**Methodological Update: Coalition Calculator (25.11.2016)**

The coalition calculator allows the display of up to three different coalitions over time since the federal election 2009 until today.

The pollytix German election polling trend provides the data base for the pollytix coalition calculator. However, as only parties passing the 5%-threshold are gaining seats in federal parliament, parties are excluded on days they are below 5% whereas parties above 5% are extrapolated proportionally in order for them to add up to 100%. Winning coalitions of more than 50% are highlighted with a green tick.

**Methode – German Election Trend**

The *pollytix german election trend* provides the daily weighted average of all published federal voting intention polls that were conducted in the previous 20 days. It is up-to-date, accurate and politically neutral

**Key**

**Date**: The current date for the values of the *pollytix german election trend*. All surveys conducted in the previous 20 days are included in the calculation of the weighted average.

**No. of polls **: Number of polls conducted in the previous 20 days which are included in the calculation of the weighted average.

**Respondents (min)**: Total number of respondents surveyed in all the polls taken into consideration for calculation of the weighted average. This is the minimum number, because the sample size of the respondents is sometimes not available for all the surveys.

**Parties**:

**CDU/CSU**: Christian Democratic Union of Germany/Christian Social Union of Bavaria

**SPD**: Social Democratic Party of Germany

**Green**: Alliance ’90/The Greens

**FDP**: Free Democratic Party

**Left**: The Left

**Pirate**: Pirate Party

**AfD**: Alternative for Germany

**Other**: Other Parties

**Weighting**

Unlike colleagues in other countries, we have opted for a relatively simple yet sound and immediately comprehensible weighting system. The *pollytix german election trend* only makes use of two weighting variables: **Last day of survey period** and **number of respondents**.

**Last day of survey period**: The last day of the survey period is the key element for the calculation of the *pollytix german election trend*, not the publication date. If 9 days separate the date on which a poll is conducted and the date of its publication, then viewed objectively these results are already quite old, even if the survey has been recently published. Therefore, a survey is awarded a weighting of 1.0 on the last day of the survey period. After that, 0.05 is deducted from the weighting every day and accordingly the poll will completely cease to be included in the calculation of the weighted daily average after 21 days.

The idea behind this is quite intuitive: The more up-to-date a poll is, the higher its weighting in the weighted daily average should be. At the same time, the case can arise with this method that data changes retrospectively through the addition of a poll. The table beneath the chart shows which polls are included in the calculation of the values.

Sometimes, a situation arises in which no survey period is publically available. In this case, an arithmetic average is assumed as the last day of the poll: the arithmetic average of the difference between the publication date and the last survey date of all the previous published election polls of the polling institute since the last parliamentary election. If no previous polls are available, the poll will not be taken into consideration for calculation of the daily weighted average.

**Number of respondents**: Put simply, the following applies in statistical theory: The higher the sample size, the lower the margin of error, and the more accurate the results will be. At the same time, a large sample size is not very helpful in survey research if the methodology is faulty – if, for instance, the random sample reveals systematic bias and is thus not a representative reflection of the general population.

During the calculation of the daily weighted average for the *pollytix german election trend*, we do therefore want to take the sample size into account, but not overrate it. So to ensure a weighting according to the sample size, we start by calculating the average sample size of polls conducted in the previous 20 days. We then give a lower weighting to polls with a smaller-than-average sample size, and conversely a higher weighting to polls which have an above-average sample size.

In the case of polls for which no sample size is available, then in the absence of more complete information, we use the smallest sample size of all the other polls of the previous 20 days as the sample size.

**Additional comments**

**Political mood vs. projection: **: In the case of polling institutes which report on the political mood and also on projections, the values of the projection are included in the calculation of the average.

**Other parties**: If „Other parties“ are not reported on separately in a poll, the following value shall be assumed for them: 100% – the sum total of the values for the parties reported on.

**Period of the pollytix german election trend**: The calculation of the weighted average starts on 17 October 2009, i.e. 20 days after the German parliamentary election of 2009. Thus only those polls conducted after the 2009 parliamentary election will be included in the weighted average.

**Methodological update referring to non-reported values for smaller parties (16.07.2013)**

In the last few weeks some polling institutes have stopped reporting the voting intention results for small parties such as the Pirate Party and AFD as they only report values for a party above a certain threshold (the institute-specific thresholds are between 1% and 3%).

As the *pollytix german election polling trend* includes the results of a number of different polls from the previous 20 days in order to calculate the weighted average, these few missing values have not been an issue in the past and only had a marginal effect on the weighted average, as long as there have been only one or two missing values for a party in the base period of 20 days.

Due to an increasing number of non-reported values in the last days we decided to apply a minor modification to our methodology in order to adapt our calculation of the weighted average to these circumstances: Missing values for a party in the base period of 20 days will now be replaced by the weighted average of values from all polling institutes in the base period.

Naturally, this modification with retrospective and future effects only affects values for small parties and doesn’t influence values for bigger parties (which are reported consistently and hence do not have missing values).