The math of gerrymandering -- how, why, and where

     Lots of news articles on the topic of gerrymandering of late -- mostly about political bias and court decisions. But just what is gerrymandering and how does it work? The word was created as a merging of the name of Governor Gerry of Massachusetts and the word salamander -- due to an artist's perception of the way the electoral districts were created (from Wikipedia).

     Gerrymandering is the process of creating boundaries such that one group has the advantage over another group. It is particularly used if the process gives a minority group control over the majority group.
     Districting occurs to divide up larger areas into smaller areas. For federal government in the U.S., it is a result of the Constitution and the periodic census. For the House of Representatives, the number of representatives per state shifts depending on population as reflected by the census. Within that state, districts are created that have approximately the same number of people within each district so that each person can have an "equal representation" compared to others in the state. For state and local districting, the rules can vary from that although the principle of "equal representation" is a common ground rule.
     Note that the representation of the Senate in the U.S. does not follow this general formula. With a fixed number of Senators per state, less populous states have greater representation per person. This was done deliberately to make sure that states had equal say in certain legislation. It carries over into the Electoral College of the U.S., with less populous states having a greater proportional say than the more populous states (although the total numbers are still greater for the more populous states).
     How does it work? Let's say that we have a state divided into 100 districts (I think of it as a 10 by 10 grid). Each box/district has 100 people in it. Thus, there are a total of 10,000 people in the state (10 x 10 x 100).
     Assume that group A makes up 65% (6,500 people) within the state. Group B makes up 35% (3,500 people, there may well be more than two groups but let's keep it simple).
     One method of districting would put 65 people from group A and 35 people from group A in each district. If this is done then, within each district, group A has democratic control (assuming equal voting by each group -- not often the case in real life). Group B has very little direct control.
     Another method would put 100 people from group A in each of 65 districts and 100 people from group B in each of the remaining 35 districts. This allows for proportional representation within the state or federal level but, locally, each group would have a monopoly within its district.
     However, if we put 100 people of group A in each of 35 districts (3,500 people -- leaving 3,000 people) and distribute the rest of group A equally among the remaining 65 districts, we would have approximately (not quite exactly) 46 (3000 / 65) people from group A in each of those 65 districts. Group B would have about 54% of the population in each of those 65 districts. Thus, group A would control 35 districts (35% of the state/federal vote) and group B would control 65 districts (65% of the state/federal vote). The power of the minority is flipped with that of the majority. This is the situation that is often the focus of the term gerrymandering.
     Sometimes, as in the case of Maryland, the term gerrymander is used in shifting of the voters -- according to percentage of registered voters, Party B should have 3 out of 10 representatives; it has 1.
     There is a limit beyond which gerrymandering is not possible. For example, if 90% of the state were in group A, it would still be possible to keep the 90% representation by putting all of group A in 90 districts but it would be impossible to distribute them such that group B would take over control.
     Often, the controlling group determines how the districts are divided. Thus, once gerrymandering has occurred, it is easy to maintain control by the controlling group (even if they are the minority group) unless the total percentage of group A grows enough to preclude gerrymandering by group B (they can try, but it won't work). This is the situation that has been, and probably will continue to be, presented before the higher courts.
     It is fairly easy to determine if the minority is overriding the majority but fair districting is difficult to do to allow proportional state/federal representation and still have local (within the district) non-monopolies of the dominant group in that district.
     One solution would be to dissolve artificial grouping (George Washington hated the concept of political parties) but that is not very likely to happen.
     Although it is usually not called gerrymandering, the same process occurs in the division of a metropolitan area into school districts. The school districts COULD be created such that each district has the same tax revenue base -- ensuring that the schools within each district have the same amount of money to spend per student as in other districts. That is not often the case and the result is school districts with a higher amount per student and other districts with a lower amount per student. This could be avoided by spreading the revenue distribution over the entire metropolitan area rather than per district -- but that is often considered "unfair" by those in wealthier districts.