Are narratives merely stories that amuse and entertain? Or are they intellectual mind-games that one may enjoy in the decadent bourgeois fashion that Richard Rorty has cultivated so nonchalantly?  Of course not. They have a very real impact on our life; they have a performative function:

"Stories order and reorder our experience; that is to say, they reveal the way things are in the real world. They reflect a given culture. Alternatively, stories may be thought to create the real world. They are 'performative' rather than simply explanatory. They give meaning to life, implicitly making proposals for thought and action which are then embodied in a re-created world. Not only that, they can become 'policemen' of that world. They 'keep us in line and tend to make us more like our neighbors' (...). Yet working against that policing function is always another possibility: stories can be subversive, a means of criticizing dominant patterns of thought and institution... and of course, such stories have the potential to create new social worlds."

In other words, narratives (=stories) correspond to regimes, governing norms and habits, or, as I shall say, to institutions (of more informal or more formal character). Indeed, they give rise to new institutions and habits, to new laws as well as different mores, the (final) reality reflecting narrative (and giving rise to new questions/answers and the change of narratives), and the narrative reflecting on the (final) reality, thereby giving occasion to change that reality.
    Why is Tocqueville so important in the debate about narratives? First of all, Tocqueville relies on a model of identity, memory and habit several times in his account of the democracy in America. For example, in his observations of slavery, Tocqueville speaks in terms of origin, memory, prejudice and habit . He effectively predicted the relevance of slavery in the discussion between the black and white race, saying that prejudice inherent in slavery prevails because concepts resulting from prejudice translate into mores, and narratives carried by prejudiced conceptions produce prejudiced institutions and habits. Institutions and habits have a perpetuating effect on the narrative, and the narrative, in turn, on the institutions and habits. In the end, institutional as well as personal prejudice prevail, and that is why it is so hard to erase.  Tocqueville has made a perfect case for the performative function of narrative (memory and prejudice) and the corresponding institutions (habits, laws and mores).
But secondly, the Tocquevillian history of democracy and equality is really the history of the stratification of (politically relevant) narratives. The (political) movement toward equality is really the movement towards the equality of the (political) validity of particular narratives (the political validity providing spill-over effects on the validity of more particular narratives in other realms). The following is an attempt to translate Tocqueville's introduction on the movement toward equality into the idea of the movement toward the equality of narratives.