Statistical analysis for predicting election results

Recently, I read an article about the bookies prediction on Scottish independence referendum (Link). Purpose of referendum was to identify whether Scots want to be independent. There were two options: yes or no. Article stated that according to bookmakers` statistics, about 75% of the voters would choose “No”, while approximately 25% would choose “Yes”.
After some research, I found another article in the news that supports the bookmakers` view (Link). Professor Bell, who is professor at University of Stirling, got the similar results during his analysis  of prediction markets. It showed that the probability of Scots answering negatively is 70%. Pr. Bell`s analysis was presented four months before the actual referendum. According to Scottish Parliament Information Centre, the results were 44.7% and 55.3% for and against Scottish independence, respectively. Consequently, the prediction of bookmakers was correct.

Interestingly, these prediction markets use the mathematical concepts of statistical analysis for their forecasts. Meanwhile, the statistical analysis uses theorems of probability. Britannica states that the theory of probability is the chapter of mathematics that studies chances of some event.

To understand how statistical analysis works it is necessary to know some basic theorems of probability. Consider the picture below.

Picture 1. Choosing the pill. Link                                  Figure 1. Basic Probability Formula

What are the chances that you will take red pill? Obviously, it is equal to 50%.  However, this example was not based on any factors. In contrast, bookmakers consider various types of factors during statistical analysis. For instance, consider football match between Real Madrid and Barcelona.

Picture 2. Match statistics. Link

Picture 3. Players statistics. Link

Picture 4.  Team statistics. Link

The pictures above show different types of factors, such as previous match results, players` conditions, date, etc. Bookmakers analyze every factor independently. Then they combine results to get the most accurate prediction. One major characteristic of the statistics is that its amount is always increasing. Bookmakers gather more statistical data everyday, which need to be sorted. Therefore, prediction traders spend their time trying to achieve the most precise analysis.

In addition, Pr. Bell argues that statistical prediction is better than commonly used opinion poll for several reasons.
Firstly, the results of the statistical analysis are more constant in comparison with the public survey. The opinion of people may change during the election period depending on the propaganda, advertisements, and recognition of new information. In contrast, statistics of the previous years, ethnic division, age, and other factors cannot change significantly in the short period of time.
Secondly, statistics are just numbers which are objective and easy to confirm. On the other hand, survey results depend on various factors. For instance, the survey-conducting organisation may be biased towards the candidate who is funding that company.
Finally, public surveys are more expensive and need more time in comparison with the prediction markets. If bookmakers have enough information, they can analyse it in several days. In contrast, for completing the survey: firstly, people should be interviewed, then survey-conducting company should sort that information, and finally, analyse it.

Some global survey companies are already combining the opinion poll and statistical analysis methods to get more accurate forecasts. Harris Interactive - one of the largest survey companies - is developing statistical research methods by collecting its online survey results. Consequently, this method might widen the use of the mathematics in the other spheres, such as economics and politics.

Additional links for further research:

Bookmakers’ Betting Odds. Link
About Referendum (continued). Link
Bookmakers' Odds and Support Theory. Link

Reference list:

"About Us." Harris Interactive. http://www.harrisinteractive.com/AboutUs.aspx (accessed October 2, 2014).

Ayton, Peter. "How to Be Incoherent and Seductive: Bookmakers' Odds and Support Theory ." Organizational Behavior and Human Decision Processes 72, no. 1 (1997): 99-115. doi: 10.1006/obhd.1997.2732

Fingleton, John , and Patrick Waldron. "Optimal Determination of Bookmakers’ Betting Odds: Theory and Tests." Trinity Economic Paper Series. Technical Paper No. 96/9 (1999): 1-48.

"Scottish independence odds: bookmakers shorten odds on No." The Week UK. http://www.theweek.co.uk/uk-news/scots-independence/60436/scottish-independence-odds-bookmakers-shorten-odds-on-no (accessed October 2, 2014).

Scottish Parliament Information Centre "Scottish Independence Referendum 2014: Results Scottish Independence Referendum 2014: Results.." Scottish Parliament. http://www.scottish.parliament.uk/ResearchBriefingsAndFactsheets/Scottish_Independence_Referendum_2014_Results.pdf (accessed October 2, 2014).

Siegmund, David. "Probability Theory." Encyclopedia Britannica Online. http://www.britannica.com/EBchecked/topic/477530/probability-theory (accessed October 2, 2014).

University of Stirling. "Bookies may be best bet to predict Referendum." Phys.org. http://phys.org/news/2014-05-bookies-referendum.html#inlRlv (accessed October 2, 2014).

University of Stirling. "Study shows risk-takers more likely to vote 'Yes' in referendum." Phys.org. http://phys.org/news/2014-05-risk-takers-vote-referendum.html#inlRlv (accessed October 2, 2014).