A few points are worth making:
First, find and read Jacques Ellul's magisterial treatment of the whole panoply of historic issues wrt propaganda in his book of that title, Propaganda: The Formation of Men's Attitudes (https://www.amazon.com/Propaganda-Formation-Attitudes-Jacques-Ellul/dp/0394718747/ref=sr_1_1?ie=UTF8&qid=1522928817&sr=8-1&keywords=ellul+propaganda, please forgive the obvious gender bias in his book's title). Written in 1973, Ellul remains the "dean of the deep thinkers" on this topic which has such resonance today wrt the perceived tsunami of fake news.
Second, Alessandro Bessi's papers are among the best contemporary treatments of viral misinformation (https://scholar.google.com/citations?user=47xtEeEAAAAJ&hl=de).
Next, among the many synonyms for one-sided reporting are the ones already noted in the comments as well as terms like cherry-picking the evidence and selection bias.
Selection bias was first studied by Nobel Laureate James Heckman back in the late 70s. His paper introduced a method for quantifying the impact of sampling bias (a subset of selection bias, https://en.wikipedia.org/wiki/Selection_bias, see the last footnote in this wiki article) on research and the need for compensating for this bias in order to obtain more accurate parameter estimates in a statistical model.
Finally, selection bias introduces the whole array of cognitive biases and heuristics that are the research focus of fields such as prospect theory and behavioral economics (e.g., https://en.wikipedia.org/wiki/List_of_cognitive_biases). Daniel Kahneman (along with the late Amos Tversky) won his Nobel for contributions to the field of decision-making and, in the process, challenged neo-classical economic assumptions of symmetric, fully informed, rational choice and replacing that framework with asymmetric (loss averse), imperfectly informed, irrational choice architecture.
Among the laundry list of heuristics and biases at least two are highly relevant to your discussion: confirmation bias:
The tendency to search for, interpret, focus on and remember
information in a way that confirms one's preconceptions.
and the bandwagon effect:
The tendency to do (or believe) things because many other people do
(or believe) the same. Related to groupthink and herd behavior.