How redistricting/political gerrymandering can change the median voter: Illinois' 10th Congressional District

Every ten years, the US conducts a population census, and from this census, congressional district lines are redrawn in each state.  In most states, lawmakers in the state legislature draft and pass the new district boundaries just like regular laws. Also, in many of these states, the governor can sign or veto the map. However, if a single political party controls both the state legislature and the governor seat, they can essentially choose the new district lines and control who falls in what district. Naturally, as any rational person/group would, that political party redraws the lines strategically to best ensure their preferences are met. In other words, to have as many candidates of their party as possible in the House of Representatives. When a party redraws electoral district boundaries to give themselves an unfair advantage, it is called political gerrymandering, and even though it seems like it should be illegal, it isn't and happens all the time. So, how do they do this? They take advantage of the median voter theorem. 

Let's say that there is a very competitive two-party district with a normal distribution where the median, decisive voter is extremely moderate, and the median voter might swing either way. Now, imagine the party with absolute control of redistricting, Party A, redraws district lines so that the new district is more in line with Party A than Party B. Now, the median voter favors Party A. One may be thinking that Party B would simply move their ideology toward Party A, but in the real world, the MVT's assumptions do not always hold. Specifically, in the real world, candidates are dealing with many single-issue debates at a time and their mobility on policy isn't as fluid as the MVT states. So, Party A is simply moving the population distribution "closer to them" and almost guaranteeing to win the election.

One real world example that is very personal to me in the redistricting of congressional lines is the 2011 redistricting of Illinois, specifically looking at Illinois' 10th Congressional District. My uncle, former Congressman Robert James Dold Jr., won the 2010 congressional election in a 51.08%/48.92% election in a very competitive race. However, Illinois is an extremely democratic state, and in 2011, Democrats in Springfield proposed a new Congressional map that was drawn without any input from Republicans and was considered to be an attempt to undo the results of the elections held just six months ago. In the redistricting process, not only was my uncle physically forced out of his district, the district was pushed further north into more democratic neighborhoods and removing some of the swing voters that had allowed him to win in 2010. The democrats used the lack of absolute policy mobility to their advantage. They redraw Illinois' 10th Congressional District so that the median voter was now further left on a political ideology scale. Because of this, he was listed as the 5th most vulnerable Republican incumbents in 2012 as a result of redistricting. Even though my uncle was a very moderate republican, he still did not have the mobility to move his political ideology far enough to the left to account for the change of the median voter and in the 2012 election, he lost.