Some Calvinists also think the double payment is a not so good argument.
"A few Calvinist theologians saw the fallacy of the double payment, that of conflating atonement provided with atonement applied. In his Dogmatic Theology,
W. G. T. Shedd dismisses the idea that God is unjust in punishing an unbeliever for whom atonement is provided.
“The fact that a vicarious atonement has been made that is sufficient to expiate his sins, does not estop justice from punishing him personally for them, unless it can be shown that he is the author of the vicarious atonement. If this were so, then indeed he might complain of the personal satisfaction that is required of him. In this case, one and the same party would make two satisfactions for one and the same sin: one vicarious, and one personal.”
[3] In Shedd’s explanation, if a person himself had paid a debt, and was charged again a second time, this would be unjust. But for one who has not personally paid, there is no injustice if satisfaction is required of him later."
One of the more popular arguments for definite atonement—that Christ died only for the sins of those who will be saved, and not for mankind as a whole—is the double payment argument. John Owen, in his book The Death of Death in the Death of Christ makes this argument. In that Owen’s work is...
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