Depends on the voting mechanism and game theory.
Starting with the game theory:
If the TCR shows a specific bias (ie: political inclination) or some form of censorship, less people will want to own the token because the "fairness" promise is broken and that should reduce the token price.
If the curated items (newsrooms in this case) have low adoption (few people use tokens to purchase viewing rights) then the tokens will lose value too.
For token holders this should motivate them to be judicious in their curation efforts.
The voting mechanism also plays a significant part on the whole system. Traditional TCRs use a partial lock commit reveal scheme that allows us to find the Schelling point for a challenge.
Personally I'm quite partial to other voting systems that reduce the impact of token ownership disparity like the one Glen Weyl, Buterin and others have called "Liberal Radical" and its simpler root the quadratic voting mechanism. The way this works is that only the square root of voter's balance counts as voter's voting "weight". So 1 vote costs 1 token but 2 votes cost 4 tokens and those with less "power" have a higher representation relative to their balances.
edit: typos