I don't want to sound rude here but your post reads like you just took a Psychology 101 course. I know what cognitive biases are.
The papers you linked do not say that supply biases are almost wiped out by competition. They say that the incentives for being biased are lowered if you assume the other features of the theoretical model that they study. There can be 101 reasons why a theoretical model doesn't map with reality.
Of course you are trying to be rude. That is a classic dismissive argument.
Yes, the incentives for being biased are lowered because the people will lose trust in the news source if they feel that it is biased. The individual determines if a source is biased based on their own ideals and values and their own personal experiences, and if the individual determines that something is biased, then he/she will consume it less. You don't determine what is biased. The individual consumer does.
That is what the article is saying about supply-side bias. If the people of Britain consume right wing media the most then they obviously don't think it is biased. Saying that these people were tricked by the evil media and political culture is just a way to make you feel better when the media lines up with these peoples values and ideals.
As for the 101 reasons why this doesnt map with reality, then lets see them backed up with a credible source.
And no, The Establishment is not 'conspiracy theory'. You might disagree with the content, but that doesn't make it 'conspiracy theory'. It's a history of how the political status-quo in the UK became so dominated by the right-wing.
In any case, until anybody in this thread posts something resembling a plausible post-Corbyn plan I'm done posting in it. I've asked like four times what people think it would look like and none of you have a clue. If you want to see why the Labour party can't get elected, you might want to start there.
I don't want to be rude here, but if you read a book written by a person who clearly has an agenda and knew the answer to his question before he began researching and writing his book, then he is going to find evidence for that argument no matter what. That is like basic argument 101. Hint - a writer who does this does not produce a credible source.
Oh, and here are some references to actual credible studies about whether the American government governs in the interest of the people and not the 'corrupt establishment'
http://www.vox.com/2016/5/9/11502464/gilens-page-oligarchy-study
They can't get elected with Corbyn, so its unlikely that it will get worse.