Suppose I wanted to claim that almost all Americans favor lower taxes on the rich. How would I show this? Easy, conduct a public opinion poll asking what the highest income tax rate should be. Here's an example from 2012:
Three-quarters of likely voters believe the nation's top earners should pay lower, not higher, tax rates, according to a new poll for The Hill.
The big majority opted for a lower tax bill when asked to choose specific rates; precisely 75 percent said the right level for top earners was 30 percent or below.
The current rate for top earners is 35 percent. Only 4 percent thought it was appropriate to take 40 percent, which is approximately the level that President Obama is seeking from January 2013 onward.
Of course today the top income tax rate is 43.4% at the federal level, and over 50% in states like New York and California. Very few people favor taxes that high.
Now suppose I favored much higher taxes on the rich, how would I show that voters agree with me? Easy, conduct a public opinion poll and ask whether we should impose heavy taxes on the rich, for purposes on income redistribution:
Since 1998, Gallup has asked Americans whether they believe the government should "redistribute wealth by heavy taxes on the rich." This year, 52 percent agreed, tying the all-time high set in 2013. While there's plenty of disagreement about who exactly counts as "rich," a bare majority of the country seems to think we should be soaking them. (I couldn't agree more.)
Notice that Slate reporter Jordan Weissmann cites the poll he agrees with, and not the one he doesn't agree with. For myself, I don't trust any poll on complex public policy issues, because the answer entirely depends on framing. Indeed it's even worse than you might think. It's not a question of finding the public's "true beliefs," as there is no such thing. Trying to find true beliefs is like trying to nail jello to the wall. You can change opinion by simply asking a question. (Insert Heisenberg Uncertainty analogy here.) Thus if you asked people if they'd rather spend $4 million executing a killer or $2 million on life imprisonment, the simple reporting of the relative costs might sway people against the death penalty, as most now assume the death penalty is cheaper. They'd learn something merely by listening to the question, and that would affect their opinion.
If you say we should ask the most basic question possible, untainted by any information that might sway opinion, then you are asking for the most ignorant views of the public. Is that what you want---pure untainted ignorance?
In any case, public opinion polls don't matter, elections and lobbying matter. The point is not to measure public opinion, the goal is to change it. Think about those conservatives who were reassured back in 1988 that only 11% of the American public supported gay marriage.