Question: The table below has an analyst’s assumptions
on the probability of the Democrat winning in 9 Senate races that are currently
in contention. Assume all races are
independent. Currently the Democrats
have 5 seats and need to gain 2 seats to get control of the Senate.
State

Prob Dem Win

Dum if State is currently
held by Democrat

AZ

0.55

0

FL

0.55

1

IN

0.55

1

MO

0.55

1

NV

0.55

0

MT

0.6

1

ND

0.5

1

TN

0.4

0

TX

0.4

0

Based on these probabilities and
the assumption of independent outcomes for state races use the RAND and IF
statement to generate the frequency of potential senate outcomes after the
November 2018 election.
Discuss how the spreadsheet
is created.
Discuss how the assumption of
independent state outcomes impacts results.
Creation of Senate Outcome Spreadsheet:
Follow these steps:
Use Rand() statement to
create at least 2000 random outcome numbers
between 0 and 1 for each state.
Columns E through M starting at row 3 have the random outcomes for the
nine states.
Row 2 of Columns 2 through M
have the probability of the Democrat candidate winning the election.
Use if statement to create a
dummy outcome variable 1 if Dem wins 0 if Rep wins for all random outcomes for
all states. Outcome variables are in Row
O to Row W.
Remember row 2 has the
probability of Democratic Candidate winning.
The syntax for first
observation on outcome AZ first observation in cell O3 is
If(E3<=E$2,1,0)
Copy O3 to P3:W3.
Copy O3:W3 down at least 2000
cells.
In column X sum columns O to
W.
Final step is take frequency
of totals for the 2000 plus observations Use the FREQUENCY function.
Total Democratic Wins

# Observations

0

3

1

11

2

84

3

310

4

514

5

602

6

382

7

135

8

20

9

0

Sum

2061

7, 8 or 9

0.075206211

6,7,8 9

0.26055313

To take Control of the Senate
Democrats need to win 7 of these races because Pence the Veep breaks the tie,
The likelihood of this
happening with these optimistic probability assumptions is around 7.5%.
Under these assumptions, the probability
of a 50/50 Senate with the tie going to the Republican is 26%.
The most likely outcome.
based on these probabilities and the assumption of independent state outcomes,
is Democrats take 5 seats and Senate remains at 5149 Republican:
The role of independent state outcomes:
The results presented here assume
state outcomes are independent. State outcomes
can be influenced by national or world events.
The Kavenaugh hearings appeared to help Republicans in several
states. A surprise event like continual
declines in the stock market or perhaps solid proof the Putin has been
controlling Trump might help Democrats in more than one states.
Also, the big unknown is who
will go to the polls. Pollsters rely on
the concept of the likely voter.
However, new people are registering, both Democrats and Republicans, and
we don’t know who will go to the polls.
The difference between likely and actual voters may not be independent
across states.