Alright, but taking this mechanic into consideration it invalidates your calculation above for about a 15% chance for a rule approval, as it adds another layer of failure of the vote.yeah it failed, because yuriko vetoed. a veto is not a simple no, it's an official protest against the topic, which automatically fails the vote no matter the remaining results.
As you already said, first make sure the player understands why the vote has failed, and probably add some sort of explanation what to do to get better chances it it happens multiple times. My personal opinion, a bit of grind is not necessarily a bad thing, but grinding without any progress indication and visible goal, also random failure without explanation is just going to frustrate the player to the point he will just stop playing. Very few people will play a game for frustration.