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The value of the antipoints assigned by a new user is zero, neither positive nor negative (depicted as a grey box), but the comments they add will be communicated to the recipient. When the new user has accumulated at least 50 positive antipoints, the antipoints they assign will begin to have a positive or negative value.
Exactly how much of an effect your AntiPoint Assignments have on another user is determined by a complex set of algorithms that make up the AntiPoints System. There are literally hundreds of checks-and-balances in place to insure that they system isn't abused. As such, the "power of your punch" may vary from day to day, and even minute to minute.