Ranking people: You're first, you're second, and so on...

Let’s take the case of a class of students who’re being given ranks based on the marks they got in English.

The person with 100/100 is first, the one with 99/100 is second and the one with 98/100 is third. Easy peasy.

Now, let’s say two people get 97/100: they are tied at fourth place.

Some ranking methods will treat the chap with 96/100 as ranked fifth, but other methods use a different system. What happens with these is that they will ‘skip’ the fifth rank and instead give the 96/100 the sixth position.

What precisely is the logic here? The kid scored a 96, which definitely is the fifth highest in class, so why does he get sixth place?

Also, and this is more of an IMHO, which method seems more logical to you? I personally don’t get the ‘skipping’ method at all. Someone explain it to me, please.

When they skip the fifth rank, it’s because the person is ranked sixth in terms of people, not scores.

ie:

100
99
98
97 97
96
96 is the 5th highest score achieved, and the person who gets 96 is the 6th highest achieving person.

Think of it this way. What if the scores had distributed like this?

100 100 100 100 100 100 100 100 100 100 100 100 100 100
62

Would you really tell the person with 62 that, hurray, it was the second highest score?

Another way of thinking about it… If the scores were:

100
98
98
98
95

you wouldn’t claim that the three people with 98 are all exactly equal in ability. Perhaps their “true” abilities warrant scores of 98.001, 97.667, 98.2, but the testing method is only sensitive to the nearest integer, so they all get 98. So, while you can’t properly order these three “98” people (you can do no better than say they are tied), you do know that they are all better than the person who got 95. When someone asks, “Who’s the 5th smartest kid in the class?” it’s that last guy. When someone asks, “Who’s the 3rd smartest kid?” you don’t know which of the three “98” people it is, but you know it is one of them (and that it is not the “95” guy.)

Well, that was simple.

Thank you all.