One advantage, as I see it, of lottery-voting is that because it treats each vote equally it can easily accommodate weighted voting: if you want someone to count double, simply give them two chances. For this reason, I'm particularly interested in proposals that might recommend such.
One is Harry Brighouse and Marc Fleurbaey's 'On the Fair Allocation of Power', now available at the revamped Equality Exchange. I first saw this presented at the Nuffield Political Theory Workshop about two years ago, and enjoyed an interesting email exchange with the latter author.
I've just come across another, a David Heyd paper on 'Democratically Elected Aristocracies'. I haven't read it yet, but it seems maybe a similar idea - people being asked to agree on voting weights in the first tier of the process, then votign according to such weights.