My theory of today is:

The personality of a person is how useful I perceive them to be.

So, basically John would think that Bill has personality if he down there estimates any merit in Bill's existence. If this is true, Turing's test is just a mark in the spectrum. People will grant the "person" flag to anything that shows up useful enough. That's no easy task. Let us believe that the personality is also the area under the skill of the entity. For example a hammer has not many uses in maybe just one field of existence. So it is obvious no one thinks of it as "person". Everyone of us lives plenty of roles, mostly with incomplete info and with real-time decisions to make. That's why the complexity of a person is above of everyone used to solve simpler problems. I believe that casual chit chat conveys the sense that you know how to move in our culture. For good or worse, people put more weight to the skill of handling other persons, than to knowing how electricity works or how to invest.
To prove my thesis we would only need to compare Alice in a grey field(Y!) vs Alice&Good Chess AI at a chess forum(maybe Yahoo Games). People who try to improve their chess skill would valorate more an entitiy who seems to play good. Of course they would still need a bit of chit chat, because people are used to it. However I think they won't mind Alice's short comings as much as in a general place.
Another benefit of my theory is that people could be more liked by following the consequences of this idea. It is well known that our western culture has embraced the specialist path. That's why most of the people in the middle of the streets seem dull, gray. They are extras in our movies. Everyone tries to be different resulting in everyone looking mostly the same in the general scheme of things. I have friends who are that way. I'm hard pressed to tell you any single field they excel at. Of course they are weird and have their own special things. Yet, ask people about their personality and they will agree "not much". My friends do recognize their weakness and can see with crystal clarity why the others don't have it. However, they don't do anything.
My proposal has traditionally be "get a dream". That would make them be a better person in some way, therefore increasing the area. Now I think the new idea should be, "learn something new".
Why? Because it will take a while to make a skill worthy. People with low skills should invest in them, but also expand their horizon. They are probably in a local maximum. If they had in themselves to be better at a known skill they would by inertia had it. Find something new and maybe that would work out. Of course, this argument is rude. People with worthy skills should probably stick with what they know. They already have something to hold. I'm talking about those poor guys who haven't yet find a lucky spot.
Yes, I know all this is politically incorrect and that people should not randomly go find skills. Just remember I'm talking about people so screwed they don't know how deficient they are.