Why comparison is dominant time consumption for comparison-based sorting algorithms? Comparison-based sorting algorithms does a number of different operations to accomplish the sorting, why comparisons are the dominant time consumption?   While I understand the standard analyses of asymptotical behavior of number of comparison operations, I don't quite understand why other costs of other types of operations are negligible.

[Edit 2014-08-26]

If I run the same mergesort implementation on two different computers (with possibly different architecture etc.), how to argue that running time of mergesort divided by the number of compares will approach (possibly different) constants as the problem size increases?
Because the number of comparisons dominates the number of other operations. Since costs of all operations are usually pretty much the same (within a constant factor), costs of non-comparison operations get eaten by constants in the asymptotic measure.