Election predictions

[David Hayden]

Given a partial vote count, what percentage of the remaining votes does a candidate need to win the election?

Let:
Rc = percent of counted votes that are for the republican.
Ro = percent of uncounted votes that are for the republican.
Dc = percent votes counted so far that are for the democrat.
Do = percent of uncounted votes that are for the democrat.
N = percent of all votes counted so far.
T = total # votes cast.

A candidate wins if they have slightly more votes than the opponent. So let's set them equal:
Total R votes = Total D votes
Rc*N*T + Ro*(1-N)*T = Dc*N*T + Do*(1-N)*T
(Rc-Dc)N = (Do-Ro)(1-N)
Do-Ro = (Rc-Dc)*N/(1-N)

That gives us the spread. To easily get a real number, let's assume that all outstanding votes are cast for one of these two candidates (Do+Ro = 1):
Do = 1/2 + (Rc-Dc)*N / (2*(1-N))

Or to allow expressing all values as a percent:
Do = 50 + (Rc-Dc)*N / (2*(100-N))
Ro = 50 + (Dc-Rc)*N / (2*(100-N))

Input: Rc [Enter] Dc [Enter] N XEQ A
Output: Do

Example: Trump currently has 49.7% in PA and Biden has 49.1% in Georgia with 95% of the votes counted. What percentage of the remaining votes does Biden need to win?

49.7 [Enter] 49.1 [Enter] 95 XEQ A
Answer: 55.7
So Biden needs 55.7% of the outstanding votes to win Georgia.

Code:

LBL A
Rv
-
R^
*
LastX
100
X<>Y
-
/
2
/
50
+
RTN