INTEGRITY is a new aspect I created for IconTrek renown after I realized that there is no renown aspect that measures honesty and trustworthiness.
Integrity measures your character's general honesty, sense of fair play, and morality in general. If your character consistently lies, cheats, steals, backstabs, and is generally immoral (at least according to most standards) then he probably has a large amount of negative Integrity renown. Positive integrity is earned if you tell the truth, obey the law, and do what's right even if it might not be in your best interests or cause harm to you and those close to you.
Also, certain Dark Secrets if revealed may cause you to earn a large amount of negative Integrity renown. For instance, if everyone finds out you commited adultery or cheated on a test at the academy, aside from other consequences of those actions Negative integrity is also earned.
BTW, here are the default cultural values on what different cultures/groups value Integrity:
Starfleet: High
Vulcan: High
Ferengi: Low
Romulan: Medium
Klingon: Medium
Bajoran: Medium
Betazoid: High
Cardassian: Low
What do you all think? Ideas, suggestions, anyone?