The True Vote Model: A Mathematical Formulation
A matrix is a rectangular array of numbers. The True Vote Model is an application based on Matrix Algebra. The key to understanding the theory is mathematical subscript notation. The actual mathematics is really nothing more than simple arithmetic.
The 1968-2012 National True Vote Model (TVM) is easy to use. Just two inputs are required: the election year and calculation method (1-5). Method 1 calculates the adjusted National Exit Poll which is always forced to match the recorded vote. Method 5 calculates the True Vote.
The True Vote (TV) is a function of the number of previous election returning and new voters in the current election and each candidate’s share of these voters.
TV = f(turnout, vote shares)
The US Vote Census estimates the number of votes cast in each election. Total votes cast include uncounted ballots, as opposed to the official recorded vote.
The True Vote Model is based on total votes cast – as it should be. There were approximately 40 million uncounted votes in the 6 elections from 1988-2008. Uncounted ballots are strongly Democratic.
Let TVP = total votes cast in previous election
Let TVC = total votes cast in the current election
The number of returning voters (RV) is estimated based on previous election voter mortality (5%) and an estimated turnout rate (TR).
For example, in 2004 there was an estimated 98% turnout (TR) of living 2000 voters. Voter mortality (VM) is 5% over four years (1.25% per year). We calculate returning 2000 voters as:
RV = TVP * (1- VM) * TR
RV = 103.2 = 110.8 * .95 * .98
There were 125.7 million votes cast in 2004. Therefore, we calculate the number of new voters TVN as:
TVN = TVC – RV
TVN = 24.5 = 125.7 – 103.2
In the base case we assume an equal turnout rate of previous election Democratic, Republican and other (third-party) voters.
V (1) = returning Democratic voters
V (2) = returning Republican voters
V (3) = returning other (third-party) voters
RV = V (1) + V (2) + V (3) = total returning voters
V (4) = TVC – RV = number of new voters.
Calculate m (i) as the percentage mix of total votes cast (TVC) for returning and new voters V(i):
m (i) = V (i) / TVC, i=1, 4
Let a (i, j) = candidates (j=1,3) vote shares of returning and new voters (i=1,4).
True Vote calculation matrix
Vote Mix Dem Rep Other
Dem m1 a11 a12 a13
Rep m2 a21 a22 a23
Oth m3 a31 a32 a33
Dnv m4 a41 a42 a43
The total Democratic share is:
VS(1) = ∑ m(i) * a(i, 1), i=1,4
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