Fairness in Perpetual Participatory Budgeting Thomas klein Goldewijk Abstract: Participatory Budgeting (PB) is a process of collective decision-making in which citizens of a municipality have a direct say in the way public funds are spent. This has recently inspired a vast amount of mathematical and computational research into the way that public funds are to be allocated given the preferences of the inhabitants. An important desideratum is that this allocation should be fair to everybody participating. In the currently dominant mathematical models of PB – where PB is modelled as a one-shot process – fair allocations cannot always be guaranteed to exist. This thesis is an investigation into the extent to which fairer allocations can be guaranteed by taking into account previous rounds of the PB process, thereby building on the recent model of Perpetual Participatory Budgeting by Lackner, Maly, and Rey (2021).