The answer to the original post is in the book linked here:
Amazon.com: The Imputation of Adam's Sin: John Murray: Books
One of the reviewers offered the following summary of the book:
This is an extremely dense book which is definitely worth reading. It contains the standard articulation of the Reformed view of man's relationship to Adam. If you purchase the book, or would just like to read a decent summary instead of buying it, perhaps the review below will be helpful. The paragraph breaks correspond with the chapter breaks.
In the opening pages Murray concerns himself with the parallelism contained in Rom 5:12. He argues that the surrounding section is a sustained argument that draws a strong analogy between the work of Adam and of Christ and the Christian's relationship to each. He begins by discussing the syntactical construction of 5:12 and then surveys and refutes the Pelagian and Roman Catholic views. He also surveys Calvin's view and while Murray agrees with Calvin's general conclusions, he believes Calvin's exegesis is inaccurate. He is critical of the Pelagian and RC views in that they do not seem to reflect the one man and one sin terminology with which Paul connects humanity with the first and second Adam. What Paul is arguing according to Murray is that all of humanity stands with Adam as their representation to the extent that both his guilt and his corruption are imputed to them. And thus those who stand with Christ as their representative receive both forgiveness and righteousness by imputation.
Murray then examines more deeply the nature of man's solidarity with Adam. He interacts with the realist view and the representational view. These two views attempt to explain the specific ground of the imputation of Adam's first sin with humanity that goes beyond the simple fact that there exists genealogical solidarity between Adam and humanity. The realist position, it seems is looking for a way to remove the difficulties regarding the punishment of someone for a sin in which he did not participate. The realist argues that human nature was present in its entirety in Adam and that each person thereafter is an individualization of this human nature and is therefore guilty of Adam's sin. But since they were really present in seed form in Adam, it is just to hold them guilty for there participation in Adam's sin. Adam's sin is therefore imputed to humanity in an immediate way. In the representational view, Adam's sin is imputed to humanity in the very same way (parallelism again) that Christ's righteousness is imputed to the believer.
Murray says that mediate imputation emphasizes the hereditary corruption as the medium or means by which Adam's sin is imputed to his posterity. This is to say that man sins because he is born corrupt, but he is only guilty in that he himself sins as a moral agent. Murray characterizes the immediate position as God looking on posterity as being one with their father Adam and their sin coexisting with his just as if it were theirs. He then argues for immediate imputation in four extended arguments. The first seems to me to be the most compelling and easiest to summarize. Murray's basic exegetical point stemming from Romans 5 has been that Paul's "one sinned" and "all sinned" language refers to the same sin viewed from the participation of Adam and his posterity. In other words, there is exact correlation between the manner and nature of sin of Adam and his posterity. Thus, since there is not any medium between Adam's sin and the death inflicted upon him, neither should we interject any medium between the sin and punishment in the case of Adam's posterity.
Chapter Four is probably one of the more difficult to comprehend and summarize, especially because of his use of Latin terminology which he does not define. But with the use of a Latin dictionary, Murray's critique of Hodge on imputation and his alternative position become clearer. Hodge argues that the imputation of Adam's sin to his posterity consists simply in the obligation to satisfy justice, i.e., the exposure to punishment on account of Adams sin - the reatus poenae. Murray responds that the reatus poenae, may be imputed only if the reatus culpa is also imputed. In other words, the demerit, or guilt of Adam's sin must also be imputed as possession of his posterity before any obligation to satisfy justice can also be imputed. The guilt is the ground of the punishment. So, Murray contends that the biblical teaching on imputation is hung delicately between two poles. On one hand, it is more than judicial liability, but it is less than considering posterity to have eaten the fruit in the same way that Adam did - it was his action not theirs. The biblical position is that in Adam's sin, humanity was constituted sinners in the same manner that the elect are constituted as righteous - parallelism again.