A lot of people seem to be concerned about how the media is influencing other people. Not as many people claim to themselves be influenced by media content.
The third person effect is the occurrence of people assuming the media will influence, well, not smart people like you and me, of course, but "them," those other people over there. Maybe it's true that only certain types of people are negatively influenced by some media content. But the third person effect could also be an overestimation of the media's persuasive power, overconfidence, or the bias blind spot.
Pluralistic ignorance is the occurrence of a majority of people assuming everyone else believes something that in fact only a minority of people believe. As a result of this misperception, the majority follow rules and norms that they privately reject or disagree with.
W. Phillips Davison cleverly spotted a connection between the two effects:
"Pluralistic ignorance, and the misperception of others' attitudes in general, may also involve the third-person effect, at least in some cases. If individuals assume that they are virtually alone in holding particular attitudes and expectations, not knowing that many others privately share them (Merton, 1968:431), it may be because they
assume others have been brainwashed by the mass media. Indeed, the tendency to perceive the media as being biased toward the "wrong" side of an issue, combined with the tendency to impute persuasiveness to the media insofar as others are concerned, creates a strong presumption that the attitudes of other people on any controversial issue that is in the focus of public attention will be widely misperceived." - W. Phillips Davison
I think, contrary to Davison's guess, that demassification, selective exposure, and the formation of "cyber ghettos" might make people more likely to believe that the majority is on their side, as they primarily view media content that is sympathetic to their own viewpoint. These biases and misperceptions can be countered by appealing to social proof.