The True Vote Model: A Mathematical Formulation

Richard Charnin

Feb.5, 2013

A matrix is a rectangular array of numbers. The 1968-2012 National True Vote Model (TVM) 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 model is easy to use. Just two inputs are required: the election year and calculation method (1-5). The calculation methods are:

1- National Exit Poll (“mix” adjusted to match the recorded vote)

Returning voter turnout calculated based on the previous election

2- recorded vote

3- votes cast (including allocated uncounted votes)

4- unadjusted national exit poll

5- True Vote

In each election, the Final National Exit Poll vote shares are used – except for 2004 in which 12:22am shares are used; they were “adjusted” and forced to match the recorded vote.

**According to the adjusted National Exit Poll, there were millions more returning Bush voters from the previous election than were living in 1988, 1992, 2004 and 2008 – a mathematical impossibility and proof of election fraud beyond any doubt.
**

It is obvious that there must be fewer *returning* voters than the number who voted in the prior election for each candidate. Approximately 5% of voters pass in the four years between elections.

The *US Vote Census* provides an estimate of the number of votes *cast* in each election. Total votes cast include *uncounted ballots*, as opposed to the official recorded vote. There were approximately 40 million uncounted votes in the 6 elections from 1988-2008. Uncounted ballots are strongly Democratic.

The * National True Vote Model * is based on total votes cast in the prior and current election. The True Vote (TV) is a function of the number of previous election returning and new voters and each candidate’s share of these voters.

**Sensitivity Matrix: alternative scenarios**

These tables gauge the sensitivity of the total candidate vote shares to changes in their shares of returning and new voters.

In 2004,Bush won the recorded vote by 3 million (50.7-48.3%). However, at the 12:22am National Exit Poll timeline (13047 respondents), Kerry had 91% of returning Gore voters, 10% of returning Bush voters and 57% of New voters. In this base case scenario, Kerry had a 53.6% True Vote share and 10.7 million vote margin.

Sensitivity analysis indicates that Kerry won all plausible (and implausible) scenarios. Bush needed an impossible 110% turnout of Bush 2000 voters to win the fraudulent recorded vote.

Adjusting the base case vote shares to view worst case scenarios:

1) Kerry has 91% (no change) of returning Gore voters, just 8% of returning Bush voters and 53% of New voters. Kerry’s total vote share is reduced to 52.1% and a 7.2 million winning margin.

2) Kerry has just 89% of returning Gore voters, 8% of returning Bush voters and 57% of New voters (no change). Kerry’s total vote share is reduced to 52.0% and a 6.9 million margin.

3) Assume the base case vote shares, but change the 98% returning 2000 voter turnout rate to 94% for Gore and 100% for Bush. Kerry’s total vote share is reduced to 52.7% and a 8.5 million margin.

4) Assume the base case 98% turnout of returning Gore and Bush voters and 91% Kerry share of returning Gore voters. To match the fraudulent recorded vote, Bush needed 61% of New voters compared to his 41% exit poll share. He also needed 96% of returning Bush voters compared to his 90% exit poll share. The required shares easily exceeded the 2% margin of error. The probabilities are infinitesimal.

**Returning voters**

The number of returning voters (RV) is estimated based on previous election *voter mortality* (5%) and an estimated *turnout rate* (TR).

Let TVP = total votes cast the in previous election.

Let TVC = total votes cast in the current election.

In 2000, 110.8 million votes (TVP) were cast. Voter mortality (VM) is 5% over four years. In the base case, we assume equal 98% turnout (TR) of living 2000 voters. We calculate (RV) returning 2000 voters:

RV = TVP * (1- VM) * TR

RV = 103.2 = 110.8 * .95 * .98

In 2004, 125.7 million votes were cast. The number of new 2004 voters (TVN) is the difference between 2004 votes cast (TVC) and returning 2000 voters (RV):

TVN = TVC – RV

TVN = 24.5 = 125.7 – 103.2

**Matrix notation**

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

This is a shortcut mathematical notation for:

VS(1)= m(1) * a(1,1) + m(2) * a(2,1) + m(3) * a(3,1) + m(4) * a(4,1)

Republican share: VS(2) = ∑ m(i) * a(i,2), i=1,4

Third-party share: VS(3) = ∑ m(i) * a(i,3), i=1,4

**Mathematical vote share constraints**

Returning and new voter mix percentages must total 100%.

∑m (i) =100%, i= 1, 4

Candidate shares of returning and new voters must total 100%.

∑a (1, j) =100%, j=1, 3

∑a (2, j) =100%, j=1, 3

∑a (3, j) =100%, j=1, 3

∑a (4, j) =100%, j=1, 3

Democratic + Republican + third-party vote shares must total 100%.

∑ VS (i) = 100%, i=1,3

**Adjusted 2004 National Exit Poll (match recorded vote)**

2000 Votes Mix Kerry Bush Other Turnout

Gore 45.25 37% 90% 10% 0.0% 93.4%

Bush 52.59 43. 9.0 91. 0.0 109.7 (impossible)

Other 3.67 3.0 64. 14. 22. 97.7

DNV. 20.79 17. 54. 44. 2.0 -

**Total 122.3 100% 48.3% 50.7% 1.0% 101.4%**

```
```**2004 True Vote Model**

2000 Votes Mix Kerry Bush Other Turnout

Gore 52.13 41.5% 91% 9.0% 0% 98%

Bush 47.36 37.7 10.0 90.0 0.0 98

Other 3.82 3.00 64.0 14.0 22. 98

DNV. 22.42 17.8 57.0 41.0 2.0 -

**Total 125.7 100% 53.5% 45.4% 1.0% 98%**

**Kerry share of New voters (DNV) **

Pct 39.% 55.% 57.% 59.% 61.%

of Bush........ Kerry % Vote Share

12% 51.1 54.0 54.3 54.7 55.1

11% 50.7 53.6 54.0 54.3 54.7

10% 50.4 53.2 53.6 53.9 54.3

9.% 50.0 52.9 53.2 53.6 53.9

4.% 48.1 51.0 51.3 51.7 52.1

............... Kerry Margin

12% 4.6 11.8 12.8 13.6 14.6

11% 3.7 10.9 11.8 12.7 13.6

10% 2.7 10.0 10.9 11.8 12.7

9.% 1.8 9.0 9.91 10.8 11.7

4% -2.9 4.3 5.18 6.08 7.00

`..........Returning Gore Voter Turnout`

Bush 94.% 95.% 96.% 97.% 98.%

Turnout..... Kerry % Vote Share

96% 53.4 53.5 53.7 53.8 53.9

97% 53.2 53.3 53.5 53.6 53.8

98% 53.0 53.2 53.3 53.4 53.6

99% 52.8 53.0 53.1 53.3 53.4

100% 52.7 52.8 52.9 53.1 53.2

............... Kerry Margin

96% 10.3 10.7 11.0 11.4 11.8

97% 9.86 10.3 10.6 10.9 11.3

98% 9.42 9.78 10.1 10.5 10.9

99% 8.97 9.33 9.69 10.1 10.4

100% 8.52 8.88 9.24 9.60 9.96