A True Vote Probability Analysis of a Kerry win in Ohio and Florida
Jan. 8, 2012
The True Vote Model (TVM) calculates vote shares and margins based on estimated returning voter mix and National Exit Poll vote shares. Popular vote win probabilities are also displayed for various vote share scenarios (“sensitivity analysis”). The analysis shows that Kerry won all plausible vote share scenarios in Ohio and Florida.
Four methods are used to estimate voter turnout based on prior election 1-recorded vote, 2-votes cast, 3-Exit Poll, 4-True Vote and an estimated turnout rate.
New voters = total votes cast in the current election – returning voters
The TVM produces sensitivity analysis (5×5 tables) of vote shares, margins and popular vote win probabilities for a range of returning and new voters. The most likely scenario is in the central cell of the table, the worst case is in the lower left cell, the best case is in the upper right cell. The win probability is a function of the 2-party vote shares and is calculated using the Normal Distribution Function.
For example, assume a 51-49% vote share split and a 3.0% input margin of error. The probability of winning a majority is given by the formula:
Win Prob = NORMDIST (.51, .50, .03/1.96, true) = 74.3%
At 7:30pm, Kerry was leading the Ohio exit poll by 52.1-47.9% (1963 respondents). He won the unadjusted exit poll (2020 respondents) by 54.1-45.9%.
At 1:41am, the poll flipped to Bush (50.9-48.6%) for the SAME 2020 RESPONDENTS, matching the recorded vote. Bush won the recorded vote 50.8-48.7%, a 119,000 vote margin.
Kerry’s Ohio win probability:
Assume 2000 election voters return in proportion to the 2000 unadjusted Ohio exit poll won by Bush (48.5-47.4%).
In the Worst Case scenario, Kerry captures 55.7% of new voters and 9.7% of returning Bush 2000 voters. He wins with 52.2%, a 313,000 vote margin and 97.1% win probability.
In the most likely Base Case scenario, Kerry captures 59.5% of new voters and 11.7% of returning Bush 2000 voters. He wins with a 53.7% share, a 480,000 vote margin and a 99.8% win probability.
At 8:40pm CNN showed a virtual tie. Of 2846 exit polled, Bush led by 49.8-49.7%.
Kerry won the unadjusted exit poll (2862 respondents) by 50.8-48.0%. But at 1:41am, the poll flipped to Bush (52.1-47.9%) for the SAME 2862 RESPONDENTS, matching the recorded vote. Bush won by a 381,000 recorded vote margin.
Kerry’s Florida win probability:
Once again, assume that 2000 election voters return in proportion to the 2000 unadjusted Florida exit poll which Gore won by 53.4-43.6%.
In the Worst Case scenario, Kerry captures 52.2% of new voters and 7.5% of returning Bush 2000 voters. Kerry has 53.2% and wins by 569,000 votes with a 99.5% win probability.
In the Base Case scenario, Kerry captures 56.2% of new voters and 9.5% of returning Bush 2000 voters. He has 54.8%, an 800,000 vote margin and 100% win probability.
Ron Baiman and Kathy Dopp at US Count Votes did a statistical analysis of 49 Ohio 2004 exit poll precincts.
The authors write:
Over 40% of Ohio’s exit polled precincts had statistically significant discrepancies. This is over four times the number of expected precincts with significant discrepancy.
• 45.1% (22 of 49) of Ohio’s polled precincts have significant discrepancy when calculations assume that official vote counts most accurately estimate actual vote share, and
• 40.7% (20 of 49) of Ohio’s polled precincts have significant discrepancy when calculated by assuming that exit poll results are a better estimate of real vote share.
Ohio’s significant exit poll discrepancies overwhelmingly over-estimated Kerry’s official vote share:
• Over 35% of precincts had official Kerry vote counts and exit poll share that had less than a 5% chance of occurring. In other words, Kerry official vote share was much smaller than expected given Kerry exit poll share in these precincts, and
• 4% (2) of Ohio’s exit polled precincts had official Bush official vote that had less than a 5% chance of occurring. In these precincts Bush official vote share (assumed to be one minus their Kerry share) was much smaller than expected, given Bush’s exit poll share.
Election Model Forecast; Post-election True Vote Model
2004 (2-party vote shares)
Model: Kerry 51.8%, 337 EV (snapshot)
State exit poll aggregate: 51.7%, 337 EV
Recorded Vote: 48.3%, 255 EV
True Vote Model: 53.6%, 364 EV
Model: Obama 53.1%, 365.3 EV (simulation mean)
Recorded: 52.9%, 365 EV
State exit poll aggregate: 58.0%, 420 EV
True Vote Model: 58.0%, 420 EV
2012 (2-party state exit poll aggregate shares)
Model: Obama 51.6%, 332 EV (Snapshot)
Recorded: 51.6%, 332 EV
True Vote Model: 55.2%, 380 EV