Suppose an election has average vote share in districts party A lost y (0 ≤ y ≤ 1 2 ) and average vote share in districts party A won z ( 1 2 ≤ z ≤ 1) with y = z. Then the Declination-preferred seat share for this set of **data** is
S = 1 − 2z 2(y − z)
Note that for S = 1−2z 2(y−z) , ∂S ∂y = 2z − 1 2(y − z) 2 ≥ 0 which indicates that, as y goes up (which can be reasonably interpreted as party A getting more cracked) then S goes up (party A wins more seats). In Figure 11 we can see the level curves for S = 1−2z 2(y−z) with the allowable values of y and z, a different visualization of the information in Figure 10. We see, for example, that when the seat share S is low, y can take on any value but z is quite restricted. Conversely, when S is high, z can take on any value but y is restricted.