So to recap the stats:

SP represents popularity. Your actions each turn/month will generally increase your popularity. SP points are translated down to simplified AI and SI ranging from 1-10.

AI represents assembly influence. Every player and CPU has AI. Combined, it represents the voting weight your faction has based on the clients you and your senators control. Your voting power is based on your relative percentage of the total AI among all players.

SI represents senate influence. Unlike AI, it is not used directly in voting on proposals. It is your relative standing and respect among the senators. It is simply used to determine attempts to recruit senators to your faction. When a vote is called in the senate, you and each of the senators you control has 1 vote out of a 300 member body. All unaffiliated cpu senators also vote and will tend to vote according to their class (pleb vs patrician)


Players will not know their exact SP balances, but will periodically increase in AI and SI. The only simplification I would offer is that we could collapse AI and SI into one single stat. I'm not sure that they will significantly different in the way the game is structured.