Double Button Go.
It uses territory scoring and pass stones. But, unlike AGA rules, White is not required to make the last pass. Instead, if the player who made the first pass also makes the last pass, she does not give a pass stone for the last pass. Also, the first pass lifts any ko or superko ban, just like a board play. Therefore, if the opponent plays the second pass immediately, the first passer can retake a ko or make a play that recreates a previous whole board position. Normally, games will end with three consecutive passes, with no pass stone for the third pass.
The reason it is called double button go is that the first pass is considered a button, or a play that loses 1/2 point. The reason for the button is so that it does not matter who takes the last dame. The last pass is also a considered a button, played so that it does not matter who makes the last pass. Having the last pass made without a pass stone if made by the player who made the first pass means that we do not have to use any buttons at all to achieve the same result.
The reason that the first button (pass) lifts a ko or superko ban is that otherwise the player would have to fill in his own territory or sacrifice a stone to lift a ko or superko ban. Those plays cost 1 point and the button is meant to be an alternative play that functions exactly like such plays, but only costs 1/2 point. Since they lift ko bans, it should, as well.
Double button go is like the AGA rules, with only small changes. It produces territory scoring, which many players like, only not Japanese-style scoring, because it counts territory in seki. It also gets rid of the rule whereby White must make the last pass, which some players find confusing and arbitrary.