Social choice, arrow's theorem and open problems ? Last few months I started to lecture myself on social choice, arrow's theorem and related results.

After reading about the seminal results, I asked myself about what happens with partial order preferences, the answer is in the paper of Pini et al.: Aggregating partially ordered preferences: impossibility and possibility results. Then, I wondered if it is possible of finding a characterization of admissible social choice functions. And again someone did it (Complete Characterization of Functions Satisfying the Conditions of Arrow’s Theorem by Mossel and Tamuz). I won't give a full list, but any of the problems related to social choice I can think of where all solved in the last 5 years :(

So, do you know if there exists a survey on what was done recently in the field and what was not done?

Another question is: are you aware of complexity and social choice related problems (for instance the complexity of finding the largest subset of users that are compatible for at least one social choice function, or this kind of question).
Your question is very well timed, because the most recent issue of the CACM has an article      that does exactly this: http://cacm.acm.org/magazines/2010/11/100640-using-complexity-to-protect-elections/fulltext

In brief, there's a lot of work by Conitzer, Tovey and others on the actual hardness, both worst-case and under distributional assumptions, of cracking voting mechanisms that are in principle breakable via Arrow's theorem.