You'll almost instantly get downvoted to at least -5, despite the verifiable truth of the statement.
It would make vote brigading really attractive as well. Imagine if /r/TheDonald users could have caused a financial impact to anyone just by downvoting their comments. Reddit would have been a nightmare.
$0.50 is a lot of money in some countries in the world. It'd make trolling vastly more expensive for people in those countries.
If you don't deal with the unpopular/controversial opinion getting downvoted problem it also devalues the unpopular/controversial opinions of those from those countries.
If you're $local_news_paper in some small US town the above is irrelevant, but NYT is read worldwide, as is HN and Reddit. (Tho I suppose Reddit more than HN.)
If you still wanna go ahead with your proposal, I think a good model on downvoting would be to see use it as currency with a relative cost plus an absolute base. E.g. absolute_base + 5%_of_current_karma. The relative cost is to avoid hoarding, the absolute cost is to avoid efficiency of karma depletion.
On the other hand, trolls and coordinated political campaigns tend to be a lot more willing to spend money to pursue their causes than people that just want to add a relevant anecdote or express their approval, so it might skew the balance of comments more towards trolling and brigading.