I expect them to have exactly the same number of swaps in every iteration of the loop past the first one, because they are doing exactly the same thing. It's not just the same number of swaps. It's essentially the same set of swaps, in a different order. In the iteration where i = 1, the number of swaps may differ. Was I wrong about that?

Yeah, 2410 vs. 2509 swaps not including the first iteration. You should try measuring these things yourself, I'm not sure if it's doing what you think it's doing.

Well, I sort of agree with you and sort of disagree.

    from random import randrange

    def list_swap(lst, i, j):
        temp = lst[i]
        lst[i] = lst[j]
        lst[j] = temp


    def icbicsort(lst):
        swap_count = 0
        n = len(lst)
        for i in range(n):
            for j in range(n):
                if lst[i] < lst[j]:
                    swap_count += 1
                    list_swap(lst, i, j)
        return swap_count

    def bubble(lst):
        swap_count = 0
        n = len(lst)
        # preprocess
        # this is intentionally identical to icbicsort with i = 0
        for j in range(n):
            if lst[0] < lst[j]:
                swap_count += 1
                list_swap(lst, 0, j)
        # go forward, bubbling backward
        for i in range(1, n):
            for j in range(i, 0, -1):
                if lst[j] < lst[j-1]:
                    swap_count += 1
                    list_swap(lst, j-1, j)
        return swap_count

    def cmp(n=100):
        alst = []
        blst = []
        for t in range(n):
            value = randrange(65536)
            alst.append(value)
            blst.append(value)
        icb_swaps = icbicsort(alst)
        bubble_swaps = bubble(blst)
        print(f"icb: {icb_swaps} swaps; bubble: {bubble_swaps} swaps")
    
    # just for completeness
    def bubble_classic(lst):
        n = len(lst)
        sorted = False
        while not sorted:
            sorted = True
            for i in range(n-1):
                if lst[i] > lst[i+1]:
                    sorted = False
                    list_swap(lst, i, i+1)
    return

26 calls to cmp() produced identical swap counts in 24 cases and slight discrepancies (of 2 and 3 swaps, both favoring icbsort) in two cases. (For statistical purposes, this was a manual inspection where I stopped after getting the second discrepancy.)

If you're regularly seeing discrepancies, something is weird. If you're seeing them occasionally, I still think something is weird, but I'm prepared to believe that it's a bug in the code.

I will note, in support of the paper's actual thesis, that I wrote icbicsort() correctly on the first try, and I had to work many bugs out of bubble(). Maybe it's still bugged.