In Beyond Opinion, I mention that Romney's quitting means that Lichtman Key 2 will probably stand. This could affect who wins in November. So the question is, how many Romney delegates would have to go to Huckabee (or Paul) to topple Key 2?
Here is the present delegate count:
McCain 714
Romney 286
Huckabee 181
Paul 16
Now suppose x of Romney's 286 delegates go to McCain. The 286 - x delegates go to Huckabee, say (they could go to Paul, too, but that does not affect the result). In that case, the delegate counts would be
McCain 714 + x
Romney 0
Huckabee 181 + (286 - x)
Paul 16
We want to know at which value of x McCain's vote is less than twice that of his competitors combined; i.e., when Key 2 falls. The resulting inequality and its solution:
714 + x <= 2(181 + (286 - x) + 16)
714 + x <= 2(483 - x)
714 + x <= 966 - 2x
x + 2x <= 966 - 714
3x <= 252
x <= 84
286-x >= 202
202 / 286 >= 72%
This means that at least 72% of the Romney vote would have to go to Huckabee. Instead, there probably will be pressure on Huckabee to withdraw, and that will clinch it for McCain and secure Key 2 as well.
Elections are good sources of algebra problems, and I will make more mention of these in the future.
