Looking for a sort algorithm with as few as possible compare operations

I want to sort items where the comparison is performed by humans:

• Pictures
• Priority of work items
• ...

For these tasks the number of comparisons is the limiting factor for performance.

• What is the minimum number of comparisons needed (I assume > N for N items)?
• Which algorithm guarantees this minimum number?

I don't think you're likely to get a better answer than the Wikipedia page on sorting.

Summary:

• For arbitrary comparisons (where you can't use something like radix sorting) the best you can achieve is O(n log n)
• Various algorithms achieve this - see the "comparison of algorithms" section.
• The commonly used QuickSort is O(n log n) in a typical case, but O(n^2) in the worst case; there are often ways to avoid this, but if you're really worried about the cost of comparisons, I'd go with something like MergeSort or a HeapSort. It partly depends on your existing data structures.

If humans are doing the comparisons, are they also doing the sorting? Do you have a fixed data structure you need to use, or could you effectively create a copy using a balanced binary tree insertion sort? What are the storage requirements?