In short, social combat system exist to inform roleplaying, and provide mechanical advantages and disadvantages to mechanical acts. If you choose not to invest in Willpower and face someone with a high Intimidation skill, that choice should have consequences; likewise, if I choose to invest in Willpower, it should give me a meaningful advantage when facing interrogation over Bob, who has no Willpower... Bob shouldn't be able to say "Well, my character wouldn't be scared, no matter what the dice say!" and then do as Bob pleases anyway. I paid for my character to not be scared; Bob is just declaring his immunity by fiat.
When a social conflict is engaged (persuasion, interrogation, con, etc.), it is a matter of one or more exchanges of conflict; these exchanges may be as short as a round or as long as several days. Unless prevented, someone can choose to leave social conflict at any time, so individuals may choose to capitulate when doubtful, providing minimal help. However, if soundly defeated in social conflict, they may find themselves Convinced or even Sure.
What is rolled will be determined by how each person is acting; someone who intends to lie through interrogation may be rolling Con v. Intimidation, two people haggling may roll Bargain v. Bargain or Bargain v. Value, and someone trying to resist persuasion might roll Willpower v. Persuasion. In each pass, whoever rolls LOWER will have the following happen:
1-3 Character is Shaken; they don't change their opinion, but they're more likely to in the conversation. Shaken penalties continue until after the next exchange, regardless of the length of those exchanges. If the conversation ends here, no one changes their position.
4-8 Character is Doubtful; remove 1D from their rolls until they recover. A second doubtful result results in someone being Deeply Doubtful, with 2D being removed from their rolls. A Doubtful or Deeply Doubtful person will acquiesce, but provide the minimum support possible. Information given may be only partially true, they may allow the favor but report it to their superior, they may give a little on the price, etc.
9-12 The character is Convinced. They will provide the favor requested, more or less, but may have conditions or ask for favors in return.
13+ The character is Sure. He provides the support requested, and perhaps a bit more.
The effects of social conflict (except for shaken) last at least one scene; thereafter, Willpower rolls are made daily against the conviction level (4 if Doubtful; 6 if Deeply Doubtful; 9 if Convinced, 13 if Sure). If the roll is successful, the character improves by one step. If the roll fails, but there is no complication, they do not improve. If the roll fails and there is a complication, then they "worsen" by one step; Convinced characters become Sure, Doubtful characters become Deeply Doubtful, and so on. Success with a complication causes the penalties to last an additional day, then improve. The Force Powers of Emptiness and Rage can be used to accelerate recovery from social conflict; every 4 hours of meditation in these powers, a Willpower+Control roll may be made towards recovery.
Persuasion and Investigation can be used in the manner of First Aid, though with similar restrictions; using it on oneself inflicts a 1D penalty, and more than one attempt per day increases the difficulty by one step (and, of course, you have to have access to information to perform an Investigation). Failure with a complication on this attempt results in one's conviction "worsening".
Special Case: Combat Intimidation
Combat intimidation is an action, taken at Point Blank or Short range. The aggressor rolls Intimidation v. Willpower against as many targets as they have dice in Intimidation. So someone with an 11D in Intimidation can intimidate 11 people per action; someone with 2D Intimidation can Intimidate 2 people. Attempting to intimidate more people at once inflicts a MAP for each multiple or portion thereof... with an 11D intimidation, trying to intimidate 12-22 people results in 1 MAP, 23-33 people in 2 MAP, etc. If facing a group, the entire group must be accounted for, but intimidation can be a combined action; if you're standing by yourself, it's just your intimidation that matters, but if your crew is with you, then they add to your effective Intimidation score. Each target individually rolls their Willpower against the resultant Intimidation score; if the Intimidation roll fails, the target is not mechanically affected.
Successful combat intimidation results in one's opponent being shaken; shaken is mechanically similar to stunned, with which it overlaps (so someone who is Shaken and Stunned only takes the penalties for one), but shaken effects do not affect the character beyond the second round, and do not contribute to unconsciousness due to stun effects. Someone may continue to attempt to Intimidate as often as they like, but those who have successfully resisted intimidation will not have to roll again, unless the situation changes in the intimidator's favor.