I think it should be possible to vote up answers for your own questions even you have less than 15 reputations. New users can't vote up answers for their questions right now.
Ask a question
If it's good you get THREE upvotes... and you can upvote.
Post ONE good answer
Have it voted up, just TWICE, or get it right... and you're there.
Link an existing account
If you already have a Stack Exchange account elsewhere with at least 200 rep and you link it, you get 100 reputation!
It isn't that hard to get 15 reputation. Getting that reputation basically means that you've bothered to make an effort and have contributed to the site.
Here's a list of similar / duplicate requests on the main Meta.StackOverflow site:
- Shouldn't a rep-less newbie at least be able to upvote a good answer to his/her own questions?
- Allow upvote for <15 rep users on own questions [closed]
- Allow new users to vote on answers they've received [closed]
- Why is 15 reputation required to upvote?
I guess you can read through them to get the idea why users want the ability, and why it is declined.
The main idea is: With 1 rep, you haven't gained any trust yet. The site only trusts you voting until you've proven that you've understood the system (i.e. by asking a good question or posting a good answer).