Prior to Caesar's reign, the Roman world was rocked by internal turmoil and chaos, which he transformed into a peaceful empire. As a result, the founder of the Roman Empire was seen by many as a savior of traditional Roman values, and he left behind a unified civilization that lasted for another 200 years.
Augustus Caesar, like his predecessors, simply tried to do the best he could for Rome under the circumstances. The military had become too powerful under Julius Caesar, and the Senate feared the worst when its members assassinated him. Augustus bore the legacy of Julius as he expanded the Roman Empire all the way north in Belgium and then to Egypt in the south. Unfortunately, the Roman legions couldn't hold the territories they gained under Augustus and then Rome started to collapse in subsequent years. Overall, Augustus tried to do the best things for his civilization, whether he was fair or not.
We have a far different meaning of the word "fair" now than the Romans did during the days of Augustus Caesar. However, for his time he was a pretty fair man. He didn't (always) choose the path that would be easiest for him, and generally looked out for the people of Rome the best that he could.
He was extremely corrupt in snagging sole power after Julius's assassination. It involved purging any enemies and slowly manipulating the system to make the Senate essentially powerless. His reforms brought stability, but the way in which he secured power for himself and all who would succeed him was anything but fair.
He may have a salad named after him, but Augustus Caesar was just like any other Roman dictator: unfair and brutal in his treatment of those who dared to cross him. These dictators were the opposite of fair because they enforced laws by their own whim, rather than following an established legal system.