An algebra problem. Find the Kerry/Bush partisan/crossover breakeven pct.

[TruthIsAll]

Let B= maximum number of Bush 2000 voters who voted in 2004.
Let G= maximum number of Gore 2000 voters who voted in 2004
Let N= maximum number of Nader 2000 voters who voted in 2004.
Let TV = Total Votes in 2004

We know B,G, N and TV.
B= 48.7 mm
G= 49.2 mm
N= 2.6 mm
TV = 122.26

Therefore we can compute the Minimum number of New 2004 Voters:
NV = TV - B - G - N.

We know Kerry got .54* NV, based on the final exit poll.
We know Bush got .45* NV, based on the final exit poll.

We know Kerry got .71* N, based on the final exit poll.
We know Kerry got .21* N, based on the final exit poll.

Assume
X1 = percentage of Gore voters for Kerry
X2 = percentage of Bush 2000 voters for Bush

Total Kerry vote is
KV = X1*G + X2*B + .54*NV + .71*N

Total Bush vote is
BV =(1-X1)*G + (1-X2)*B +.54*NV + .21*N

Next step:
Calculate the percentages X1, X2 for which KV = BV.

Anyone care to try?

[Geoff R. Casavant]

1. Infinite number of solutions

I don't have the time to show my work, but essentially you end up trying to solve for two independent variables with a single equation. If it were possible to state some kind of relationship between X1 and X2, then a single solution becomes possible.

[salinen]

2. Here's the answer

2 + 2 = we were sodomized without permission.

[wli]

3. the solution is an equation between X1 and X2

X2 = -1.010266940 X1 + .9917864476

Got any more equations and/or questions?

[TruthIsAll]

4. TYPO ERRORS IN ORIGINAL PROBLEM FIXED HERE

Let B= maximum number of Bush 2000 voters who voted in 2004.
Let G= maximum number of Gore 2000 voters who voted in 2004
Let N= maximum number of Nader 2000 voters who voted in 2004.
Let TV = Total Votes in 2004

We know B,G, N and TV.
B= 48.7 mm
G= 49.2 mm
N= 2.6 mm
TV = 122.26

Therefore, we can compute the Minimum number of New 2004 Voters:
NV = TV - B - G - N.

We assume the following percentages from the Final Exit Poll:
Kerry got .54* NV (54% of new voters)
Bush got .45* NV

Kerry got .71* N (71% of Nader voters)
Bush got .21* N

Let
X1 = percentage of Gore voters for Kerry
X2 = percentage of Bush 2000 voters for Bush

Then the Total Kerry vote:
KV = X1*G + X2*B + .54*NV + .71*N

Total Bush vote:
BV =(1-X1)*G + (1-X2)*B +.45*NV + .21*N

Next step:
Calculate the breakeven (tie vote) percentages X1, X2
That is, KV = BV.

Anyone care to try?

[TruthIsAll]

5. And the answer is...

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

[tommcintyre]

6. kick - In tribute to his tremendous contributions - WHY??? :( n/t

[bleever]

7. Kicking for truth, justice, and TIA's invaluable work.