There is of course the famous John Barden "sing - a - zed" which involves John selecting people at random, but as we all know random number theory is fair eventually. This is even easier when the host is pissed (you said it first John).

I favour "loose chairs" in which the principle is rotation, chair by chair, with the occasional intervention when the host wants one or a really good idea occurs to someone, and I am also occasionally guilty of "wandering mandolins" or "wandering harmonies" in which I and/or others follow the singing around the better to join in!