Mergers, Migration, and Signaling

The interaction between learning at the individual level and the trajectory of a population over time is fundamental to our understanding of linguistic change. Here we use game theory as a mathematical framework for formulating and testing hypotheses about this interaction. We formalize two hypotheses regarding the spread of vowel mergers and use them to derive the proportion of merged in-migrants that would precipitate a merger in a previously non-merged speech community. The first hypothesis stems from Herold’s (1990) conjecture that mergers spread due to contact between merged speakers and non-merged hearers. Merged speakers do not use a phonemic distinction to differentiate meanings, but non-merged hearers rely on the distinction as a semantic cue. The misunderstandings caused by this mismatch lead non-merged learners to abandon the distinction. We will refer to this hypothesis as merger-by-misunderstanding. The second hypothesis stems from Trudgill’s (1986) supposition that accommodation plays a central role in contact-induced changes, and the observation that contact systematically favors mergers. If learners abide by the simple maxim “talk like others talk” (Keller, 1994), then this reveals an asymmetry in identifying how others actually talk. A tendency to misidentify non-merged speakers leads non-merged learners to abandon the distinction. We will refer to this hypothesis as merger-by-misidentification. In the next section we provide a brief overview of game theory and offer a general characterization of the conditions for merger. With this more abstract criterion in place, we spell out the details of two models based on the hypotheses and derive concrete predictions. We test these predictions against the spread of the low-back merger along the Rhode Island-Massachusetts border (Johnson, 2010). In light of these results, we consider the impact of social network structures on both models. Finally, we conclude with a brief discussion of our results and avenues for future research.