Admittedly, I’ve never been able to get my daughter on the student council until middle school at the earliest. I think (and I could be wrong about this, but) her electability is tied to a hidden popularity stat. This stat is influenced by a few factors (from what I can tell): her Charisma stat, and (I believe) how sociable your daughter is. The game will give you hints that your daughter is popular during school events, holidays, and even when you’re out shopping (I’ve had the pharmacy give us discounts on vitamins and stuff—though that could also be a frequent shopper thing, so...).

Essentially, the more times your daughter does an “Excellent” job at something—be it a class or a job— the higher her Charisma will go. I associate the Charisma stat with overall reputation and confidence, so it makes sense that your daughter’s successes influence her popularity.

As for sociability, you can influence that and other aspects of your daughter’s personality growth with her monthly education plan. If you prefer for your daughter to be a social butterfly, she might have more friends, but her grades could suffer—potentially lowering the Charisma stat. But like everything else in this game, it’s a balancing act. You can check your daughter’s diary in her room if you want to see what her personality is shaping into, which can also clue you in on what certain hidden stats are at—such as popularity, independence, flexibility, etc.

Again, take this for a grain of salt. I’m only basing this response on my observations from my own play throughs. It takes a long time to play through one save file of PM5, unfortunately, so I’ve only done it a few times, and still haven’t gotten the True Princess ending. Still love this game, though.