Question: I'm a Libertarian who gets into arguments with a lot of people who are pro-big government, regulation, welfare, etc. I always reject their arguments because they are purely based on subjective criteria. I know that subjective criteria are not legitimate justifications for coercive government policies, but I have a hard time articulating why. One thing I can think of is that anything subjective can't be proven. What are some others?
Answer: Subjective criteria like "I like it" of course can't be proven as you say. And that is, in fact, why they are wrong. I can't add any more logic than you already have on your side.
However, here are some rhetorical ploys that occur to me that may move your interlocutors when logic doesn't.
1. Appeal to abstraction: Perhaps you can point out to them that a concrete policy (minimum wages, for instance) is not a good place to make a strong subjective commitment. What do they REALLY like? Then at least more ground is open to factual discussion. For instance, perhaps they value human happiness. Then at least we are getting somewhere. Encourage people to not be promiscuous with their intuitions and to settle on a few or very few clear "intuitions" of what is good.
2. Appeal to diversity and tolerance: Most liberals appreciate that it is one thing to disagree with someone, and another to repress his speech by force. Invite them to extend this reasoning to the economic realm. For example, they may find work in X job repugnant for its long hours, dirty work environment, low pay, etc. Ask them to think of the values of the people who take that work, to imagine what reasons they might have for taking the job.
3. Appeal to consistency: If everyone tries to impose their subjective desires on everyone else, it makes politics a war of all against all. Is there some social order that leaves it open to us to pursue our own values, but free as well? Yes: liberty.
In the end, however, these are rhetorical tricks. The basic fact is that any argument that is not based on facts is arbitrary, i.e., a lot of hot air.
As a final note, I wonder whether some of the people you argue with simply are not interested in reaching reasoned political conclusions. Ah, there's the suggestion I forgot to make: Give your opponents Navigator [or The New Individualist] and let them chew on that!