Projecting the Electoral Vote: A Simple formula, Monte
Carlo, Meta-analysis and Undecided Voter Kool-aid
It’s very surprising that election forecasting blogs and academics who use the latest state polls as input to their models don’t apply basic probability, statistics and simulation concepts in forecasting the electoral vote and corresponding win probabilities.
A meta-analysis or simulation is not required to calculate the expected electoral vote. Of course the individual state projections will depend on the forecasting method used. But the projection method is not the main issue here; it’s how the associated win probabilities are used to calculate the expected EV, win probability and frequency distribution.
Note that the 2008 Election Model includes a
sensitivity (risk) analysis of five Obama undecided voter (UVA) scenario
assumptions ranging from 40-90%, with 60% as the base case. This enables one to
view the effects of the UVA factor variable on the expected electoral vote and
win probability. Electoral vote
forecasting models which do not provide a risk factor sensitivity analysis are
incomplete.
These
are the steps used in the 2008
Election Model.
1. Project the 2-party vote share
V(i) for each state(i) as the sum of the poll share PS(i) and UVA(i):
V(i)= PS(i) + UVA(i)
2. Calculate the probability P(i)
of winning state (i) assuming a 3% margin of error (95% confidence) based on
the average of the latest 2 or 3 polls
(1200-1800 sample size):
P(i) = NORMDIST (V(i), 0.5,
.03/1.96, true)
3. Calculate the total expected
electoral vote EV as the sum:
EV = ∑ P(i) * EV(i),
for i = 1,51
The 2004
Election Model allocated 75% of the undecided vote to Kerry and projected
that he would have 337 electoral votes (99% win probability) with a 51.8%
two-party vote share. The unadjusted,
pristine state exit poll aggregate provided by exit pollsters Edison-Mitofsky 3
months after the election indicated that Kerry won 52.0% of the vote with an
identical 337 electoral votes.
The challenger is expected to win the majority (60-90% UVA) of the undecided vote, depending on incumbent job performance. The Gallup poll allocated 90% of undecided voters to Kerry in their final projection, pollsters Zogby and Harris: 75-80%. The National Exit Poll indicated that approximately 65% of final week undecided voters broke for Kerry. Bush had a 48% approval rating on Election Day 2004.
After calculating the individual state probabilities, we can calculate the EV win probability. The best, most straightforward method is Monte Carlo simulation. This technique is widely used in many different applications when an analytical solution is prohibitive and is perfectly suited for calculating the EV win probability. The Election Model uses a 5000 election trial simulation. The win probability is the total number of winning election trials/5000. What could be simpler?
The average
electoral vote is calculated for the 5000 election trials. What could be
simpler? Of course, the average will only be an approximation to the
theoretical average computed by the summation formula. But the Law of Large Numbers (LLN) applies: the 5000 trial EV average
is always within one electoral vote of the formula. Furthermore, the average
(mean) is always within one electoral vote of the median. The close match between the Monte Carlo simulation electoral vote mean,
median and summation formula is proof that 5000 election trials are more than
sufficient. And it takes less than one second to calculate. With all due
respect to Professor Sam Wang, Meta-Analysis is an
unnecessarily complex method for calculating the expected Electoral Vote when
it can be calculated by the simple summation formula: EV =∑ P(i) * EV(i),
i=1,51
Professor Wang had it right in his initial 2004 model which projected that Kerry would win over 300 electoral votes with a 98% win probability. But he was wrong to drink the Kool-aid from the Mystery Pollster and other naysayers that Bush won the undecided vote and that the Bush 286-252 EV win represents the True Vote. Like the AAPOR, the media and other election forecasters, he never mentions Election Fraud. The vast preponderance of statistical and documented evidence indicates that the election was stolen in 2004, just like it was in 2000. His meta-analysis does not include the most important factor: fraud. The 2008 Election Model provides a sensitivity analysis of two major fraud components: uncounted and switched votes.
