there is no unique solution.
But... we can still come up with a mathematical relationship
to calculate the breakeven Kerry vote.
Given a Kerry percentage of Bush 2000 voters, we can determine
the percentage of Gore votes he needed to tie Bush.
TV 122.26 Total 2004 votes
MaxVotes Pct2004
G 49.2 40.24% Gore
B 48.7 39.83% Bush
N 2.6 2.13% Nader
Total 100.5 82.20%
NV 21.76 17.80% New voters
Kerry
KNV 11.750 54% New votes
KN 1.846 71% Nader votes
KGV X1*49.2 X1 Gore votes
KBV X2*48.7 X2 Bush votes
Total 13.5964 + X1*49.2+ X2*48.7
Bush
BNV 9.792 45% New votes
BN 0.546 21% Nader votes
BGV (1-X1)*49.2 1-X1 Gore votes
BBV (1-X2)*48.7 1-X2 Bush votes
Total 10.338 +(1- X1)*49.2+ (1-X2) *48.7
Total Kerry = Total Bush
x1*g + x2*b +.54*nv +.71n =(1-x1)*g+ (1-x2)*b +.45*nv
+.21*n
2x1*g - g +2x2*b -b +.09*nv + .50*n = 0
g * (2x1-1) + b *(2x2-1) +.09*nv +.50*n =0
49.2 * (2x1-1) + 48.7 *(2x2-1) +.09*21.76 +.50*2.6 =0
98.4*x1 - 49.2+ 97.4 * x2 - 48.7 + 1.9584 + 1.30 = 0
98.4*x1 + 97.4*x2 = 49.2 +48.7 -1.9584 - 1.30
98.4*x1 + 97.4*x2 = 94.64
x1= (94.64 -97.4x2)/98.4
x1=.9618 -.9898*x2
x1 x2
K%G K%B
95.19% 1.00%
94.20% 2.00%
93.21% 3.00%
92.22% 4.00%
91.23% 5.00%
90.24% 6.00%
89.25% 7.00%
88.26% 8.00%
87.27% 9.00%
86.28% 10.00%
85.29% 11.00%
84.30% 12.00%
Using the Final Exit Poll, modified for the new
weightings.
If Kerry gets 2% of Bush 2000 voters, he needs 94.20% of Gore
voters to tie
2000 Pct K B N Votes
NV 17.80% 54.00% 45.00% 1.00% 21.76
G 40.24% 94.20% 5.80% 0.00% 49.2
B 39.83% 2.00% 98.00% 0.00% 48.7
N 2.13% 71.00% 21.00% 8.00% 2.6
Total 100% 49.83% 49.83% 0.35% 122.26
If Kerry gets 6% of Bush 2000 voters, he needs 90.24% of Gore
voters to tie
2000 Pct K B N Votes
NV 17.80% 54.00% 45.00% 1.00% 21.76
G 40.24% 90.24% 9.76% 0.00% 49.2
B 39.83% 6.00% 94.00% 0.00% 48.7
N 2.13% 71.00% 21.00% 8.00% 2.6
Total 100% 49.83% 49.83% 0.35% 122.26
If Kerry gets 8% of Bush 2000 voters, he needs 88.26% of Gore
voters to tie
2000 Pct K B N Votes
NV 17.80% 54.00% 45.00% 1.00% 21.76
G 40.24% 88.26% 11.74% 0.00% 49.2
B 39.83% 8.00% 92.00% 0.00% 48.7
N 2.13% 71.00% 21.00% 8.00% 2.6
Total 100% 49.83% 49.83% 0.35% 122.26