The Ascendant or Rising Sign determines the primary nature, temperament, physical appearance and outlook on life... all of which characterizes our outer orientation to the outside world. Yet this factor alone does not determine everything about our personality as the world perceives and vice versa... There is also the Sun, Moon and Inner Planets, not to mention the Lunar Nodes and Part of Fortune, all of which play a part in the expression of character. Speaking as one with mostly all Earth and Water Signs to color and influence my Natal Luminaries and Planets, I find that having a dynamic Leo Ascendant is not enough by itself to make me an extrovert life of the party kind of individual... in my own private personal space sometimes, but never in group or social situations.
Do we look to the Ruling Planet of the Chart... its Sign, House and Aspects? How about Planets located in the 1st and 7th Houses of the natal chart, and those close to the Ascendant (or closely aspecting it) especially? This provides some modification as does weighing the emphasis of different Elements in the Chart. I think these factors all play a part in determining how introvert or extrovert the native is, and yet there is something more to consider here...
The Core of the Individuality, Personality and Self-Image, is The Sun and The Moon. Regardless of how the outer persona of the Ascendant plays out when the individual is simply "being oneself", without the mask of outer personality and purpose used as a front... the Ascendant here simply provides a focus of perception and expression consistent with the luminary (inner) nature of the individual in question. It adds a third component of expression natural to the Ascending Sign which modifies but does not change the nature of the Sun and Moon positions.
There are those who say the Sun represents the Inner Character while the Moon rules over our more superficial personality traits in response to environment. Others say it is The Moon that is inner reflection and feeling while The Sun is the outward expression. Given the nature of the Sun and Moon as rulers of Leo and Cancer respectively, I am inclined of the Sun as outer and the Moon as inner, though recognizing it may be a bit more complex than this.
What do others think about this?