How can we judge and what we can say about the personality of Gatsby in The Great Gatsby by F. Scott Fitzgerald?

In judging Gatsby's character in The Great Gatsby, it is probably best not to see Gatsby on a scale of good and bad or positive and negative but instead in a somewhat more complex way. We might argue that the best way to judge Gatsby (and the other characters in the novel) is by considering the question of a capacity to maintain innocence, resist corruption, and believe purely in the achievement of perfection.

Many of the most direct characterizations of Gatsby deal with ideas of hope and insistence on the potential for the realization of perfection of a dream.

"If personality is an unbroken series of successful gestures, then there was something gorgeous about him, some heightened sensitivity to the promises of life.… [Gatsby had] an extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which it is not likely I shall ever find again."

Moments like these are perhaps the most pointed judgments of Gatsby's character presented in the narrative. 

Of course, Gatsby is not entirely honest and is prone to habits of speech and mannerisms that Nick finds offensive. The performance-orientation of Gatsby's character bothers Nick because there seems to be little integrity in a man so ready to wear a mask, to deceive, and to dissemble. Gatsby is a deceiver and an adulterer. He is a man of obvious self-indulgence and self-exoneration. So, there are ways that he is not a person of great moral strength.

Nick sees a strange set of values at work in Gatsby. While Gatsby is a materialist, amassing clothes and cars and money, he is also a romantic. He believes in the impossible. He believes he can erase history and replace it with a preferred love story between he and Daisy. 

It is this specific trait—the ability to look past surface realities and firmly grip a dream—that most distinctly defines Jay Gatsby and so it seems that this trait should be the basis of any judgment of his character. 

How do we judge a bootlegging optimist? What value scale do we apply to a criminal romantic? 

To answer these questions we need to look deeply at the novel's underlying themes and interests. Gatsby is deemed to be "worth the whole damn bunch put together" because he does not give in to cynicism or despair. When Myrtle is killed and Daisy is in trouble, Gatsby stands his ground and refuses to leave Daisy to face her trouble alone. Daisy, on the other hand, runs away. 

The "rotten crowd" of Daisy, Tom, and Jordan are characterized as cynics. They are people who do not pursue a dream but instead mock the dreams of others or play at dreaming from a distance. (One has a difficult time determining Daisy's sincerity in her affair with Gatsby, especially when she lets Tom sweep her away after the accident.)

There is sincerity in Gatsby and this sincerity is noted by Nick and held up for praise. This sincerity does not void Gatsby's shortcomings or make him a "good" person. But, again, the scale of good (moral) and bad (immoral) does not seem applicable here. 

If we take The Great Gatsby to be a novel about corruption (i.e., the tendency of wealth to corrupt, the corruption of the American Dream), we might judge Gatsby to be a hero because he is not corrupted into cynicism or insincerity. He maintains the specific hope with which he started. 

If we take The Great Gatsby to be a novel about one's relationship to the past and to the future, then Gatsby is perhaps the only character who stays true to the essence of his past (even while he betrays his family name and his actual, factual history). He stays true to the idea of his past in order to fulfill the promise he sees there. Admittedly, this is a somewhat complicated reading of Gatsby's character but the novel points specifically to Nick's struggle to attain a view of Gatsby wide enough and sophisticated enough to take in the complexities this man presents.