In the increasingly connected world that we live in, it is unbelievable that almost one third of the world's population is not ensured this basic liberty.
What does the "world being more connected" have to do with "freedom of the press"? The
bold part should state why it's incredible that freedom of the press is not ensure.
A country cannot in good faith consider themselves wholly democratic if they do no allow free discussion.
Not every country is a democracy. This sentence seems to me like you're saying "only democratic countries needs freedom of the press" instead of "every country needs freedom of the press."
Privately owned media serves a variety of valuable purposes. Oftentimes, media corporations serve as watchdog of government and have uncovered corruption from Watergate to illegal government weapon trading in India.
I'd replace "watchdog" since it really have a negative connotation in this context. Unless you want to convey that the media is bad, choose another word!
This increases overall quality of life and promotes a stronger society as a whole.
How?
Though not explicitly stated, most essays wants you to incorporate yourself into the essay and tell colleges about YOU. I think they could careless what you think. With argumentative essay like this, it's good to give some concession to the other side of the arguments as well. Also, your essay gives a feel of being too "finalize" because you use a lot of strong language like "must" or "need."
I think that it's good that you're trying to show your conviction toward this issue, but I just feel like you're being too critical of the government and the UN.
P.S. I'm not trying to rip on you or anything, just being honest.
Good luck :)
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