I really don't think this should be THE priority in this area- and I also don't think it would in fact change a lot in the scientific publishing process (not to mention that I doubt it would ever work: eg, I bet with everyone that I can find the author of a paper from its title and content, in most cases- hence, 'double blind' is already useless). Au contraire, I would be more than fine with publishing/disclosing the referee reports (with the names of the referees) completely ( if I am not mistaken, something similar materialized in a very serious proposal of one of the very ambitious former editors of the PNAS): that would make people more objective, more careful and more serious in refereeing. A scientist should do a "scientific" job, as objective as possible, when refereeing, no matter his/her relationship or attitude towards the person who's article is refereed and, in particular, both friendship and animosity should be left outside the scientific domain.
Next to that, in certain disciplines the biggest problem is the ridiculously long time it takes to get the referee reports (Economics is very much one of the worst fields in this respect), hence one ambitious (and equally 'utopian' idea, from the perspective of the scientific administrators and decision makers nowadays, as the triple-quadruple-etc blind review) idea would be allowing any paper to be sent simultaneously to more journals, at the same time. This could be done by eventually compelling the author to accept publication in the journal that moves fastest with a positive decision and to immediately withdraw the paper from the refereeing process in the other outlets; and eventually also asking a fee from the author if the paper has to be withdrawn in the refereeing process from any of the the outlets, proportional to the number of those outlets. This should be an incentive for the author to target very carefully the journals and to choose only a very small number of them (one-three) to start with, but also an incentive for the journals to compete for fast paper review processes.
The link for the 'triple blind review' proposal is via Marginal Revolution.