A central aspect of narcissism is grandiosity. That is, narcissists tend to think highly of themselves. In particular, they tend to have a positive view of themselves compared to other people.
To be fair, almost everyone has a reasonably positive view of themselves. The “Lake Wobegon effect” is the observation that people generally think they are better at a variety of skills than they really are. The name comes from the radio show created by Garrison Keillor in which all of the children in the fictional town of Lake Wobegon are “above average.” Of course, everyone can’t be above average...
A central question about narcissism, then, is whether this tendency to enhance one's opinion of oneself applies to every trait. A paper by Emily Grijalva and Luyao Zhang in the January 2016 issue of Personality and Social Psychology Bulletin explored this issue.
The researchers did a meta-analysis of a number of studies relating people’s degree of narcissism to their tendency to enhance their view of themselves. (A meta-analysis examines the data from many different studies to capture broad trends in research that may only be evident when looking across a large number of studies.) In the studies within the meta-analysis, participants filled out an inventory that measured their degree of narcissism, and then rated themselves along a number of personality traits. In these studies, other people who knew the participants also rated them along those traits. The key question for the team was whether one's degree of narcissism predicts the difference in ratings one gives to oneself compared to the ratings other people give him or her.
Overall, there was a tendency for narcissists to have an enhanced view of themselves. Interestingly, narcissists were particularly likely to enhance traits that reflect their ability to influence the world. So narcissists perceived themselves to be more arrogant, extroverted, honest, and open than other people thought them to be. They also thought themselves to be more intelligent, better leaders, and more physically attractive than others thought them to be.
Narcissists did not strongly enhance all traits, though. Traits that reflect an ability to be part of a community did not tend to be enhanced. Narcissists did not think they were more conscientious, fair, likable, or reliable than others thought them to be.
This pattern reflects that narcissists inflate their view of themselves in order to enhance their self-esteem. That means narcissists are focused on having an outsize impact on the world around them. They want others to know them for their individual ability rather than their ability to work with a team. As a result, they are focused mostly on traits that reflect individual leadership and greatness rather than positive traits that would make them better members of a community.