To me, of course, welfare is an economic triviality. Excluding Social Security and Medicare/Medicaid (providing pensions and medical care for old people who have worked for decades is hardly welfare), we spend a tiny fraction of our Gross Domestic Product on welfare. I really don't care whether welfare recipients are "deserving"; I'm pleased that for just pennies we can at least ensure no one freezes nor starves, regardless of their virtues or vices. No one can "put one over" on me in this sense: because there's nothing I expect in return, no one can fail to deliver it.
In political science as well as popularly, political "ideology" is usually described along the axes of freedom and equality. I think these are poor axes. Both words describe concepts that are complex and operate at many layers of abstraction. Freedom, for example, sounds good, but freedom to do what? I don't want people to be free to hurt or kill me; I don't want people to walk off with the stuff I need to survive and operate effectively in the world. Do I want the freedom to eat broccoli, or the more abstract freedom to eat what I choose? More directly, do I want to have — and allow others to have — the freedom to do anything I want economically, even to economically exploiting others? Equality is a little better: we can measure certain kinds of equality (such as equality of nominal wealth or income), but no one, I think, wants (or would admit to wanting) a Harrison Bergeron model of everyone being the same. Evaluating ideology on these axes seems to shed little light on how people actually think about underlying political issues.
Based on my conversation with my friend, and many other conversations, I think there is a better axis to label political philosophy, which I'll arbitrarily term moralism vs. pragmatism. Terms in ethical and political philosophy can have widely divergent definitions, so let me be explicit about what I mean. Moralism means the notion that there is some intrinsically good way of living, or at minimum some intrinsically bad ways of living. To the moralist, the proper function of the state* is to reinforce the intrinsically correct way of living and to suppress the intrinsically incorrect ways of living. In contrast, pragmatism is not concerned with the intrinsic ways of living, but with outcomes: a way of living is good or bad only to the extent that it produces a good or bad outcome. To the pragmatist, the proper function of the state is to produce a good outcome. Both of these paradigms entail making moral judgments: the moralist must (somehow) judge which ways of living are good or bad; the pragmatist must (somehow) judge which outcomes are good or bad.
*In the canonical sense of the state as the institutions that hold and exercise a monopoly on the use of violence.
One interesting result of evaluating political ideology on this axis is the observation that most ideologies are mixed: almost all ideologies contain moralist and pragmatic elements. Even so, we can generally observe that "right" ideologies are more strongly moralistic; "left" ideologies are more strongly pragmatic. In the example at the start of this post, we can see that my friend is more strongly moralistic: she is concerned that people not "put one over" on her, regardless of the outcome. In contrast, I'm more pragmatic: I can ensure with little personal cost that a person on welfare does not starve or freeze. Pragmatism does not mean "amoral": I am still making the moral judgment that starving and freezing are bad outcomes.