When doing e.g. a seminar talk, it is customary for the hosting institution to pay for the speaker's trip. If it is just an isolated trip to a point A, life is simple; so far, so good.
However, I usually try to lump different talks together. The simplest case is where I go from home to A (where I do a talk) to B (where I do a talk) to home. In this case, I have to choose between having the A -> B segment reimbursed either by institution A or by institution B. (Assume that every segment is on an undivisible, nonstop ticket. I think it is usually not possible to split 50/50 in such a situation.) Based on what criteria should I make this choice?
For example, what if B is much closer to home than A, basically a small detour on the way back. Is it more fair to charge the intermediate leg to A (on the grounds that if I did not have to go there, I would not have made such a long trip) or to B (out of a desire to split the costs evenly)?
Or if A and B are roughly equidistant from home, are there any factors I didn't think of that could tip the scales in favor of one or the other?
(There are countless other configurations one can think of, possibly involving much more than two institutions!)
(I am aware that I am probably overthinking it, and that I probably not such an important decision after all. However I would be curious to know what are the possible arguments to consider, if only out of purely academic (ha ha) interest.)