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 devised and studied in social choice literature to elect projects that are popular, while others prioritize on a proportional representation of voters' preferences, for instance, 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 framework for impact and novelty assessments. This papers 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.
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