The correct answer for the author of the book "The Idea of Justice" is option 1, Amartya Sen.

Amartya Sen is an Indian economist and philosopher who has made significant contributions to the fields of welfare economics and social choice theory. He is known for his work on poverty, famine, and development economics. In "The Idea of Justice," Sen explores the concept of justice from a philosophical perspective. He argues that justice should be seen as a process of removing various types of injustices rather than achieving a perfect, ideal state of justice.

Option 2, Arundhati Roy, is a well-known Indian author, but she is not the author of "The Idea of Justice." Roy is best known for her novel "The God of Small Things" and her activism on social and political issues in India.

Option 3, Amitav Ghosh, is another acclaimed Indian author, but he is not the author of "The Idea of Justice" either. Ghosh is known for his works of fiction, such as "The Shadow Lines" and "The Glass Palace."

Option 4, Anurag Adiga, is not a well-known author, and there is no known book by him titled "The Idea of Justice."