Purple hair characters are a mix of red head and blue personalities. They are noble and have a deeper understanding of purpose and existence much like their blue counterparts. Like the Red, they seek to attain power. Unlike the Reds, Purples don’t have to use force or violence. They are the blood of royalty; power is in their blood. Purple-heads often lose touch with the people beneath them.
Purple characters can sometimes seem erratic, mysterious, or complex. Like Orange-heads, they have 2 different (and conflicting) color personalities to balance. Purple characters are also sometimes undeserving of their noble status. They can be egotistical, pompous, and consumed by wealth and power. Of course, this is a problem with any character, but Purples are more prone since they are natural royalty in their character.
Ghost in the Shell’s Major Motoko Kusangi is one of the most famous purple-heads. She leans toward the blue side of the blend with her lack of emotion. However, the red’s focus on power sometimes surfaces when she is pushed. She is complex and aloof simply because she is different from most people. She is a full cyborg. The only living part of her is her brain, and the series even casts that into question.
The Major is even disconnected from her own body since it is an interchangeable machine. This general disconnect is common of purples but not to the extreme of the Major.
Being a Purple, the Major does have a temper. It just takes a while for the red to overwhelm the cooler emotions of the blue. The Major has a deeper understanding of the way technology works than most other characters of the Ghost in the Shell series. She also has a sense of purpose that guides the members of her team. She is the leader of Section 9, and the team just isn’t the same without her presence. Yet, she doesn’t use the role or her almost goddess-like power on the internet for her own ego. She leans toward the knowledge side of her personality more than the physical.
As opposed to hair color, wearing purple is a projection of self-worth to other characters. Purple-heads are viewed as natural as opposed to projecting. The shades of purple used denote how much the character leans toward either the red or the blue. Kusangi, for example, is a blue-violet shade.
I have to note that hair color isn’t a hard or fast rule for characterization. Purple, however, has strong historical ties with the ruling class across many cultures because of the rarity and difficulty of extracting the dyes. Because of this historical trend, the color has the most hard set personality association of all the personality color relationships.