He motivates the connection between design and justice this way:
"Social justice research has an inherent interest in how people, groups, or societies deal with competition over scarce resources. Many theories of social conflict suggest that at instances when people try to allocate scarce resources, individual (or group-based) egoistic inclinations lead to competitive action that ultimately result in social harm (Lind, 1995). A key challenge for social justice research is to overcome these harms. Market design and the related field of behavioral economic engineering (e.g., Bolton & Ockenfels, 2012) designs real-world institutions and mechanisms that align individual incentives with the underlying goals set by societies, companies or other social groups. Market design is a hybrid between theory and application as it has a strong focus on (economic and related) theory but a strong interest in applying insights in the real world, leading to the connotation of the economist as an “engineer” (Bolton & Ockenfels, 2012; Roth, 2002)"
"To sum up, I think that Roth’s (2015) book “Who gets what and Why?” provides a viable opportunity for social justice scholars to familiarize themselves with the main ideas and selected achievements of market design. Wrapped up in personal anecdotes from an exciting research life, Roth manages to introduce a topic to a broader audience that has been traditionally dominated by complex game-theoretical jargon. The mere fact that market design has been influential in many fields, among them law, medicine, education, but also government auctions, makes the field interesting to our community. In his final conclusions, Roth states that markets are not a natural phenomenon, but human artifacts that can be maintained, improved, and sometimes even newly created. With justice being a core concern of humans, market design as a method to increase procedural and distributional justice can be a valuable add-on to the justice researcher’s toolbox, especially when we adopt Roth’s relatively broad conception of a market."