Stephen also hints at the idea that people deserve reward in proportion to how hard they try. My previous post criticizes this notion. While I'm on the topic of what Leftism shouldn't be, another bad habit is to be concerned about the welfare of (minority) groups rather than individuals. The "favouritism" which results from this is inconsistent with showing equal concern for all people -- and it's little wonder that we suffer at the polls in result.
There is still much that sets us apart from the Right. For one thing, we should care about well-being and quality of life, not merely economic prosperity. Utilitarians want to maximize happiness, not GDP. And the evidence suggests that, above a certain point, having more money doesn't make people happier at all. It just makes everyone else more miserable. So we might end up embracing some degree of economic egalitarianism, but we should be clear that the motivation for doing so is to benefit people's well-being, not merely equalize it. This is a much more admirable end.
A similar conclusion could be reached through taking autonomy as our core value, as I wrote last year:
Anyone who truly values individual freedom and independence is committed to the necessity of some degree of wealth redistribution. Without this, less fortunate citizens could find themselves forced to submit to the will of (richer) others in order to satisfy their material needs. Rousseau's answer was that "no citizen should be so opulent as to be able to buy another, and none so poor as to be constrained to sell himself."
This too, I think, sounds more admirable than brute "bring everyone down to the same level" egalitarianism. We should distance ourselves from such envy-driven rhetoric -- it makes far too easy a target for our right-wing opponents!
I recently suggested that differing interpretations of freedom might underlie the left/right divide:
Those on the right have a thin or 'formal' conception of freedom as the absence of external constraints. Hence the lower taxes. Those of us on the Left, by contrast, value something rather more substantive: the ability to achieve one's goals in life. "Freedom as capability", you might say. Hence the higher taxes, to pay for public goods and welfare that supports people in pursuing their conception of the good life, whatever it may be.
Naturally, I see this as a huge advantage for the Left, and one that we really should be doing more to highlight. After all, given a choice between thin and substantive freedom - mere absence of obstruction, or actual positive help - which are you going to choose?