Current work revolves around understanding the core principles in Stephanopoulos and McGhee's Efficiency Gap article. A simpler introduction to efficiency gap is at the Brennan Center. We are attempting to get ahold of the methods paper that is referenced in note 12.
Most states use a first-past-the-post voting system, combined with a districting mechanism, and a bicameral legislative branch. (Well, all the states we presently care about, i.e., Texas.) The same mechanism is used at the Federal level, as well. The "districting mechanism" means we physically divide the population into equal-population chunks of land, where the land isn't broken into different pieces—it's all one big piece.
By definition, there is no way to "fairly" break up a state into multiple districts (it's even more unfair when there's only one district), because in a first-past-the-post system, the winner takes all: the loser gets no representation. However, in larger states, e.g., Texas, there's enough variability in the way people live in different areas that we kind of expect there to be some representation for different political parties. (We will not discuss why there are only ever two political parties in a first-pass-the-poll system.)
By cleverly arranging district boundaries, it is possible to make districts are are "more unfair" than you would otherwise expect. When that occurs, we call it gerrymandering.
The efficiency gap represents a measure (this is a math term) of the intent of the district-boundary-deciders to specifically disenfranchise political opponents, ethnic, racial, and religious groups.