As I pointed out in that thread, their solution doesn't work. You would need to choose an aggregation mechanism to combine votes. Different mechanisms will cause different systematic outcomes. Notably, some mechanisms will result in always choosing actions from one category; some mechanisms will result in sampling from different categories proportionally to their votes (much as, eg., the American system always chooses the most popular candidate, resulting in a 2-party system equilibrium; many European systems allocate seats proportionally to votes, allowing equilibria with more than 2 parties.)

You need to choose which kind of outcome you prefer in order to choose your aggregation mechanism, in order to implement their solution. But if you could do that, you wouldn't need their solution in the first place!