We can derive a mathematical relationship to calculate what it
would take for Bush and Kerry to tie. Given Kerry's percentage
of Bush 2000 voters (X1), we can determine the percentage of
Gore voters (X2)he needed to tie Bush. Or vice versa.
We hold the Nader and New voter percentages constant.
x1 x2
K%G K%B
94.94% 1.00%
93.95% 2.00%
92.96% 3.00%
91.97% 4.00%
90.98% 5.00%
89.99% 6.00%
89.00% 7.00%
88.01% 8.00%
87.02% 9.00%
86.03% 10.00%
85.04% 11.00%
84.05% 12.00%
Assume Final National Exit Poll percentages, with maximum
weightings based on actual 2000 votes:
Assume Kerry gets:
1) 2% of Bush's 2000 vote, he needs 93.95% of the Gore vote.
2000 Pct K B N Votes
NV 17.31% 54.00% 45.00% 1.00% 21.16
G 40.24% 93.95% 6.05% 0.00% 49.2
B 39.83% 2.00% 98.00% 0.00% 48.7
N 2.62% 71.00% 21.00% 8.00% 3.2
Total 100% 49.81% 49.81% 0.38% 122.26
2) 6% of Bush's 2000 vote, he needs 89.99% of the Gore vote.
2000 Pct K B N Votes
NV 17.31% 54.00% 45.00% 1.00% 21.16
G 40.24% 89.99% 10.01% 0.00% 49.2
B 39.83% 6.00% 94.00% 0.00% 48.7
N 2.62% 71.00% 21.00% 8.00% 3.2
Total 100% 49.81% 49.81% 0.38% 122.26
3) 8% of Bush's 2000 vote, he needs 88.01% of the Gore vote.
2000 Pct K B N Votes
NV 17.31% 54.00% 45.00% 1.00% 21.16
G 40.24% 88.01% 11.99% 0.00% 49.2
B 39.83% 8.00% 92.00% 0.00% 48.7
N 2.62% 71.00% 21.00% 8.00% 3.2
Total 100% 49.81% 49.81% 0.38% 122.26
4) 10% of Bush's 2000 vote, he needs 86.03% of the Gore vote
to tie
2000 Pct K B N Votes
NV 17.31% 54.00% 45.00% 1.00% 21.16
G 40.24% 86.03% 13.97% 0.00% 49.2
B 39.83% 10.00% 90.00% 0.00% 48.7
N 2.62% 71.00% 21.00% 8.00% 3.2
Total 100% 49.81% 49.81% 0.38% 122.26
5) 12% of Bush's 2000 vote, he needs 84.05% of the Gore vote
to tie
2000 Pct K B N Votes
NV 17.31% 54.00% 45.00% 1.00% 21.16
G 40.24% 84.05% 15.95% 0.00% 49.2
B 39.83% 12.00% 88.00% 0.00% 48.7
N 2.62% 71.00% 21.00% 8.00% 3.2
Total 100% 49.81% 49.81% 0.38% 122.26
************************************************************
Derivation of the formula:
MaxVotes Pct2004
G 49.2 40.24% Gore
B 48.7 39.83% Bush
N 3.2 2.62% Nader
Total 101.1 82.69%
NV 21.16 17.31% New voters
Kerry
KNV 11.4264 54% New votes
KN 2.272 71% Nader votes
KGV X1*49.2 X1 Gore votes
KBV X2*48.7 X2 Bush votes
Total 13.6984 + X1*49.2+ X2*48.7
Bush
BNV 9.522 45% New votes
BN 0.672 21% Nader votes
BGV (1-X1)*49.2 1-X1 Gore votes
BBV (1-X2)*48.7 1-X2 Bush votes
Total 10.194 +(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*21.16 +.50*3.2 =0
98.4*x1 - 49.2+ 97.4 * x2 - 48.7 + 1.9044 + 1.60 = 0
98.4*x1 + 97.4*x2 = 49.2 +48.7 -1.9044 - 1.60
98.4*x1 + 97.4*x2 = 94.3956
x1= (94.3956 -97.4x2)/98.4
x1=.9593 -.9898*x2