I would find this helpful - I'm tired of being downvoted when I provide useful information to support an argument that people overall disagree with!

Seems useful, especially for critical posts. I may want to upvote them to show my appreciation and have more people read them though still disagree with e.g. the conclusion they draw.

Big support!

1. By making agreement a separate axis, people will feel safer upvoting something for quality/novelty/appreciation with less of a risk that it's confounded with agreement. Unpopular opinions that people still found enlightening should get marginally more karma. And we should be optimising for increased exposure to information that people can update on in either direction, rather than for exposure to what people agree with.^[1]
2. We now have an opinion poll included for every comment/post. This just seems like a vast store of usefwl-but-imperfect information. Karma doesn't already provide it, since it has more confounders.

But, observing how it empirically plays out is just going to matter way more than any theoretical arguments I can come up with.

Although, if it's not too late, maybe 'two-factor' could use a better name? I suspect many people get confused because they associate it with 2-factor authentification.

+1 to "post author chooses what the agreement target ('central claim') is"

I can't think of many examples where I agreed with a position but didn't want to see it or wanted to see a position that I disagreed with. I think that I've only experienced the latter case when I want to see discussions about the topic. In those cases I feel like you should balance between the good and the bad on upvoting and choose between the 5 levels (if you take into account the strong votes and no vote) that the current system provides. Also, if you believe that a topic that you want to talk about (and believe that others too) is going to be divised, you can just write "Let's discuss about X" and then reply it with your opinion.

I read examples on the comments that I disagreed with and I feel more comfortable counterarguing them all in this comment:

• Useful information for an argument that people disagrees with: Then how is it useful?
• Critical posts which you disagree with that you appreciate and want other people to read: Then why do you appreciate them? It seems you like them in part but not fully, I would just not vote them. And why do you want people to read it? Seems like a waste of time.
• Voting something for quality, novelty or appreciation: I believe that the voting system is better as a system where you vote what you want other people to read or what you enjoy seeing. And I think that we should appreciate each other in other ways or places (like in the comments).
• Unpopular opinions that people still found enlightening should get marginally more karma: That sounds like opinions that change the minds of some people, but get little karma or even negative points. I don't know how would the people that disagrees with it would downvote it less than other opinions which they disagree with. In other words, I don't know how exactly the "enlightenment" is seen by the ones blind to it lol, or what would "enlightening" mean.
• And we should be optimising for increased exposure to information that people can update on in either direction, rather than for exposure to what people agree with: How is that useful? I'm not that familiar with the rationalist community so maybe this is obvious, or maybe I'm misunderstanding. Are you saying that you agree with some arguments (so you update beliefs) but not all of them and you don't change the conclusion? That probably would mean no vote at all from me, and depending the specifics weak upvote or downvote.
• It prompts people to distinguish between liking and agreeing: Why would you like a contribution to a discussion when you don't agree with the contribution?
• There would be fewer comment sections that turn into 'one side mass-downvotes the other side, the other side retaliates, etc.': Why would there be a difference with this new axis?

Agree with:

• Goodwill and trust is generated when people are upvoted in spite of having an unpopular view.

But I believe that the downsides are worse. So, if you were to encourage people to upvote unpopular views, then they could get even more points that the popular views, no matter how "bad" they are. Also there could be more bad arguments at the top than good ones. That sounds pretty confusing and annoying honestly. I think better options are to reply to those comments and upvote good replies and to not show points below 0 nor hide those comments.

Also:

• It sounds to me that to vote in a two vote system would be to vote something and then to think if I agree or disagree with the comment and then to vote again >95% of the time for kinda the same thing (agree after like, disagree after dislike) and then to see the same number repeated or to see a difference in them and wonder about what does it mean and if it exists because people are voting in just one system.
• Really bad for new people.
•  There are cases where there isn't anything to agree or disagree with, like information and jokes.