@toby-pereira We introduced MES originally in this paper https://arxiv.org/abs/1911.11747 for committee elections, but allowing rules to select "up to k" candidates rather than "exactly k" candidates. As you say, MES can select fewer than k candidates (including no candidates at all). We have discussed ways to top up the committee to contain exactly k candidates in various places. In the linked original paper, we suggest continuing with Sequential Phragmén. In the participatory budgeting focussed follow-up paper https://arxiv.org/abs/2008.13276 we propose (but don't necessarily endorse) "epsilon-completion" which behaves quite differently. As far as I know, there is not yet a principled approach to decide which completion is the best one.

@toby-pereira We introduced MES originally in this paper https://arxiv.org/abs/1911.11747 for committee elections, but allowing rules to select "up to k" candidates rather than "exactly k" candidates. As you say, MES can select fewer than k candidates (including no candidates at all). We have discussed ways to top up the committee to contain exactly k candidates in various places. In the linked original paper, we suggest continuing with Sequential Phragmén. In the participatory budgeting focussed follow-up paper https://arxiv.org/abs/2008.13276 we propose (but don't necessarily endorse) "epsilon-completion" which behaves quite differently. As far as I know, there is not yet a principled approach to decide which completion is the best one.