Question

In class we discussed the disputed election that ended up in the case DeMartini v. Power, 262 NE2d 857. A similar case (Ipolito v. Power 241 NE2d 232) had one candidate receiving 1422 votes and the other 1405 votes. After the election, it was determined that 101 ineligible voters had voted. (a) What is the probability that the outcome of the Ipolito election would change if 101 votes were removed at random? (In this part, leave your answer as a sum involving binomial coefficients.) (b) Write a python 3 program to compute the probability given in the previous part. (c) If you were the appelate court judge, would you rule that the vote should be redone or not? Why?

Answer 1

a) There are a total of votes. Let votes from the candidate receiving 1422 vores and from the other candidates were removed. Then

That is follows hypergeometric distribution.

If , then the number of votes for the first candidate becomes and the number of votes for the second candidate becomes . So the outcome of the Ipolito election would change if . So the required probability is

b) The Python program to compute the above probability is below

import math
p = 0
def binom(n,k):
    if k > n:
      return(0)
    else:
       a = math.factorial(n)
       b = math.factorial(k)
       c = math.factorial(n-k)
       return (a /(b*c))
    m = msq = 0.0 # 5
for x in range(60,101):
     p += binom(1422,x)*binom(1405,101-x)/binom(2827,101)
print ("Required probability is : p = %f" % p)

The output is:

Required probability is : p = 0.038723

We can verify the probability using R command:

> 1-phyper(59, 1422, 1405, 101, lower.tail = TRUE, log.p = FALSE)
[1] 0.03872303

c) Since the probability that the outcome of the Ipolito election would change is very low, the vote should not be redone.

If you have doubt pleae revert. Kindly upvote.