The notion that the Left stands for cuddly togetherness, while the right stands for nasty selfishness makes no sense.
Spot on. I'd add that, if it's "cuddly togetherness" - community and collectivism - you want, you should favour free markets.
Hayek called the market a "catallaxy", a word meaning not only "exchange" but also "to admit into the community" - thus capturing the fact that markets can build fellow-feeling.
One reason for this is in the very nature of markets. Success in a genuine market (as distinct from rent-seeking exploitatitive hierarchies) requires one to ask: what can I do for others? That builds a regard for others. And markets allow minorities to integrate into society, by showing that they have valuable talents. It's a small step from there to being valued as people.
And as Deirdre McCloskey shows in here and in this book, markets can promote virtues the "left" has traditionally identified with collectivism - trust, faith, even love.
Indeed, even what seem to be the most ruthlessly individual markets of all - Chicago futures pits - can develop norms of reciprocity. In this book, Donald Mackenzie shows how Leo Melamed used these norms to encourage trading in new index futures in the early 80s.
So, markets can build community.
By contrast, the "left's" efforts to do so can easily spill into a nasty narrow-minded nationalist exclusivity: take (please do) Hodge or Byrne. Indeed, the "little platoons" of Womens' Institutes, boy scouts, and churches - self-governing collectivities - are at least as valued by the "right" as left".
So, Will's right. Collectivism (in its best sense) and community are not leftist values, still less anti-market ones.