|
State
Poll Avg MoE |
|
LATEST
STATE POLL AVERAGE |
|
|
|||
|
3.0% |
|
|
|
|
|
|
|
|
|
|
|
Current |
|
|
Obama |
|
|
|
|
Vote share |
Obama |
McCain |
Spread |
2-pty Proj |
Win Prob |
|
|
Last Poll |
Popular |
51.34 |
43.77 |
7.57 |
54.28 |
100.0 |
|
|
Date |
Electoral |
367 |
171 |
196 |
370 |
365.3 |
|
|
|
|
|
|
|
|
|
|
10/28 |
9 |
36 |
61 |
(25) |
37.8 |
0.0 |
|
|
10/30 |
3 |
40 |
58 |
(18) |
41.2 |
0.0 |
|
|
10/30 |
10 |
46 |
50 |
(4) |
48.4 |
14.8 |
|
|
10/31 |
6 |
44 |
51 |
(7) |
47.0 |
2.5 |
|
|
10/31 |
55 |
60 |
36 |
24 |
62.4 |
100.0 |
|
|
|
|
|
|
|
|
|
|
|
11/4 |
9 |
51 |
45 |
6 |
53.4 |
98.7 |
|
|
10/22 |
7 |
56 |
35 |
21 |
61.4 |
100.0 |
|
|
9/13 |
3 |
90 |
9 |
81 |
90.6 |
100.0 |
|
|
10/28 |
3 |
63 |
33 |
30 |
65.4 |
100.0 |
|
|
11/3 |
27 |
49 |
47 |
2 |
51.4 |
82.0 |
|
|
|
|
|
|
|
|
|
|
|
10/30 |
15 |
46 |
49 |
(3) |
49.0 |
25.7 |
|
|
9/20 |
4 |
68 |
27 |
41 |
71.0 |
100.0 |
|
|
9/17 |
4 |
33 |
62 |
(29) |
36.0 |
0.0 |
|
|
11/1 |
21 |
60 |
37 |
23 |
61.8 |
100.0 |
|
|
11/3 |
11 |
46 |
48 |
(2) |
49.6 |
39.7 |
|
|
|
|
|
|
|
|
|
|
|
11/1 |
7 |
54 |
39 |
15 |
58.2 |
100.0 |
|
|
10/28 |
6 |
39 |
56 |
(17) |
42.0 |
0.0 |
|
|
11/1 |
8 |
41 |
55 |
(14) |
43.4 |
0.0 |
|
|
10/29 |
9 |
40 |
50 |
(10) |
46.0 |
0.4 |
|
|
11/1 |
4 |
56 |
43 |
13 |
56.6 |
100.0 |
|
|
|
|
|
|
|
|
|
|
|
9/20 |
10 |
57 |
38 |
19 |
60.0 |
100.0 |
|
|
10/28 |
12 |
55 |
37 |
18 |
59.8 |
100.0 |
|
|
11/1 |
17 |
53 |
38 |
15 |
58.4 |
100.0 |
|
|
11/2 |
10 |
53 |
43 |
10 |
55.4 |
100.0 |
|
|
10/29 |
6 |
42 |
53 |
(11) |
45.0 |
0.1 |
|
|
|
|
|
|
|
|
|
|
|
11/3 |
11 |
47 |
46 |
1 |
51.2 |
78.3 |
|
|
11/2 |
3 |
48 |
47 |
1 |
51.0 |
74.3 |
|
|
9/30 |
5 |
37 |
56 |
(19) |
41.2 |
0.0 |
|
|
11/2 |
5 |
51 |
44 |
7 |
54.0 |
99.6 |
|
|
10/30 |
4 |
53 |
42 |
11 |
56.0 |
100.0 |
|
|
|
|
|
|
|
|
|
|
|
10/30 |
15 |
55 |
38 |
17 |
59.2 |
100.0 |
|
|
10/31 |
5 |
53 |
45 |
8 |
54.2 |
99.7 |
|
|
10/28 |
31 |
64 |
31 |
33 |
67.0 |
100.0 |
|
|
11/3 |
15 |
49 |
48 |
1 |
50.8 |
69.9 |
|
|
10/29 |
3 |
46 |
47 |
(1) |
50.2 |
55.2 |
|
|
|
|
|
|
|
|
|
|
|
11/3 |
20 |
51 |
45 |
6 |
53.4 |
98.7 |
|
|
10/29 |
7 |
34 |
63 |
(29) |
35.8 |
0.0 |
|
|
10/30 |
7 |
56 |
39 |
17 |
59.0 |
100.0 |
|
|
11/3 |
21 |
52 |
43 |
9 |
55.0 |
99.9 |
|
|
10/1 |
4 |
58 |
39 |
19 |
59.8 |
100.0 |
|
|
|
|
|
|
|
|
|
|
|
10/29 |
8 |
43 |
53 |
(10) |
45.4 |
0.1 |
|
|
10/31 |
3 |
44 |
53 |
(9) |
45.8 |
0.3 |
|
|
10/22 |
11 |
40 |
54 |
(14) |
43.6 |
0.0 |
|
|
10/21 |
34 |
44 |
54 |
(10) |
45.2 |
0.1 |
|
|
10/30 |
5 |
32 |
56 |
(24) |
39.2 |
0.0 |
|
|
|
|
|
|
|
|
|
|
|
10/26 |
3 |
60 |
36 |
24 |
62.4 |
100.0 |
|
|
11/3 |
13 |
51 |
46 |
5 |
52.8 |
96.6 |
|
|
10/31 |
11 |
54 |
39 |
15 |
58.2 |
100.0 |
|
|
11/3 |
5 |
42 |
50 |
(8) |
46.8 |
1.8 |
|
|
10/29 |
10 |
54 |
40 |
14 |
57.6 |
100.0 |
|
|
10/29 |
3 |
35 |
58 |
(23) |
39.2 |
0.0 |
|