If I understand OP’s situation correctly, he/she has been offered admission to at least Columbia, Duke, Dartmouth, and Amherst as a transfer student from an LAC with a weak economics department and an uncomfortable social environment. OP is concerned about which option offers the best law school placements.
All 4 options place many students into elite law schools each year. All 4 options have strong econ departments. The issue, therefore, seems to be which option(s) offer a different social environment than OP’s current LAC. This is unnecessarily challenging to do without knowing more about OP’s current school or the school’s name. (I can guess which school OP currently attends based on some information shared in OP’s earlier thread. But why do we need to guess ? This is a potentially life altering decision in my view.)
What we do know is that neither Columbia nor Duke is an LAC, therefore, the social scene at either school should be quite different than that at OP’s current LAC. And maybe this already understood by OP and the reason that OP has narrowed his/her options to these two universities.
Between Columbia and Duke, the choice should be easy as either one wants to attend school in NYC or one doesn’t.