If I were to offer a more serious side to this:
I personally reckon half of the Japanese people who signed the petition claiming they can't get a life partner are young, like, 25 years and below. The guy who started it? He's probably so obsessed with his manga that he can't find a girl out there. Doesn't mean he goes and marries a manga character, he should put the manga down and go socialise. Chances are he's young enough that he just hasn't found someone right for him. The same goes for the others, too.
Allowing marriage to manga characters doesn't help the marriage deficit in Japan. It makes it worse, and only means the manga-obsessed become more manga-obsessed, claiming they are spending time with their spouse.
There's the issue of people wanting to marry the same manga character too.
How do you get the consent of a manga character? How are they actually married, process-wise ? Does the person have to get the permission of the manga artist? What happens when the manga and/or anime stops being made? What happens if the character dies? Does the real person have to draw out every event in order for their marriage to actually 'go' anywhere?
That's my two cents.
TL;DR: Dumbasses haven't even thought this through.
