It would be fun (at some point…way in the future) to add a trustworthy stat to each minister. You could choose to use a minister with extreme loyalty and experience at the price of them boosting corruption
and maybe even random dilemmas where a minister causes a scandal that reduces some of your perceptions - you keep them on-board at the cost of trustworthiness / compassion / etc (depending on the scandal), or you fire them & lose a presumably-capable minister.