Polling and Math

Every time there is an election, we are bombarded with polls giving predicted voter results. Sometimes they are pretty close, sometimes they are not but it is important for people to understand the statistics involved in polling.

There are two reasons to know about this topic, especially from a mathematical point of view.  First, sometimes polls are designed to steer people towards a certain position and second, sometimes the results are not properly interpreted by the reporting body.

Polls themselves are designed to determine the opinions of the population without asking everyone.  They ask a subset or sample whose opinion is believed to represent to whole population. One of the most important things is to select a sample whose diversity represents everyone.  Early polls from the 19th century relied on people responding with the ballots printed in newspapers.  Later on, they'd get the sample from telephone lists, automobile owners, or voting lists which means they were going with the opinions of the upper class, not the everyday man.

Often the polls quoted at news sites may be biased in that the news site is asking people to call in to register an answer and the sample comes from the views so it is not a scientific poll which takes great care to use a sample representing the population properly. 

All polls have a margin of error because the results could be different if a slightly different group of people were chosen for the sample so all margins of errors are expressed as + or - 3 %, which means that if the poll says that Dewey would beat Truman with 54% of the population's vote, they mean he might get anywhere from 51 to 57%.  In general scientific polls are considered to be correct about  95% of the time. 

If the error of margin is narrower, it means they had a larger sample.  The mathematical formula for the error of margin is basically 1/sqrt of the number of people in the sample.  So if you had a sample size of 1600 people it would be 1/sqrt(1600) or 1/40 = 2.5% error.  The error of margin helps you determine the accuracy of the poll.

Furthermore, many polls are broken down by ethnicity, gender, age, religion, or other subgroup so the over all sample size must have enough members of the particular subgroup so the error of margin stays reasonable.  Many times, the criteria for the perimeters of the poll are set by the person who designed the poll and that can effect the results.


To prove this, someone took the raw data from one pollster's prediction for the winner of the 2016 election and gave it to four respected pollsters to see how they used it to obtain their prediction for the winner of the presidential race.  The original person predicted that Hillary would win by one percentage point.  Three of the four predicted Hillary would win with an error margin of between one and four percentage points while the fourth predicted Trump by one percentage point.

As we know, Trump won. Why were four of the five wrong?  A lot of it has to do with how they designed their survey, determining likely voters, and adjusting for the actual demographics of the area.  All of these are done before the survey is done.

So today's I've covered a bit about the math behind polling as polling is so much a part of our lives and elections. 

Let me know what you think. I'd love to hear.  Have a great day.