Making people have to pay to downvote will result in them feeling like they've invested in the notion that a post is bad.

That cognitive bias would certainly come in to play. Although part of the appeal of the concept is that it would partially replace a far worse contributor to that bias.

When we encounter 'bad' posts - usually a combination of bad rhetoric with disrespect - the natural reaction is make a counter signal, to punish the slight and to assert a boundary to observers, showing that you are not someone that it is ok to walk all over. Without downvotes really meaning anything the way people do this is via conflict in comments. That is to say, minor social trauma combined with public commitment. This is an order of magnitude or three more significant than spending some karma.

Seeing the karma it costs right there in simple integers puts things into perspective. How much do I really care about some silly non-sequitur or straw man that Bob is throwing at Sally? Or the patronising ignorance that Sally is throwing at me? Is it worth spending 7 karma on? Is it worth paying any attention to at all? Why don't I just ignore the crap and go find some interesting, insightful comments to engage with?

Moreover, they will be more likely to blame the individual in question for the loss.

Or less likely to experience situations where a clever rhetorician is able to bluff the casual observer into thinking that their 'opponent' is worth downvoting. If it costs to downvote you aren't going to do it unless you look more closely the comments. There are few things that can influence the way I think about someone more than if they manage to turn the crowd against me unjustifiably. To my instincts that is a big deal.

This could when combined with standard cognitive biases be quite damaging to good thinking.

I expect there would be some who would find it easier to think clearly with the actual system and others who would find it easier to think clearly in the speculative one. I have no doubt that I would be in the latter category.

In conclusion: I find counterfactual system intuitively appealing. The dynamics are too complex and too distant for our speculation to be reliable. I could just as well have my press secretary challenge yours to a duel. ;)