Shouldn't that be: 1. $10 1. $10 3. $8

The way I see it, the person with $8 is ranked third, not second.

Think of what would happen if you extended it. If you had 99 people earning $10 and 1 earning $8, it would be misleading to rank that bottom individual 2nd.

You are absolutely right, that was more what I was thinking about when I wrote that. I just edited it to match with your proposal.

For what it's worth, this is quite easy to compute in a way that works with any number of ties, and doesn't require computing the whole list in order. Your rank is the number of people above you plus one.

I must be missing something. That's a N^2 operation on an unsorted list. ~N Log N if you sort it first. And N to insert a new entry to a sorted list.

Yes, it requires a sorted list, but so does the naïve implementation. The performance is equivalent to binary search to find the entry, although you then have to scan backwards to make sure you have the first entry with the same value.

Since performance is probably not an issue for most rankings, the biggest benefit is a clear, easy to remember definition, which should reduce the chances of making the same mistake landhar did.

If you are inserting 3 into an indexed and sorted list (1,2,4,5) you can calculate the index of 3 in O(Log N). But you also need to update the index of 4, and 5 which is an O(N) operation.