David Leonhardt, in a recent column in the New York Times (on-line Nov. 9, 2016), argues that the most important response to the Republican takeover of the U.S. is to convince Republicans that global warming is real and serious. Failure to address this problem now has very long lasting effects.
Most of the effort to convince skeptics takes the form "95% of climate scientists agree ...". This sort of argument from authority is useful only if two conditions are met. First, people have to understand that the authorities in question derive their status from a superior method, namely, actively open-minded thinking. Science is inherently actively open-minded because scientists are constantly looking for reasons why conclusions might be wrong. Scientists (and many other scholars) get credit for poking holes in conclusions, even tentative conclusions of their own. As J.S. Mill and others have pointed out, such active openness to criticism is the only way to have confidence in any conclusions. Without the search for counter-arguments, you don't know if they exist.
Second, even with this understanding (which is not widespread), people may distrust a consensus view. Science works slowly. It took quite a while for people to accept Copernicus's alternative to Ptolemy's theory of the planets. Other false views have been the "conventional wisdom" in science for decades. People may suspect that the 95% of scientists are just engaging in herd behavior, not listening sufficiently to the 5% who disagree (if, indeed, they really exist).
Here I think we need to point out to skeptics that the argument from authority is not the only one. In particular, the existence of the (somewhat misnamed) greenhouse effect has been well known for over 100 years. It follows from a couple of basic principles of physics (or physical chemistry). Thus, in addition to acceptance of authority, there is also a role for understanding.
The two principles are roughly these: First, carbon dioxide (and other "greenhouse gases") absorb heat from infrared radiation, while the more basic components of the atmosphere (oxygen and nitrogen) do not. This fact can be demonstrated in table-top experiments, e.g. https://www.youtube.com/watch?v=kwtt51gvaJQ. Second, the earth's surface itself emits infrared radiation when it is warmed by the sun, which, in turn, warms the atmosphere, which then emits radiation as well, thus increasing the overall temperature of both air and land.
Some understanding of these principles leads to the conclusion that global temperature will increase as the amount of carbon dioxide increases, other things being equal. This fact was well understood by the end of the 19th century. Thus, if we understand these principles, we can see that the burden of proof now shifts to those who want to say that warming will not occur. Other things being equal, it must occur.
The extensive efforts of climate scientists have thus been mainly about determining whether these other factors are in fact equal, or whether some of them might reduce -- or increase -- global warming. It turns out that some reduce it and some increase it, leading to uncertainty about how large the effect will be, quantitatively. (This uncertainty poses risks of its own, as the effect could be larger than expected as well as smaller.) The 5% and the 95% may disagree about the relative importance of these other factors, without denying the basic facts.
My conclusion is that, if people understood the basic science, they would have some additional reason to trust the expert consensus. It might help even if they just knew that it existed. Some attempt to explain the basic science should be part of the public argument. It should not be limited to high-school science courses.
Likewise, actively open-minded thinking itself should be understood, not just accepted on the basis of authority.