Here's a parliamentary system I thought of yesterday, which would limit the vulnerability to kingmaker scenarios. Perhaps it'll be of interest :-) - Legislature seats are allocated according to a ranked party list method, e.g. my Bucklin party list method. - Each seat in the executive counts as some fraction of a seat of the legislature, so that parties who are in government have a bonus to their number of votes in the legislature. (The fraction is a tunable parameter.) - Forming government involves passing a decision of which parties should participate in the executive, but it is not possible to decide the composition of the executive on a finer level than this in the bill in question. The proposal thus lists the parties that will participate in government, but not the proportion of ministers they get. - When forming a government, the number of ministers from each party is given by running a house monotone k-winner election method, with the same ballots as for the legislative election, except that every party not in the proposal is eliminated. - When the proposal is considered, the parties that would get seats in the executive have their vote numbers increased as if they already were in government. - Once some proposal passes, the ministers are allocated by Brams' fair sharing protocol. Since the executive election method is house monotone, one can say "the first seat is party X's, the second seat is party Y's" and so on. So party X first gets to pick what ministry or department it wants, and gets to choose a party member for this position; then Y goes next, and so on. At any point, a party might swap the position that's up next for a position that's already allocated if the party holding that other position agrees. (E.g. the order goes X (PM), Y (Defense), Z; and Y would rather have defense; then if Y agrees, Z gets the defense position and Y gets to choose from the remaining seats as if the order had been X (PM), Z (Defense), Y.) - If the house-monotone method is Condorcetian in the sense that it initially elects centrists and then moves out towards the wings, the additional weight given by the parties in government should break ties in the legislature in favor of the centrists, which is what we'd want. I can see three problems. The first is that it's complex. The second is that it's hard to determine which proposal will win due to the bonus being "as if the proposing parties were already in government". The third is that the centrist-favoring effect depends on the size of the executive, because as k increases, the k-winner method will become increasingly proportional. So if the executive grows in size, kingmaker scenarios may return. It'd be possible to fix this by only giving a bonus to say, the first p seats (as given by the house monotone method), but then what remains of its simplicity is lost.