Before we can plan such an experiment in any rigorously scientific sense, we must understand what "liberal" is. There lies the difficulty. There are a huge variety of issues that a newspaper may be biased on; how do we resolve the various positions on these issues into the category "liberal" or "not liberal" (in the first writeup, assumed to be "conservative")? Is a labor leader, in favor of raising the minimum wage but decreasing environmental controls, a "liberal"? Would some hypothetical scientist, in favor of increasing environmental controls but decreasing the minimum wage, also be a "liberal"? The political "spectrum", unfortunately, does not lend itself easily to a one-dimensional analysis like the one desired.
Let us say that we were capable of categorizing an arbitrary set of positions on different issues into "liberal" and "conservative". Could we then categorize a politician as "liberal" or "conservative", only on the basis of those views that the politician has made public to us? Assuming we could, does the fact that the newspaper targets the politician as cartoon fodder make the newspaper the "opposite"? A cartoon could lampoon a person who is ostensibly conservative for not being conservative enough, for example. How much subjective judgement do we allow ourselves as experimenters in deciding what the intent of the newspaper was? Do you "just know" intuitively what the cartoonist's intent was? How is this different from "just knowing" what the bias of the newspaper is?
Lastly, is the use of the political cartoons the best measurement? Presumably, one is interested in the effective bias- that bias that has some potential to sway the reader. Isn't the bias of a newspaper much more subtly persuasive in the use of affective words in the supposedly objective reporting of the main pages? However much our news sources give us the denotative truth, how much are we subconsciously led by the connotative aspects of their word choices? When one reads opinion pages, one is on guard, ready for the subjective. When one reads the "news", is one still on guard? Or does one take the newspaper's word for it?