Mathematical Models of Politics Meet OWS
I came across this interesting pair of posts   this evening while searching for a picture like the one above. This is a rudimentary basis for thinking about the general instability of majority voting in multidimensional policy space. The basic insight is that, via majority vote among individuals represented by their ideal points P1, P2, P3, an agenda setter can move policy from the status quo x to any point in the shaded green 'win set' and from there to any point in the similarly constituted win set that would surround the new status quo, and so on throughout the entire policy space. You can find a fuller but brief explanation of the underlying logic in the second of the links above.
That link leads to the text of a talk given by a fellow named Felix Breuer at a teach-in last year in Berkeley under the auspices of an ad hoc group of "Mathematicians against Police Violence." (See the first link above.) I think it is fabulous that Breuer is talking about this stuff in the public square and that he infers from the model that dissent/protest (insofar as it helps establish the agenda) is more basic to democracy than is voting!
In any case, here are two clips of Breuer giving the talk:
P.S.: What is so cool about this is that faculty and alumni from the department where I teach were instrumental in the elaboration of this sort of model. And, by and large, political scientists presume - mistakenly in my view - that the models have anti-democratic implications.