99% is much further from 98% than 51% from 50%. As an example, getting from a one in a million confidence that Alice killed Bob (because Alice is one of a million citizens) to ten suspects requires much more evidence than eliminating five of them. Probabiliy differences are measured on the log-odds scale, in order to make seeing reason A, then B have the same effect as seeing B, then A. On that scale, you could in fact take two statistically independent reasons and say how many times more evidence one gives than the other.

I had in mid when writing the cases that the confidences could be degrees. I don't see how the realness instead of binariness explains any disparities.

Trying to be clear what I mean and how I effectively communicate it I did think that I probably define both "realness" and "cruxiness" to be similar continuums instead of binaries which probably wanst apparent in my expression but I was thinking of expressing it through the poles. But I think that a belief can be "half-real" where you have a mix of reasoning you don't know whether you state in name only or whether they actually convinced/convince you. Similarly the other aspect has a slide in it. I will reserve the name "crux" for the concept used in the post. Rename my other aspect as "stateness". I think they are the same but I am not entirely sure.

Someone close to me pointed out that being smart can make you argumentative as non-smartasses might disagree with a claim but if two smartasses agree with a claim they can disagree on why that position should be held. I have found it very helpdul for myself to have debates over whether the reasons I find something are correct or not, or to phrase it differently if I get something right based on luck, I did an error because I should have arrived at the answer in a systematic way that can be relied on. In more middle cases when I apply a heuristic, the heuristic can be more or less applicaple to the situation and applying a heuristic where it is not meant to is a error-like thing.

Using propabilities can be very model ambivalent which makes different models somewhat interoperable. But it makes it so that model sensitive aspects of arguing are going to be hidden or very hard to express in that kind of language. I still think there is a danger that any claim that has 0 probability moving power would be judged to be a free-spinning wheel. Then there is the issue whether valuable 0 probability moving issues exist and whether it is productive to such bring entities into a co-op deliberation or argument. The point of the crux method is to identify points that lead to effective resolvation. Thefore it depends whether we use resolvation to be more deliberative / communicative or view the agreement as the higher goal so that deliberation and communication are tools to get to agreement.

In the coin flip example, say that you flip the coins and somebody says "there are as many tails as heads". When you start to think what you would belive if one of the flips had a different result there are multiple paths: 1) coin #1 is different, the bystander commenter doesn't say that the amounts are equal 2) coin #1 is different, the bystander commenter does say the amounts are equal, coin #2 is different also 3) All coins are have the oppostie result, the bystander says the amounts are equal. It seems strange to me that every single one of your cruxes could be different yet you would still maintain that the coin was fair. That doesn't sound like a move in confidence. That doesn't seem to fullfill the definition of a crux.

I kinda get that you want to express that the result of the coin flips are materially connected to the belief that the coin is fair. But the definition of the crux as stated doesn't really express that kind of thing. Or in the alternative if the definition is supposed to cover that kind of case then the case where the belief is materially connected but doesn't push the conclusion confidence in any direction ought to also be covered.

I also furher more started to doubt if there is more hidden conceptual disagreements. To me "why" is about the past and the causal history. However the "why" asked here seems that it concerns the future as in "what keeps you believing that thing" as opposed to "what made you adopt that belief". I also realised that I think it should be easy for participants to reveal if their beliefs formed under questionable circumstances (and that this is not trivial and not everybody has policies to this direction). Answering the attitude of "what keeps you believing" makes one endorse those standards differntly and might lead to endorsements that would not exist without asking.

Disambiguation are hard to get exhaustive. I guess the focus on that disamgiuation would be the "why" part. It can just get confusing whether we are talkikng about the level of what the speaker intends or what is offered for the hearer to interpret. I realised that big part of the crux approach can be that the YOU is emphasised (there is no crux for objective facts it require subjective judgement). It could also make sense to emphasise the WOULD (we are about to actually change opinions and not just wave flags for our sides) or BELIEF (we are not caring about professing or side-picking just what you think is the case). But it muddies the waters that context where any of the crucial part here are demphasised in perfectly sensible activities (YOU,why would the general population have sympathy for your views,WOULD for Aist which we don't know whether they exist or their other attributes how they would take that, BELIEF winning a debate where your position is picked at random at start, WHY decision by vote possibly by irrational or populist voters)

You need to answer the question before introspection so you don't have time to doubt your stance. You would need to assume or guess that the other implications would not be so out of wack to make it implausible or impossible to adopt the new stance. If I declare no prospect of position moving the thing is declared moot and we don't discuss.

I think there can be a big gap between the embeddeness of a proposition between the participants. Somebody that doesn't belive in ghosts can treat it like a stand-alone fact. But somebody that does believe will (might) have it entangled with other beliefs. This effect is more pronounced the less anticipated the question is and the deeper it cuts. A ghost belief can be entangled to memories of fear of death. Those associations can be hard to articulate yet they can have real effects on positions held.

It is amgibious what you refer to as "telling them". Doing reassurances without reasons would be equivalent to a kind of "we are just separately doing intellectual stuff, there won't be any discussion breaking forces invoked". The other would be to argue that belief in the important things can be justified even after changing the stance. That kind of guarantee probably can fail. One could argue that the other could just adopt your belief system verbatim to be atleast as prosperous as you are. But it would come with having to adopt your positions on everything. If being of different opinion in a different field comes to cognitive dissonance with the new stance that could be a psychological problem they would have to deal with that you do not have to. That is there is a chance that there is a legit crisis of worldview after the discussion.

I guess the contrast in my mind is that argumentation takes the form of very small steps that are very well founded where all doubt is resolved as soon as there is the smallest hint of it. In a mathematical proof as you follow along you should be convinced that each line is warranted by the previous line. Sometimes when somebody assumes a lot of mathematical competency they use fewer midsteps. Then you can say "I don't see how that follows from that" and the other person can expand the one step into multiple smaller steps. The method here seems that the question "Would you adopt X if Y was not the case?" is not particualrly amendable to going closer into detail how it is answered in the positive or negative. But I think there are lot of hard/laborusome cases where a lot of judgement needs to happen and it happens not in the interactive space but hidden in the private space of one persons head.

I don't feel that was my point but I think it cuts close to the space. I think it now gets lucky that treating the question as a short story or a isolated fact is commonly easy but it has no guarantees that it will be easy or any tools to tackle things when things are hard. Does the method offer any advice when there is no quick or clear "yes" or "no" answer to "would you belive X if Y were the case"?