I remember once reading an opinion piece that I found to be particularly outrageous and deeply offensive. While I considering taking the time to write a letter to the editor, I decided against it and reasoned that there were undoubtedly many others who agreed with me, and some them were bound to submit a letter far more persuasive than anything I could articulate. A few days later the paper printed four letters to the editor on that opinion piece, all of them enthusiastically supporting it.
After overcoming my initial shock, I considered the various possibilities. Perhaps over 90% of the letters were in support of the opinion piece, and so printing four letters in support was representative of the overall views of the readers. Perhaps none of the letters opposing the opinion piece were well written enough to be worthy of publication. Neither of these options sounded very likely to me, and so I was led to consider the inevitable conspiracy theory: The "letters to the editor" editor approved of the op-ed, and was therefore reluctant to print letters refuting it.
Unfortunately, there is no way for anyone outside the newspaper to know to what extent the personal bias of the letters staff affects what they choose to print. Unlike opinion pieces or editorials, which can be tracked by media observers for traces of bias, letters to the editor reflect the opinions of outsiders, and so you can't know to what extent the bias they exhibit is merely an attempt to accurately reflect the overall views of those who submitted letters.
There seems to be a simple method by which a newspaper or magazine can show everyone that they are relatively free of bias in choosing which letters to publish. They can have a section on their website in which they post every email to the editor, and keep it up there for two weeks. This way outsider observers can see what percentage of emails were in favor of a certain editorial, and what percentage were opposed. The various bloggers will undoubtedly crunch all sorts of statistics in an attempt to detect every conceivable form of bias, and will publish their finding on their websites. A good newspaper though should have internal mechanisms of tracking the same thing, and so would have no reason to fear outside scrutiny. There may also be other benefits. For example, someone who submitted a letter only to have it rejected could analyze the difference between the accepted and the rejected letters in an attempt to gain tips on how to better craft a letter to the magazine's liking for next time.
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Most papers have a bias when the issues are political or when they effect local issues. There are token letters printed with opposite views, but the bias is always evident both in content,and numbers of letters printed. It is almost impossible to get a letter printed that exposes their bias. Brief letters are also easier to get into print. Many papers do tell how many letters were received on a subject and the "for" and "against" ratio when there is a hot topic.
Most newspapers have a comments section on every article, but the problem is that there are so many comments they all just get buried. There is always selection bias (self selection, as you yourself have done) and editorial selection bias. The real problem is how to convey a true idea to a reader in a way that represents an overall collection of any known logical arguments.