The left-right division tends to center around the distribution of power. In both the economic and the social spheres, power is distributed unequally. Liberalism is about distributing that power more equally, and conservatism represents the opposite. I don't mean to create a definition that stacks the deck. It's certainly possible to carry the spirit of egalitarianism too far in either sphere. An economic policy that imposed a 100% tax on all six-figure incomes, or a social policy that imposed strict race and gender quotas on every university or profession, would be far too egalitarian for my taste. Soviet Russia or Communist China are handy historical cases of social and economic leveling run amok.
But in any case, there's a coherence between the two spheres. Liberals see a health care system in which tens millions of people can't afford regular medical care, or a social system in which gays face an array of discrimination, and seek to level the playing field. The inequality may be between management and labor, or rich and poor, or corporations versus consumers, or white versus black. In almost every instance, the liberal position is for reducing inequalities of power -- be it by ending Jim Crow or providing food stamps to poor families -- while the conservative position is for maintaining those inequalities of power.
Economic liberalism usually (but not always) takes the form of advocating more government intervention, while social liberalism usually (but not always) takes the form of advocating less government intervention. If your only ideological interpretation metric is more versus less government, then that would appear incoherent. But I don't see why more versus less government must be the only metric.
The one area where I think the liberal and conservative coalitions truly do not fit is foreign policy. I don't see any natural reason why the right should be more hawkish and the left more dovish. It's true that military expenditures compete with social programs for resources, but they also force higher taxes. Wars generally cause liberals to make the same kinds of arguments about futility and unintended consequences that conservatives make about social programs, while the reverse is true for conservatives. - Jonathan Chait
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