1) Extension of country's boundaries: Trajan was highly admired for his military campaigns. He had won over Dacia and Parthia and extended the boundaries of Rome. If India was under him, it would have been reckoned for its expansionist achievements. However, such moves would have forced the country to make more enemies than friendly neighbours.
2) No secularism: India, as we know, is a secular nation. Here, people of all religions are treated as equals. Everybody has the right to practice, profess and propagate one’s own religion. However, it would not have been the same under the rule of the Roman emperor Trajan. Trajan practised persecution of Christians during his reign. He was indeed the first Roman emperor to have officially sanctioned the persecution of Christians. It can thus be estimated that the condition of India under such a fanatic would have been such where persecution of the heretics would be the norm of the land.
3) Administrative transparency: The news of scams is not infrequent these days in India. However, there were chances of reduction of such issues under the rule of Trajan. Trajan accepted the authority of the Senate and citizens of the Roman Empire. He promised to respect the freedom of his people and also keep the Senate informed about of his decisions. These measures surely could have helped to keep the people better informed of the decisions of the ruling authority. A well-informed citizenry and an active executive body could have made India more successful as a democracy.