The sentence as it stands is thus.
- I decided not to vote for your candidate for president.
A candidate stands for office. There is an implied "the office of" here.
- I decided not to vote for your candidate for the office of president.
It is very usual to leave out that part. Usually people will only put that in when they are trying to be formal, or when they are using it to to make a speech and they want to have a particular rhetorical effect. It becomes a verbal fanfare that gives an annoucement an air of seriousness. And sometimes a newspaper will put it in a headline for siimilar motivations.
- I give you our candidate for the office of president.
You can either put in the "the office of" part or you can leave it out. You can't put in only part of it. So the following would be wrong.
- I decided not to vote for your candidate for the president.