This study examines legitimacy in municipal budgeting decisions, focusing on input, throughput and output dimensions. Using data from four Swiss studies, we explore how citizens assess these dimensions across traditional and innovative decision-making processes and investigate the impact of different voting methods on legitimacy perceptions. Our findings reveal that in routine processes using traditional voting, legitimacy dimensions are considered collectively. Conversely, in innovative participatory budgeting, dimensions are judged separately, involving more active evaluation. Throughput legitimacy (perceived fairness) emerges as crucial in both contexts, while input and output legitimacy's importance varies by process type. The Method of Equal Shares voting system shifts focus towards procedural fairness, increases representation and is perceived as fairer than the traditional Greedy method. However, even fair processes cannot fully compensate for outcome dissatisfaction, highlighting the complex interplay of legitimacy dimensions. This research contributes to understanding legitimacy construction in municipal decision-making, offering insights into the relationship between voting methods and legitimacy perceptions. The findings have implications for policy-makers seeking to enhance the effectiveness and acceptance of budgeting processes. This article is part of the theme issue 'Co-creating the future: participatory cities and digital governance'.
Keywords: democratic decision-making; fairness; legitimacy; measurement; voting methods.