Surely you 'should' only do something like this iff acquiring this amount of money has a higher utility to you than not ruining this lady's day. Which, for most people, it doesn't.
Since you're saying 'you are very rich' and 'some money which is a lot from her perspective', you seem to be deliberately presenting gaining this money as very low utility, which you seem to assume should logically still outweigh what you seem to consider the zero utility of leaving the lady alone. But since I do actually give a duck about old ladies getting home safely (and, for that matter, about not feeling horribly guilty), mugging one has a pretty huge negative utility.
If there's such a small chance of your vote making a difference in the election, you should be comfortable voting for trump.