Yu. Yu. Petrunin, Yu.A. Zernova

There are several different approaches to forecasting the results of political elections. The first - a questionnaire. It is used as a method of polling the electorate, and various methods of deriving estimates of experts. The second approach to predicting the outcome of political elections can be called mathematical. Most often when this is used as a simple index model and more sophisticated methods of regression analysis and time series. A third approach is based on predicting elections, based on the biography of applicants. In this paper we develop a method of forecasting based on regression analysis, which is supplemented by more powerful methods of finding logical patterns (rules) and neural networks. Regression analysis of the presidential elections in France in 2007 showed that the results of the candidates most significantly influenced by: Royal - the number of people without a diploma and the average number of persons in the family in this region; Sarkozy - the number of citizens born abroad, and the percentage of citizens tenants ; Bayrou - the number of people without a diploma, the level of economic activity and unemployment in the region, Le Pen - the number of people without a diploma, the unemployment rate and the average number of persons in the family in the region. Regression analysis showed that the set of selected variables that characterize the social, economic, demographic and other indicators of regional development, the influence of only 3-4. The coefficient of determination in this case ranges from 0.38 to 0, 62 for different candidates. For the resulting laws to predict the election results almost impossible. To create a more powerful and accurate forecasting models used by the neural network with error back-propagation, which has three hidden layer neurons with different activation functions. The coefficients of determination using this model showed that it had identified patterns cover 93% of the sample for Royal, 95% ? for Sarkozy, 83% ? for Bayrou and 96% for Le Pen. The correlation and prediction of actual results is 0.95 for Royal, Sarkozy to 0.97, 0.85 for Bayrou and Le Pen 0.96. The mean absolute error is 0.457%, 0.322%, 0.516% and 0.284% for Royal, Sarkozy, Bayrou and Le Pen, respectively. The maximum absolute error for each candidate is 2,6%, 1,96%, 3,21% and 1,97% respectively. Thus, the used model of neural network in comparison with regression models showed the best results in coverage of the independent variables, coefficients of correlation and determination, the value of the prediction error.