POLISH PRESIDENTIAL ELECTION 2010. ANALYSIS OF THE FIRST ROUND AND FORECAST OF THE SECOND ROUND RESULTS

Analysis of the first round of presidential election, performed using methods and tools available in STATISTICA package, is shown below. All of the analyses were performed exclusively on the basis of data from the table below, that is the results of first round of presidential election, announced by the National Electoral Commission (June 22^nd 2010).

Correlation matrix is required to calculate “distance” between candidates. Correlations marked red are statistically significant, thus they can not be consider as random. Take note of very high negative correlation coefficient between two major candidates: -.966. Similar polarization took place in presidential election in year 1993. Correlation coefficient between Lech Wałęsa and Aleksander Kwaśniewski was -.92 after the first round. Positive correlation coefficients imply direction of flow of votes from the candidates who were defeated to two candidates who remained.

Correlation matrix transformed into normalized distance matrix according to the formula d=(1-r)/2. Such distance ranges from 0 to 1.

Distance matrix calculated from correlation matrix shows distances between candidates in sixteen-dimensional space of provinces. Given matrix is an input value for Multidimensional Scaling. This method locates objects (candidates) on the plane to project distances calculated in original space of provinces as exact as possible. Absolute values of coordinates of points on diagram obtained using multidimensional scaling have no interpretation. Studies related to elections in Poland have confirmed frequently that two primary dimensions are: ideological dimension and urbanization dimension (see: Pietrzyk-Zieniewicz i in. (1996, 1998), Sokołowski 1996, 2002, 2005)).

Arrangement of points-candidates on diagram obtained using multidimensional scaling allows to forecast the results of second round of presidential election. Forecast will prove correct, if between the first and the second round nothing significant will happen and there will be any significant changes in political preferences and in attendance in individual groups of voters. Assumptions were made:

• Those, who supported Bronisław Komorowski and Jarosław Kaczyński in the first round, will support them in the second round as well.
• Kaczyński’s electorate will be more “disciplined”, so 97.5% of his supporters from the first round will participate in the second round. In case of Komorowski, this figure will come to 95%.
• Half of the electors, who supported candidates defeated in the first round, will not participate in the second round.
• The other half of electors will be divided inversely to the square of distance on multidimensional scaling diagram.

The result of such procedure can be turned into forecast of the second round of the election: KOMOROWSKI – 53.96%, KACZYŃSKI – 46.04%.

In the next part analyses of the results of first round are showed. The following table contains correlation coefficients between particular candidates and attendance during the election. There is only one statistically significant correlation and it is negative. Andrzej Lepper lost because of relatively high attendance. His sparse indivertible electorate is less significant in that sort of situation.

This lack of connection with attendance is noticeable on the following charts considering major candidates. Fitted parabolas are not statistically significant. They are like mirror reflection – it is another confirmation of high negative correlation.

On the basis of election results conclusions on similarity of perception of candidates can be made. Taxonomic Ward’s method was used and afterwards dendrogram shown below was obtained.

It is reasonable to divide dendrogram on the level 1.2 (it is so-called “linkage distance”). Four groups of candidates were obtained, each one with just indicative tags: “Right-wingers” – Jurek and Korwin-Mikke, “Rural” – Kaczyński, Pawlak (although this tag is an overuse for Kaczyński), “Urban” – Komorowski, Olechowski, Morawiecki (it seems to be an overstatement for the last one), “Left-wingers” – Lepper, Napieralski, Ziętek.

Interesting observations can be deduce from correlation diagram showing distribution of provinces by votes for major candidates. Estimated linear regression function has a regression coefficient smaller than one. It means that every percent of votes for Komorowski increases the number of votes for another candidates and in a result Kaczyński lost 1.03% of votes.

The next correlation diagram contains the same points, although through its center (diagonally) line of perfect equality was drawn. In provinces “under” that line Komorowski had advantage and “over” that line – Kaczyński. On the each side of that line two groups of provinces can be identified – the one with stronger and lesser support. It seems that Komorowski will hold the advantage in “his” provinces, however still he can win Mazowieckie and Łódzkie provinces over to his side.

Occurrence of territorial diversities is proven by dendrogram from Ward’s method, used for provinces in candidates space.

The results of one-way ANOVA shows that territorial diversity was caused by the distribution of votes between Komorowski, Kaczyński, Pawlak and (more or less) Olechowski. In the next table average percentage of votes in groups of provinces are listed.

The largest values (in columns) are marked in green, the smallest in pink. It allows to point out the significance of individual regions for considered candidates.

Group 1: Dolnośląskie, Śląskie, Kujawsko-pomorskie, Warmińsko-mazurskie, Wielkopolskie (the best group for Napieralski).

Group 2: Lubuskie, Zachodniopomorskie, Opolskie, Pomorskie (Komorowski gained more than 50% here, the best group for Olechowski).

Group 3: Lubelskie, Podkarpackie, Świętokrzyskie (supremacy of Kaczyński, the best group for Pawlak).

Group 4: Łódzkie, Mazowieckie, Małopolskie, Podlaskie (the worst for Napieralski).

LITERATURA

Pietrzyk-Zieniewicz E., Sokołowski A. (1996) ,„Scena polityczna w oczach wyborców - wybory parlamentarne 1993”, w: Studia Politologiczne, vol. 1, „Trudna sztuka polityki - szanse, ryzyko, błąd”, (red. Klementewicz T.), Instytut Nauk Politycznych Uniwersytetu Warszawskiego, Dom Wydawniczy Elipsa, Warszawa 1996, 139-155.

Pietrzyk-Zieniewicz E., Sokołowski A., Zieniewicz A. (1998) Jak Polak z Polakiem ...., Ciechanów: Krajowy Ośrodek Dokumentacji Regionalnych Towarzystw Kultury, s.132.

Sokołowski A. (1996), „Unemployment and Presidential Election in Poland 1995” w: Statistical Methods of the Analysis of Socio-Economic Aspects of Labour Market in Poland and Slovakia. Kraków: Akademia Ekonomiczna, 49-51.

Sokołowski A. (2002), „Polska scena polityczna 2001 – wyniki wyborów parlamentarnych”, Prace Naukowe Akademii Ekonomicznej im. Oskara Langego we Wrocławiu, Nr 942, Taksonomia 9. Klasyfikacja i analiza danych – teoria i zastosowania. (Jajuga K., Walesiak M., pod red.), Wrocław, 417-419.

Sokołowski A. (2005), „Analiza wyników wyborów w III RP”, w: „Przegląd programów z rodziny STATISTICA”, StatSoft Polska, Warszawa – Kraków, 57-66.

StatSoft, Inc. (2009). STATISTICA PL (systemy analizy danych i data mining), wersja 9.0. www.statsoft.pl.

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