Bettys bathhouse side quest

[53 & still gaming]

I failed the side quest to help Betty to discredit the other bath house (just because this was a timed quest - I hate timed quests as I juggle like 20 quests in my log at the same time).
But then I got a 2nd chance to bribe a different council member, who needed some aid with a duel. I managed the duel and he promised to vote for me.
Nevertheless Betty lost the council vote and the quest was failed.
WTF? what is the 2nd chance then good for ?

[Jeza]

It was never a second chance, she always asks for help with both those council members because she is trying to bribe/persuade as many as possible and doesn't know exactly how many votes she'll get.

So from a story perspective even though you failed with the first member she still hopes winning over the second one will be enough.