What would John Rawls say about Plato's conception of social justice depicted in The Republic, and what would Plato say about John Rawls's theory...

Plato's sense of justice came from his desire to make Athens less corrupt and to rectify what he saw as the degeneracy of the world around him. He defined justice as "Dikaisyne," which roughly means "righteousness," and stated that it involved setting aside one's desire to achieve only selfish aims and get benefit out of every situation—instead, one should think of the greater good.

Plato believed that the human soul contained the elements of reason,...

Plato's sense of justice came from his desire to make Athens less corrupt and to rectify what he saw as the degeneracy of the world around him. He defined justice as "Dikaisyne," which roughly means "righteousness," and stated that it involved setting aside one's desire to achieve only selfish aims and get benefit out of every situation—instead, one should think of the greater good.

Plato believed that the human soul contained the elements of reason, spirit, and appetite, and that people were able to exercise justice when none of these elements was supreme over the others. Similarly, he saw society as divided into three classes, the philosopher (similar to the individual function of reason), the warrior (similar to spirit), and the farmer (similar to the appetite). For society to achieve justice, each group had to do its duty, or specialize, without interfering with other groups. Each individual had to follow his or her duty to pursue justice, just as each group in society had to follow its own special role to achieve justice and make society function well. 

Rawls's two principles of justice were 1) each individual should have at the least the most basic liberties that others have, and 2) social opportunities should be arranged so that those with the greatest need benefit the most. Rawls's idea of the "original position" is that everyone must determine principles of justice from behind what he calls "a veil of ignorance," not knowing if they are privileged or not privileged in status. 

Rawls and Plato might disagree on some points. For example, Plato was a defender of totalitarianism, while Rawls was a liberal democrat. However, in the Republic, Plato speaks of specialization, of each person fulfilling a responsibility in society, that is similar to what Rawls speaks of in the "original position," as it's not clear what roles people have when they agree to work together to create a just and harmonious society through specialization. In the Republic, Plato speaks of Cleinias of Knossos organizing a Pan-Hellenistic society in which people must come together, and these people occupy a form of the "original position" that Rawls writes about because they don't know the status of the other people. They all must agree to the rule of Law (713-715), and the power of the many is not above the power of the few. In this sense, Plato endorses the kind of "original position" that Rawls advocates, and they are in agreement about Rawls's two principles of justice. Rawls might say that Plato's description of this society meets his two principles and the requirements of the "original position."