I have, at long last, finished a manuscript on FBC. https://sites.google.com/site/physicistatlarge/FBC09.pdf
In brief, I prove that methods satisfying Strong FBC can be grouped into 4 categories. One encompasses point systems that give equal points to first and second place. Another is closely related, involving point systems and thresholds of support. Methods in the third category are hard to construct, but if we relax my very strict phrasing of SFBC to allow for cases where voters sometimes (but not always) have incentives to rank 2 candidates in first place, you get MDDA. The 4th category is shown to be "uninteresting" because the methods make mathematical sense (they divide the space of all possible electorates into non-overlapping and symmetric regions without violating FBC) but no practical sense (you can't really interpret these methods in terms of any simple, meaningful criteria). In order to get feedback on this, I've started a blog where readers can critique the manuscript in comment threads, and where I will also be posting on other election-related matters as the mood strikes me. http://votingmath.blogspot.com/ Anyway, I welcome comments. If critiques show that the results and methods are valid, I hope to submit to a peer-reviewed journal. Alex Small
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