Equal Shares and Then Some

In participatory budgeting, residents vote on how part of a city's budget gets spent. Just funding the most popular projects is not proportional, because a majority can take the whole budget. I cover the Method of Equal Shares (Peters, Pierczyński, and Skowron): divide the budget equally among voters, and fund a project only if its supporters can collectively afford it, splitting the cost as evenly as possible among them. I go into the proportionality guarantees behind the method (from justified representation to EJR up to one project), what properties it does and does not have, participatory budgeting in Pune, and open questions.