When one person is stranded on an island, there's no question as to whether he's an individual. It's a moot point--there's nobody else to make decisions for him.

Add a second person, however, and things get interesting. Now we have to give these people names, to distinguish them. Let's call our first guy Juan and his new companion Fiona. Juan and Fiona have different names, sure, but if Juan has no preferences or quirks of his own and lets Fiona make all his decisions for him, we don't really care what his name is. We could fully interact with him through Fiona. A person has to have personal agency to be an individual.

Fortunately, this never totally happens. While they may decide it's Fiona's job to decide what to eat for dinner for both herself and Juan, Juan probably makes decisions about other things, like what upgrades to make to their hut. Yet, with only one other randomly selected person on the island, it's unlikely they would find much in common. If Juan doesn't respect Fiona's culinary taste or Fiona doesn't think that a rec room is a pragmatic addition to their shared shelter, then they'll still have to make decisions for themselves. They mostly remain individuals.

Say Juan and Fiona are joined by a whole life raft full of survivors from a local cruise shipwreck. Now there are ten people on the island. Some of them want coconuts for dinner, some want mangoes. (Unfortunately, those are like the only foods readily available on the island.) Thus they separate out into a group of six, called the Coconuts, and a group of four, called the Mangoes. It only takes one member of the Coconuts to make decisions about dinner for the rest of that group, and if someone from the Mangoes is curious about what the Coconuts are thinking for dinner, she can interact with the whole group through any one of them. Groups are a kind of heuristic society uses to expedite the division of decision-making.

One's identity in a sufficiently complex society becomes just a list of groups determined by his preferences. Juan becomes an islander, because he prefers to live on an island (though not by choice), and a Mango, because he's sick of coconuts.

In my case, I'm an American, because I prefer to live in America, a Cornellian, because I prefer to go to school at Cornell, an AEPi Brother, because I prefer to belong to that fraternity, and so on and so forth. My "identity" is just a list of groups of people with whom I share preferences, and if you know my list, then you can know how I feel about everything by talking to people in my groups. That's why the Master of my fraternity can represent me to other fraternities, Cornell's President Skorton can represent me to other colleges, and President Barack Obama can represent me to other countries. I may not agree with any of those people about their preferences on many things, but I know I agree with them better than I would with someone who did not prefer to live in America, go to Cornell, or join AEPi. I'm only a 'unique' human being insofar as nobody else perfectly overlaps with all my preference-groups, though I'm not sure that's true.

Even when I'm not participating in groupthink, there's almost always at least one other person who agrees with me and who can therefore speak for me. I de facto engage in groupthink every second of my life by deferring decisions for almost everything to the leaders of the various groups to which I belong. What people call "Daniel Seth Lewis" is really just a list of other people to whom I defer responsibility for the various aspects of my life on earth.