instance, the rule of equal shares. However, the anticipated impact and novelty in the broader society by the winning projects, as selected by different algorithms, remains totally under-explored, lacking both a universal theory of impact for voting and a rigorous unifying framework for impact and novelty assessments. This paper tackles this grand challenge towards new axiomatic foundations for designing effective and fair voting methods. This is via new and striking insights derived from a large-scale analysis of biases over 345 real-world voting outcomes, characterized for the first time by a novel portfolio of impact and novelty metrics. We find strong causal evidence that equal shares comes with impact loss in several infrastructural projects of different cost levels that have been so far over-represented. However, it also comes with a novel, yet over-represented, impact gain in welfare, education and culture. We discuss broader implications of these results and how impact loss can be mitigated at the stage of campaign design and project ideation.

Figures (9)

• Figure 1: Equal shares is likely to sacrifice projects among the top-4 popular ones that would otherwise get elected with the utilitarian greedy method, motivating the study of a potential impact loss. Likewise, the most popular projects have a higher share of very expensive projects compared to other cost levels. Nevertheless, compared to utilitarian greedy, equal shares is likely to select (i) more projects that are (ii) less popular. The plot shows the selection rate (Y axis) of the top-20 most popular projects (X axis) for utilitarian greedy and equal shares over 811 voting instances collected in Pabulib faliszewski2023participatory. These are 613 approval, 103 cumulative and 95 ordinal voting instances counting the scores or votes that the proposed projects receive.
• Figure 2: Impact and novelty assessment framework for voting outcomes by different aggregation methods in participatory budgeting. For each impact area, the metrics characterize the winning set (share), the proposal set (representation) and both the winning and proposal set (proportionality). These metrics are measured in terms of cost, number of projects or popularity (votes). These metrics are calculated both at the voting outcome and ballot level. The novelty metrics capture the exclusive winning projects by a ballot aggregation method and are distinguished into within-impact-area and between-impact-areas measurements, see Section \ref{['sec:methods']} for more information.
• Figure 3: Equal shares results in voting outcomes with a more frequent impact loss in infrastructural and sustainable development projects, while an impact gain of larger magnitudes is observed in welfare, education and culture projects. For the depicted metrics, (A) cost share, (B) projects share, (C) popularity share, (D) cost representation, (E) projects representation and (F) popularity representation, positive loss (Y axis, UG - ES) in an impact area (colored lines) shows outperformance by utilitarian greedy (UG), while negative loss shows outperformance by equal shares (ES). The X axis denotes election instances sorted according to impact loss. A circular marker is placed for each line to easier distinguish the number of voting instances with positive/negative loss. The four numbers next to each impact area denote the (i) % of voting instances with positive loss, (ii) the mean '$\mathtt{\sim}$', (iii) mean positive '+' and (iv) mean negative '-' impact loss. Two additional numbers with the prefixes '+' and '-' placed on each of the metrics signify the overall mean positive and negative impact loss respectively across all impact areas.
• Figure 4: Equal shares (ES) shows impact gain in projects proportionality for education, welfare, culture and health, with an impact loss in all other impact areas. Equal shares over-represents the impact areas of culture and education, while it under-represents the area of public transit. In contrast, utilitarian greedy (UG) over-represents urban greenery, environmental protection and public space, while under-representing welfare projects. For each impact area, a projects proportionality value (Y axis) of '1' represents a proportional representation of the impact areas in the winning outcome with respect to the proposed projects. The X axis denotes voting instances sorted according to projects proportionality. The numbers in the parentheses next to each impact area denote the impact loss measured by the mean difference of projects proportionality between utilitarian greedy and equal shares with respect to the value of utilitarian greedy i.e., (UG-ES) / UG.
• Figure 5: Equal shares preserves the voters' satisfaction levels for projects with impact gain, while the satisfaction levels are reduced under projects with impact loss. Equal shares shows increased voters' representation levels for projects with impact gain, while the representation levels are not influenced under projects with impact loss. For each impact area, the fraction of voters (Y axis) for different levels of (A) projects share and (B) projects representation is shown along the X axis for utilitarian greedy and equal shares. A total of 345 approval voting instances are counted, with the value of $N$ denoting the number of election instances with at least one proposed project belonging to the corresponding impact area. The numbers in the parentheses next to each impact area denote the impact loss measured by the mean difference of projects representation at the ballot level between utilitarian greedy and equal shares with respect to the value of utilitarian greedy i.e., (UG-ES) / UG.