I've read more than once that the closest eye to the camera should be focused on a portrait with people. But why not focus in the eye that is in the middle, so in average, all eyes in the picture will be more focused than the first approach?
Because the way human vision perceives a two dimensional representation of the three dimensional human face if the nearest eye is in focus it looks to us more like the whole face is in focus.
Even if the question is regarding group portraits (the question is rather nebulous at this point) it still holds true. A group portrait with the front person(s) in sharpest focus looks more natural to our eyes than a group portrait where a face in the middle of the pack is sharper than the closest faces.
Returning to reasonably tight portraits of a single person with two eyes:
Although the rear depth of field (DoF) will theoretically be larger than the front DoF, at typical portrait focal lengths, apertures, and subject distances the difference is so negligible as to not even be measurable except under very well controlled laboratory conditions.
The following all assume an image from a 35mm or full frame camera being viewed at an 8x10" display size from a distance of 10 inches (25cm) by a person with 20/20 vision and figured using the advanced options here:
Even if we use much narrower apertures the difference is still negligible.
There's more depth of field behind the focus than in front of it. So focussing on the near eye gives you the best chance of getting the whole face in focus. If you can't do it focussed on the near eye, you can't do it without changing something (position, angle, aperture).
In addition, you'be got a good chance of a clear view of the near eye, making focussing (manual or auto) easy to get right. By clear view I mean free of things like hair, or fur/feathers in animal portraits; for wildlife if you can't get the near eye in shot without a twig in the way it's not going to be a good shot.
It's only a rule of thumb, but one of those useful rules which you can apply if you don't want to think too much.
Although my immediate thought was reflected in @mattdm 's comment (funny) I guess you mean when shooting groups, so that there are more than two eyes in the shot.
In that case you're not really bound to pick the closest eye, IMO.
You need to choose a point of focus that creates a composition you like. I'd probably go with e.g. rule of thirds or something like that to decide how to frame/compose the shot and what to focus on. Which person seems the most important/attractive/biggest tipper is also something to give some thought to.
I don't think for groups you have to obey quite the same rule as you would for single person shots.
My guide in this case would be, to quote a great movie, "look into your heart". I think a lot of people forget their instincts and think in terms of rules, but a portrait should be about the emotional response to and from the people in it, so start there and focus on what works to convey what you see.
One more possibility, which would also apply to group portraits:
An old rule of thumb is that out of focus objects ahead of the point of focus are less pleasant to the eye than out of focus objects behind the point of focus; in other words, you generally want to keep the foreground clear of out of focus objects as much as possible, or the viewer may feel disturbed. (this can of course be used on purpose for artistic effect)
Focussing on the nearest eye will tend to keep the OOF area behind the point of focus for most subjects; this applies regardless of the number of eyes per subject. :-)
In the example of your photo, focusing on the near eye also has the benefit of keeping the DOF narrower on your group. You want your group to be in focus, not the people in the background. When everything is in focus in a photo, the eye has more difficulty (OK, it's your brain) in figuring out where to look/what's important. Of course, if your aperture is set at f11, the background still is in focus.