To be a president and vice president, you have to become a Student Council member, which is Masachika and Yuki are already part of the Student Council, along with that glasses girl, just like now with Yuki and Alya who are already part of the Student Council High School, so it's easy to conclude that Masachika also knows that glasses girl and probably gets along with her. But that election was a mismatch, Yuki was trained by the family of diplomat, the Suou, and Masachika, kicked out by Suou has showed us that he can still use his "Suou" skills like how he lifted up his classmates during his middle school days with Alya.
Second, Yuki's a nobility from a family of aristocrats who produces
diplomats, for a country that favors "male heirs", it's simple to deduced that Masachika was kicked out because he is not competent enough, he is way too emotional for them just like this chapter, he let his emotion take control of himself way too much, and he knows it which is eating him inside.
Yuki also knows the problem with Masachika, which is why she is asking Masachika to run with her because Masachika is a former "Suou" family, he has the skills but importantly, it will help Yuki as a heiress of "Suou", to join the elites of former President and Vice President club, but now Alya is in the position like that "glasses girl" which he was trying to avoid repeating again, he hasn't realized it yet, but he is sick of destroying people's goals in their life while he laze aimlessly.