I have a proposal to introduce some new badges to increase participation (and to introduce some competitive spirit): how about awarding badges for being a top-rated (say top 3) contributor in a league-table on a given site in any given week / month / year?
(example here: https://stackexchange.com/leagues/69/week/math, i.e. "top rank")
Something along the lines of: top contributor in any given week = bronze badge, top contributor in any given month = silver badge, top contributor in a given year = gold badge (for the avoidance of doubt, I mean top contributor in a given league table, not in a specific tag).
Also some badges for being top 3: perhaps something along the lines of being top 3 in any 3 weeks is a bronze badge, being top 3 in any 3 months is a silver badge, and being top 3 in any given year is another silver badge of a different sort. Should encourage consistency.
Introducing these badges would increase participation from already top participants as there would be an element of competition. Additionally, badges for being top-rated in a given week might increase participation from new quality contributors (i.e being top rated in a month or a year might be very difficult, but it might be achievable for new contributors to be top-ranked in a given week).
Of course, the general idea is to increase participation and quality of posts, so variations of the above proposals are welcome: i.e. badges for being top 10 contributor, instead of top 3, etc.
Edit: guys, this is a genuinely well meant proposal for increased quality participation on the various sites. If you take a step back and give it some deeper thought, hopefully you'll start to see / imagine the added value this could generate. Everyone loves being awarded badges! :)