Unfortunately, no, because control of the higher-level perception ‘a greeting’ is not modeled. ‘A greeting’ is a complex perception with many possible inputs which may be concurrent or not. The perception of a handshake is just one of them. A brief look and nod followed by turning back to a conversation might be met quite justly with the comment ‘that’s not much of a greeting’, but it would still be a greeting.
There’s a parallel in your model of Labov’s data. You modeled the assumption that individuals control to talk like those with whom they most frequently talk. Your model demonstrated that when that is the perception that the individual agents control, and there are no disturbances that prevents control (there are none), they control it successfully. That’s not the topic of Bill Labov’s paper. It’s taken for granted by linguists, no Columbia U MA thesis for him in that. Eh, says your audience, isn’t that kind of obvious? Linguists have observed that forever. A CT explanation is nice, but there are lots of exceptions of various kinds. And it’s not what Labov’s paper was about.
Quotations now are from your book The study of living control systems (SLCS) rather than from your post.
Labov found that there was a substantial difference between Up and Down Islanders in their average CI index for both /ai/ and /au/. For Up Islanders, the average CI index was 0.61 for /ai/ and 0.66 for /au/; for Down Islanders, the average CI index was 0.33 for /ai/ and 0.35 for /au/.
That is part of what he found, but was not the topic of his research. The diachronic (historical) sound change that was the research topic is in the unexpected fact that the centralization index is virtually identical for the two diphthongs in each of the Islanders.
Unexpected? Why was that unexpected? The significance of this is that earlier in the 19th century ~0.35 for /ai/ and ~0.65 for /au/ were the norm for all Islanders, preserving pronunciations of 17th- and 18th-century English.* The first-order question was why did that change at the beginning of the 20th century. What was the motivation for Islanders reversing this trend and reverting to the pronunciation of their deceased ancestors?
The reason that Bill put the phrase “social motivation” in the title of his paper is (I’m putting PCT terms into his mouth now) that his data identify different perceptual inputs for control of a perception of being, or intending to be, a person of one kind (on Island) or another (off Island). Call these Si and So. Those who control Si have the higher CI values because hearing oneself producing higher CI values for /au/ has been an input to Si for generations of Islanders. Gain on controlling Si, was weakening until the rise of tourism and the promotion of it by business interests around the turn of the 20th century, after the collapse of demand for whale oil and the demand for corsets braced with baleen from right whales and other baleen whales. Differentiation from ‘summer ginks’⁑ (schismogenesis, Bateson 1935) was controlled by higher gain on control of Si. One of the many inputs to the complex perception Si is pronunciation of /au/ with a higher CI index, hence, the return of higher CI values, among the diverse inputs to Si.
Control of Si and So (or equivalent) is not mentioned in SLCS and has no place in your model.
But that is a secondary matter in Bill’s findings. The sound change that is the topic of Bill’s paper is not the restoration of /au/ to CI ~0.65. It is the change of /ai/ from CI ~0.35 to ~0.65 also, which is not a restoration of the ancestral pronunciation at all. Your model does not explain this, and your description in SLCS does not mention it. Why did that happen? And in what individuals did it happen, because it wasn’t uniform.
The age of individuals is an important variable in Bill Labov’s data. His data showed that teenagers who controlled Si with higher gain raised Ci of /au/ higher than most adult Islanders did. And here was the social motivation for the sound change which is the real topic of his paper, the raising of Ci for the /ai/ diphthong as well as for the /au/ diphthong. The kids were doing what is called hypercorrection, and what I called ‘overshooting the mark’.
Bloomfield gave a nice example of hypercorrection in his classic book Language (which has been not-PC in the politics of linguistics). Scotch-Irish immigrants to the mid-Atlantic states brought a dialect in which “sofa” was pronounced “sofie”, as in “set raht theah on the sofie and have a drink”. Little Johnnie’s family moved westward to Ohio and Missouri, and when he went to school his teacher taught him “it’s not ‘sofie’, Johnnie, sofa”. So for Johnnie and his family and their population of immigrants from Kaintuck it wasn’t “Missouri”, it was Missoura.
However substantiated or not that story may be, it’s a real phenomenon, and Bill documented a real instance of it on this Island. Neither SLCS nor your model recognizes this phenomenon or its social motivation in controlling one’s perception of oneself as perceived by others socially.
Bill further found that not all of the kids did this. Only those who self-identified as intending to continue to live on the Island, differentiating themselves (schismogenesis) from their peers who intended to ‘get off the rock’ (it’s actually more a sandbar, a glacial moraine), go to school, and build a life on the mainland ‘in America’. Those kids who were controlling So instead of Si maintained lower CI values that they heard from summer visitors, and from the hoteliers, restaurant owners, and merchants who catered to them in the down-Island port towns. (There are no large ports up Island; Menemsha is a fishing harbor.) For that portion of the population and for those kids your model would be adequate if those were the only people they talked to. In 1960 the tourists did not outnumber natives 5 or 6 to 1 as they do today, so your model would predict that the summer residents would raise their CI values. As I recall, that wasn’t investigated.
Your model could be extended to model control of these other variables, control that avoids talking like another kind of people as well as control of talking about one’s own kind of people, presence of an off-Island population with their own CI references, and control by a subset of the population (the teenagers) of a decision which kind of person they will be. With these kinds of further development a model could provide a CT explanation of Bill’s data. As it is, it’s a beginning. Please keep going.
* No: 19th century pronunciations were not quantified in terms of ‘centralization index’, which depends upon sound spectrography invented in the early 1950s, however it may have been adumbrated by Alexander Graham Bell, Henry Sweet, and others, but descriptions by dialect geographers competent in phonetics are quite reliable. And no: dialect geographers were not actively surveying pronunciations in the 16th and 17th centuries, but inferential evidence about historic pronunciations is pretty good, Sturtevant’s The pronunciation of Greek and Latin is a good example.
** Note that these are different inputs to a complex higher-level perception, not scalar values of one CV. Perceptions at the system concept level have lots of perceptual inputs. Perceiving oneself as wearing one kind of clothing or another would strengthen the desired perception or be a disturbance to controlling it, for example.
⁑ A term from my mother’s childhood, disused for many decades.