Forest-- You mathematicians are more versatile than most of us, and can perceive things that for many, are way too confusing. The mathematicians' descriptions & discussions of XA are confusing for me, which is why I just call that method "Approve To Desired Total" (ATDT). The version of ER Bucklin that is now my favorite, with equal-ranking anywhere allowed, and with skipping allowed, and without that automatic skipping that I used to suggest (for preserving MMC) is, of course equivalent to MJ. You said that ATDT is better than ER Bucklin/MJ because, with an electorate polarized about a candidate, ER Bucklin tends to put that candidate at top or bottom, rather than at a more middle place that better reflects hir average likedness. But I _want_ to send the good candidates to top, and the bad candidates to bottom. So how is ATDT better than ER Bucklin, as regards voting strategy? Michael Ossipoff