Arguments over how to determine depth of field

For several years now, this forum has had frequent and quite heated arguments about depth of field and how it is or should be defined and measured.

Having followed many of these arguments (and contributed to some), it seems to me that, for the most part, the participants fall into two camps:

1. Those who accept the traditional definition of depth of field based on viewing the image at a standard size and distance to determine what appears sharp.
   
2. Those who believe that the image should be viewed at the maximum possible size (meaning the largest size before the individual pixels become visible) to determine what appears sharp.

I haven't noticed any significant number of people supporting possible definitions other than these two (but I would welcome comments either in agreement or disagreement with this statement).

Of course, what is usually argued about is the resulting properties of depth of field that are implied by these definitions.

For instance, cropping an image reduces the depth of field for Case 1, but makes no change for Case 2.

Also, increasing the number of pixels in the image (but keeping the same sensor size) makes no difference to the depth of field for Case 1, but reduces the depth of field for Case 2.

Etc.

I don't want to reopen the same arguments yet again, but I would be interested in others' views on whether these two possible approaches to defining depth of field exhaust the possibilities, or whether some people advocate yet different approaches that I have missed.