The Bixby Letter

[Gene C]

As far as Lincoln knew when the Bixby letter was written, Mrs Bixby had lost 5 sons due to the war.
As a father who had also lost two sons, he was in a slightly better position to write a letter of sympathy than John Hay.
Add to that, he was close to Elmer Ellsworth when he wrote to the parents, knew Fanny McCollough and her father, I think he is touched by the horrors and responsibility of war more than John Hay.
Of Lincoln's secretarys, I personally think if he were to assign the responsability of writing the letter, he would have given the assignment to John Nicolay, the senior secretary, if he was available.

I would also expect the wording of the letter to be slightly more formal since Lincoln did not have a personal relationship with Mrs. Bixby compared to the Elsworth family and Fanny.

IMO a computer program can not adequately determine the intricacies of matters of the heart.