A True Vote Probability Analysis of a Kerry win in Ohio
Richard Charnin
Jan. 8, 2012
A table of win probabilities has been added to the True Vote Model
(TVM).
The TVM is a post-election model which calculates vote shares and
margins based on various estimates of returning voters from the prior
election. The TVM uses intermediate vote shares of returning and new
voters (based on the national exit poll) to determine total vote
shares.
There are four calculation methods which estimate voter turnout from
the prior election: 1- recorded vote, 2-votes cast (recorded
+uncounted), 3- Exit Poll, 4- True Vote.
New voters are simply the difference between returning voters and
total votes cast in the current election.
Because of the inherent uncertainty in these estimates, the TVM
calculates vote shares over a range of the estimated shares of
returning and new voters (scenarios). Two 5x5 tables of resulting vote
shares and corresponding vote margins are generated. The most likely
base case vote share in the central cell of the table, the worst case
share is in the lower left cell, and the best case share is in the
upper right cell. This is called a sensitivity analysis of vote share
scenarios.
The win probability in a pre-election or exit poll is a function of
the 2-party shares and the polling margin of error, calculated by the
normal distribution function.
For example, assume a 51-49% vote share split and a 3.0% input margin
of error (MoE).
The probability of winning a majority of the vote is given by the
Excel formula:
Prob = NORMDIST (.51, .50, .03/1.96, true)
Win probability = 74.3%
For example, consider the Ohio 2004 presidential election.
In the base case (most likely) scenario, Kerry wins 59.5% of New
voters and 10% of returning Bush 2000 voters.
The probability calculations assume a 3.0% margin of error.
The base case (most likely) scenario in the central cell of the table:
Kerry captures 59.5% of new voters and 10% of returning Bush 2000
voters.
Kerry wins Ohio with a 51.7% share (a 258,000 vote margin). His win
probability is 94%.
The best case scenario in the upper right cell:
Kerry captures 63.5% of new voters and 12% of returning Bush 2000
voters.
Kerry has 53.2%, a 427,000 vote margin and 99.5% win probability.
The worst case scenario in the lower left cell:
Kerry captures 55.5% of new voters and 8% of returning Bush 2000
voters.
Kerry has 50.2%, a 90,000 vote margin and 70.6% win probability.
https://docs.google.com/spreadsheet/ccc?key=0AjAk1JUWDMyRdGN3WEZNTUFa...
Base Case
Ohio True Vote Model Method 3
Unadjusted Ohio Exit Poll
2000 Voted Mix Kerry Bush Other
Turnout Mix Kerry Bush Other
New/DNV 995 18.1% 59.5% 38.5% 2.0% - 18.1% 62.2%
35.8% 2.0%
Gore (47%) 2,109 38.4% 91.0% 8.0% 1.0% 98% 38.4% 95.1% 3.9%
1.0%
Bush (49.5%) 2,221 40.5% 10.0% 90.0% 0.0% 98% 40.5% 10.4% 89.6% 0.0%
Other (3.6%) 160 2.9% 64.0% 17.0% 19.0% 98% 2.9%
66.9% 14.1% 19.0%
True Vote 100% 51.7% 47.0% 1.3% 100% 54.0%
45.5% 0.5%
Recorded 100% 48.7% 50.8% 0.5%
Kerry Share of New Voters (DNV)
55.5% 57.5% 59.5% 61.5% 63.5%
Share
of Bush Kerry Vote Share
12% 51.8% 52.2% 52.5% 52.9% 53.2%
11% 51.4% 51.7% 52.1% 52.5% 52.8%
10% 51.0% 51.3% 51.7% 52.1% 52.4%
9% 50.6% 50.9% 51.3% 51.7% 52.0%
8% 50.2% 50.5% 50.9% 51.3% 51.6%
Kerry Margin (000)
12% 268 307 347 387 427
11% 223 263 303 343 382
10% 179 219 258 298 338
9% 134 174 214 254 294
8% 90 130 169 209 249
Kerry Win Probability
12% 94.7% 96.8% 98.2% 99.0% 99.5%
11% 91.1% 94.4% 96.6% 98.1% 98.9%
10% 86.0% 90.6% 94.0% 96.4% 97.9%
9% 79.1% 85.3% 90.2% 93.7% 96.2%
8% 70.6% 78.3% 84.7% 89.7% 93.4%
