  In multilingual societies, it is common to encounter different language
varieties. Various approaches have been proposed to discuss different
mechanisms of language shift. However, current models exploring language shift
in languages in contact often overlook the influence of language ideologies.
Language ideologies play a crucial role in understanding language usage within
a cultural community, encompassing shared beliefs, assumptions, and feelings
towards specific language forms. These ideologies shed light on the social
perceptions of different language varieties expressed as language attitudes. In
this study, we introduce an approach that incorporates language ideologies into
a model for contact varieties by considering speaker preferences as a
parameter. Our findings highlight the significance of preference in language
shift, which can even outweigh the influence of language prestige associated,
for example, with a standard variety. Furthermore, we investigate the impact of
the degree of interaction between individuals holding opposing preferences on
the language shift process. Quite expectedly, our results indicate that when
communities with different preferences mix, the coexistence of language
varieties becomes less likely. However, variations in the degree of interaction
between individuals with contrary preferences notably lead to non-trivial
transitions from states of coexistence of varieties to the extinction of a
given variety, followed by a return to coexistence, ultimately culminating in
the dominance of the previously extinct variety. By studying finite-size
effects, we observe that the duration of coexistence states increases
exponentially with network size. Ultimately, our work constitutes a
quantitative approach to the study of language ideologies in sociolinguistics.
