# STAR and the Nader problem

#1

I believe I found a situation in which, by honestly voting Nader 5, you can cause both Nader & Gore to lose, but by voting Gore5 Nader1, you can cause Gore to win.
Here is the model:
4 B=5 G=0 N=1
3 B=5 G=1 N=0
1 B=2 G=5 N=0
x B=0 G=4 N=5
7-x B=0 G=5 N=4

Where x represents how many are bold enough to score a third party highest. I think somewhere in the 2-5 range, Bush wins by defeating Nader in the runoff (due to that one center-left voter). However the model I posted requires x=7 for this, so something must be off.
Can someone do me a favor and check my math on this? If my conclusion is valid, then it seems that if STAR did get implemented, we would need to see an explosion in third parties and independents on the ballot in order to avoid 2PD.

#2

Let me be clear on that third paragraph (“Where x…”). I originally thought of a model where the Nader pathology worked for x=4 and above, but I either miscalculated or misremembered and the one I posted only has the pathology when x=7.
If someone could find a reasonable tweak to make x=4 have the pathology it would be greatly appreciated.