The legitimacy of bottom-up democratic processes for the distribution of public funds by policy-makers is challenging and complex. Participatory budgeting is such a process, where voting outcomes may not always be fair or inclusive. Deliberation for which project ideas to put for voting and choose for implementation lack systematization and do not scale. This paper addresses these grand challenges by introducing a novel and legitimate iterative consensus-based participatory budgeting process. Consensus is designed to be a result of decision support via an innovative multi-agent reinforcement learning approach. Voters are assisted to interact with each other to make viable compromises. Extensive experimental evaluation with real-world participatory budgeting data from Poland reveal striking findings: Consensus is reachable, efficient and robust. Compromise is required, which is though comparable to the one of existing voting aggregation methods that promote fairness and inclusion without though attaining consensus.
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