This was some what of a disappointing debate.  Only two people had arguments to offer. 

Those that contended for frivolity -

ronandjess - contend that our children should be allowed to spend their money on the things they want and that they should not be responsible for the things that a parent should provide for them. 

Those that contended for responsibility -

None

Those that contended for moderation -

DreweLlyn - You should teach a child to set aside a tithe, and to set aside money for a larger purchase.  The rest of the money our children should be allowed to spend as they please. 

From the debate it is obvious which side has won.  I would like to say that if my child is in 4-H knitting and I only have a budget for one kind of yarn, and she really would like the fancier yarn, then it is her responsibility to pay for the difference.  You either live within the budget the family can afford, or you pay for it yourself.  Some may see that as frivilous, she got to spend the money on what she wanted.  I see it as responsibility, it was outside my realm of responsibility to my child and her activity and it fell into her realm of responsibility. 

On a different note, what if you don't allow your child to have sweets?  If you have set the guidelines that they may spend their money as they please, then they may very well buy a coke while at an activity.  The child was able to spend their money as they wanted: friviolous.  You could also say it was responsibility, or rather a lack of it.  If your child is always spending money on the little things they won't be able to afford the bigger things.

As I said, this debate was more a matter of personal oppinion.  As per the arguments, frivolity wins.