Certainly the expectation of aggression risk taking and sex drive is valid, but I don't think testosterone and 'fairness' is an accurate conclusion. T with the correct cells among other things yields a superior stress response... the ability to think, react, and handle decisions while under pressure.
I've asked this before in the social circles I run in. Crying, outside of physical trauma, occurs when a person is mentally and emotionally overwhelmed. How many times have you ever seen a man cry on the job/because of job pressures? I have never seen or heard of a instance. How many times has a woman? I have personally seen quite a few women break down in my office and I've heard of many others.
Effective leading requires a certain level of aggression, of balls, to handle all the personalities, challenges, and potential hostility. Without help, and someone to defer to when overwhelmed women quite frankly break down. With help they may overcompensate with the dreaded I must prove myself chip.
The exception to this for normal healthy women is the handling of the kind of stresses involved with children, but this in my opinion does not translate to other types of stresses.
Testosterone gives men the edge when imposing ones Will and dealing with any kind of response when making decisions for a group.