@lime trying to imagine what PB-VCG would look like practically in this context, given we're electing voters to offices of varying power rather than fulfilling projects with known costs. Each member votes with virtual assets, single offices "priced" and allocated with normal Vickery, set of comparable offices with VCG? Auction order would have a large effect. Would expect many offices to have multiple all-in bids, which is problematic when they're using equal virtual assets.

So much of voting reform is focused on election to office when mechanism choice is only more important within office. The US House Speaker (a sort of constitutionally fictitious position, for what it's worth) was unseated for several weeks last year for reasons tied up in voting pathologies. You could imagine using some kind of cardinal multi-winner method to elect a steering committee that then simply appoints positions, but Nebraska seems to indicate this gives undesirable self-appointment authority to those winners. Is there some kind of asset voting method that would allow members at the beginning of a session to negotiate for committee positions, who then use a simple cardinal method to elect their own leaders from among themselves? I'm sure there is literature on this, so casting a wide net in hopes of reference.