deletions | additions       diff --git a/Seats distribution forecasting.md b/Seats distribution forecasting.md  index 33d58f6..74b2c9e 100644  --- a/Seats distribution forecasting.md  +++ b/Seats distribution forecasting.md 
...
The basic problem is how to standardize our voters sample, which, although consisting of over 7,000 voters, can be biased due to several factors such as age, socio-economical status, and party activist propaganda. Our current approach to control the sample biases was designed together with Omri Dor.  We started asking users for their 2013 elections choices on February 13th 2015. We used this information, together with the 2013 elections [official results](http://www.votes-19.gov.il/nationalresults).  First, we took only the latest vote for each device id, both from the 2013 and the 2015 datasets. Next, we calculated a counts matrix \(C\) with rows for 2015 parties, columns for 2013 parties and values for the number of votes in each row-column combination. Thus, $C_{i,j}$ \(C_{i,j}\)  is the number of voters that voted for party $j$ \(j\)  in 2013 and will vote for party $i$ \(i\)  in 2015. Next, we used the counts matrix $C$ \(C\)  to estimate the transition matrix $M$ \(M$  in which $M_{i,j}$ \(M_{i,j}\)  is the probability that an individual who voted for party $j$ \(j\)  in 2013 will vote for party $i$ \(i\)  in 2015. We then generated the 2013 results vector $v$ \(v\)  from the results data, removing counts of parties for which we have no information and illegal or discarded votes. We multiplied the transition matrix by the results vector to get the forecast vector $f \(f  = C \cdot v$. v\).  The forecast vector $f$ \(f\)  now describes our prediction of the number of votes each party will get in the 2015 elections. To get a forecast of the number of seats for each party we then processed the votes forecast vector $f$ \(f\)  using the [Bader-Offer method](https://www.knesset.gov.il/lexicon/eng/seats_eng.htm), also known as the [Hagenbach-Bischoff system](http://en.wikipedia.org/wiki/Hagenbach-Bischoff_system). In our version of the Bader-Offer method we disregarded surplus vote agreements. As another layer of bias correction, we experimented with fixing of number of votes received by four major demographies to the number of votes in 2013. These demographies are: