Certainly not the traditional ethnic one. A traditional ethnic culture is inherited rather than self-selected, so it fails the test of allowing self-definition.
Liberals, therefore, have offered two basic alternatives. The first, most popular on the left, is multiculturalism.
The good thing about multiculturalism, from the left-liberal viewpoint, is that it apparently offers the chance to select. There is no longer a single ethnic monoculture for the individual to fit into, but many different cultures to choose from, and to construct our "self" from.
This multicultural self need not settle on any one cultural standard, but can seemingly be multiple, hybrid and fluid, further ensuring the sense of continuing self-authorship.
Here is left-wing Melbourne academic Mary Kalantzis giving her version of the benefits of a multicultural identity:
Instead of a nation as it might be represented through some 'distinctively Australian' essence, the essence of a postnationalist common purpose is creative and productive life of boundary crossing, multiple identities, difficult dialogues, and the continuous hybrid reconstruction of ourselves. This is the new reality of Australian identity, multicultural and multilingual.
To summarise, the left-wing multicultural "solution" is to replace an ethnic monoculture, in which self-definition seems limited, with multiple ethnic cultures, in which we can selectively move about and hybridise ourselves.
But it doesn't work. First, we generally maintain a primary loyalty to our own ethnic tradition and feel most comfortable within it. Second, we don't really continuously reconstruct our self-identity from multiple ethnicities paraded before us - this isn't the reality of what happens. Third, having 150 ethnicities in the same place is really the same as having none, since an ethnic culture requires its own territory to create a distinctive cultural environment, which might then be picked up on and reproduced as an ongoing tradition.
The reality is that the main effect of multiculturalism is to undermine the influence of the mainstream ethnic tradition, thereby allowing a more commercialised pop culture to extend its influence.
The left itself has noted this effect and railed against it. One of the foremost figures of the Australian left, Phillip Adams, is a good case in point. He has written on the one hand that "the things which divide us create a cultural diversity that's endlessly fascinating".
At the same time, he has attacked the influence on Australian children of a "global culture of breathtaking crassness and stupidity," which has left them with "fully fledged appetites for junk - junk food, junk films, junk ideas, junk toys and junk culture."
He has similarly complained about Aussie kids wearing "reversed baseball hats, baggy shorts and those preposterous brand name shoes" while "giving each other fives" and "talking jargon derived from rap and LA gang talk".
Adams doesn't get it. He doesn't understand that the "diversity" he finds fascinating (multiculturalism), in undermining the place of the established national culture, has inevitably allowed the internationally dominant pop culture to fill the vacuum.
Two further points. What is it which comes closest to fulfilling the multicultural ideal, in which we self-select according to multiple ethnic cultures? Restaurants! We do get to choose between a whole variety of different ethnic cuisines, and what's more we enjoy it.
So it's no surprise that liberals often emphasise restaurants and food as a justification for multiculturalism. It might seem shallow to do so - to base such an important policy on cooking - but it makes sense in that it's the nearest that multiculturalism really gets to fulfilling its aims.
Second, it's noteworthy that the established, mainstream ethnic culture isn't allowed to be celebrated within a multiculture, as the others are. Again, I think this makes sense within the terms of multiculturalism.
Wouldn't a multiculturalist fear most the reassertion of the traditional, mainstream culture? Isn't it this culture which is the only likely candidate to become a mainstream, national "monoculture"? So why would a multiculturalist want to give it equal treatment and celebrate it like the other ethnic traditions?
Furthermore, the "threat" of a return to a national culture is made all the more real by the fact that right-wing liberals often call for this to happen.
Right-liberals commonly prefer the idea of assimilation into a single national culture. They often criticise multiculturalism as being too divisive, too much based on collectives and too negative toward the mainstream.
The right-liberal "solution" to establishing a communal identity, is to have a single identity but to base it on liberal political values, rather than ethnicity. The identity, in other words, is based on a commitment to qualities like tolerance, democracy, the rule of law and so on, which do not limit individual self-definition.
Leftists often don't get this aspect of right-liberalism. They frequently express the fear that right-liberals want to go back in time and reassert the mainstream ethnicity etc. It's a little bit dopey of left-liberals to think this way, but their fear does make some sense if you remember that the big threat to multiculturalism is the reassertion of the traditional ethnic culture, and that right-liberals do often criticise multiculturalism and urge assimilation to the mainstream.
In practice, there is an overlap between the politics of the left and right on this issue, which is to be expected since both accept liberal assumptions about self-definition as a goal of individual life.
Even so, there is also room for a sharpening of political differences, given that the left want to replace the traditional ethnic culture with a multi-ethnic one, whereas the right's strategy is to replace it with a non-ethnic one.
At the moment, the right is ascendant, perhaps because the argument that multiculturalism is divisive seems more pressing given the existence of home-grown Islamic terrorism. So there is a greater stress on assimilation than multiculturalism in today's political climate.