Binary/paired Comparison With Majority rule Person 123 1st xY Z 1:X>￥ Pref. 2nd Y Z X for(x,y)2: Y>X, X>Y 3d Z x Y 3:X>Y Similarly, for(Y, z) we can get Y>Z; for(z, x)we can get z>X · Then x>Y>Z>X( cycling), transitive→Not rational• Person 1 2 3 1 st X Y Z 1 : X>Y Pref. 2nd Y Z X for (x,y) 2 : Y>X➔ X>Y 3 rd Z X Y 3 : X>Y • Similarly, for (Y,Z) we can get Y>Z; for (Z,X) we can get Z>X. • Then X>Y>Z>X (cycling) , Intransitive → Not rational Binary/paired Comparison With Majority rule