In that context you could simply pick another thing as the tie breaker, like the IP address expressed as an integer (ie, remove the periods and treat like a number) being lower.
But then there is reliance on an underlying platform to resolve the conflict by providing a globally unique identifier. Instead of process ID, there is the IP address mechanism.
So it's turtles all the way down, if I understand correctly.
Not really. Each process could, at the beginning, generate a random nonce and broadcast it and thereafter use that as its tiebreaker number. The point is to just have a consistent way to break ties that is convenient to implement in whatever domain you’re working in. And in a networked domain, without a valid IP address, the worker isn’t going to be doing much in the process anyway since it wouldn’t be able to communicate at all.
But then there is reliance on an underlying platform to resolve the conflict by providing a globally unique identifier. Instead of process ID, there is the IP address mechanism.
So it's turtles all the way down, if I understand correctly.