# Why is the number of array accesses not considered in analyzing the complexity of mergesort?

I'm reading Robert Sedgewick's Algorithms and in the section about The complexity of sorting, I found the following paragraph:

Proposition. Mergesort is an asymptotically optimal compare-based sorting algorithm. Proof: Precisely,we mean by this statement that both the number of compares used by mergesort in the worst case and the minimum number of compares that any compare-based sorting algorithm can guarantee are $$\sim N\lg N$$.

One analysis appears earlier in the book shows that mergesort uses $$6N\lg N$$ array accesses in the worst case and this number is $$6$$ times higher than the number of comparisons. And for large values of $$N$$, this would make a big difference between number of array accesses vs. number of compares. But still the model of computation only counts compares.

So why is the compare-based model of computation used here instead of access-based?

I'm aware of several related questions such as this one, but none seems to have answered my question.

The above argument only remains true under standard computational models, such as a RAM model. As soon as we are concerned with memory read/write complexity, we of course need to focus on the hidden constants under the asymptotic notations, such as $$O$$. Suppose we have two $$O(n\log n)$$ sorting algorithms, namely MergeSort and HeapSort. Once might be better than the other under a certain computational model, and the other way around in some other model. See here and here. External sorting algorithms are often concerned with access costs.