Hey guys! Me stuffing my maths up yet again! I was worried about not really understanding or trusting Saari's derivation of the space of ratios of votes (especially as it fails apparently to include the opinion of those who are indifferent between options) so I tried to derive it myself, using a few tricks from linear algebra... Problem is I get the following description which I am having problems simplifying- The space of the admissable ratios x (those who prefer candidate A to B over those with some opinion of difference between A and B), y (blah blah A to C) and z (blah blah B to C) is such that 0<=x,y,z<=1 and within this restraint is the union of the following spaces- Two families A: 2xyz-xy-yz+y-xz>=0 and B:2xyz-xy-yz+y-xz<=0 B(i) -yzx+yx-y+zx<=0 1+zx-z-x>=0 A(i) -yzx+zy-y+x>=0 -y-z+zy+1>=0 A(ii) -y+zy-yzx+yx+zx>=0 B(ii) -yzx+z+x-1<=0 B(iii) zx-yzx+zy-y<=0 A(iii) -yzx+yx-y+z>=0 A(iv) -y+x>=0 -2z-y+2zy+1>=0 B(iv) -y+x<=0 -2z-y+2zy+1<=0 A(v) x+z-1>=0 -2y+2zy-z+1<=0 -yx-zy+y+x+z-1>=0 B(v) x+z-1<=0 -2y+2zy-z+1>=0 -yx-zy+y+x+z-1<=0 A(vi) -2x+1>=0 z-y>=0 B(vi) -2x+1<=0 z-y<=0
