[maxerickson]

In the case that there is at least 1 member of the tribe with blue eyes, all the people with brown eyes can see his eye color. So they satisfy the question of who the traveler is talking about with the blue eyed member.

The blue eyed member doesn't see anyone else with blue eyes.

[Jehar]

That's a good point, but then the critical factor is that nobody knows how many people have blue eyes. More specifically, each person has to hold the possibility that n = observed persons with blue eyes + 1, which is himself.

[maxerickson]

That's why it takes n days.

Each blue eyed person can see n-1 others. If nothing happens on day n-1, they learn that they have blue eyes.