well... the button I proposed would save you time and effort - this has to come at a cost.
It is the same with the auto-fight button. The risk of losing units is most often higher when using the button (unless the fighting% are ridiculously high) - such the cost of using the button is measured in units lost.
It would only be appropriate to have a similar loss for negotiations. In regards to "doubled cost"... that was just a rough guess of what could be appropriate and easy to calculate without having to deal with half goods...
On that thought... there are tons of LB and special buildings that increase your fighting chances (in giving you att/def % and similar) - but there is nothing in that regard for the negotiations - that partially lies in the nature of the negotiation game though as it is (at least in its basics) a game of logic. One way for an LB to work would be to have a chance to repay (a part of) spent resources with X% chance when the negotiation was successful.
Another way an auto-negotiate button could work was to have a certain amount of fixed costs (like on the map) that could be paid instead of doing the negotiation game. The amount of those resources should also be higher than what would typically be spent in the negotiation game.
I think the main reason we don't see much in that line is that the negotiation feature is a comparatively recent minigame. Very early on the friends tavern which came out around the same time gave one bonus to make it standable in GE - but that bonus has remained only for GE.
A reduced goods cost GB could be popular with some now that everyone has an opportunity to negotiate if they want to - but since we only get 1 GB an age these days, it would probably meet with significant outrage from the "I don't ever negotiate" crowd.
It's also not however really a parallel to fight buildings where they make fights easier and more able to auto so faster... You'd still have to click just as much for the negotiation game.
The trouble with a truly viable auto for goods is just how much better it might be than fighting at that point - it got the 2 advances instead of 1 partly because it's *slow*. If it's no longer slow, then the potential to just make a ton of goods and outperform the most developed fighters is very real. The cost is not that much of a factor as many top players aren't even making the amount of goods they could be because they just don't *want to* negotiate that much - and they already have more goods than they'd need to do what they do want.
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In terms of our Random-Selection button, as I mentioned earlier, I do feel it saves a few clicks as-is. You just have to use your brain a little to evaluate whether to hit the random-selection button again, or change 1 or 2 goods that it chose poorly. Overall I'd say it can turn round 1 and possibly 2 of negotiation from 10 clicks to ~5 (say ~1-3 hits of "random" + ~1-2 changes of goods to what they should be * 2).
The improvements I think it could use:
1) If you've manually set a good, it shouldn't change it on you - to help with the "I just had my answer entered and then hit the wrong button" grief.
2) I think it could try to not duplicate offers - this isn't exactly the mentally challenging part of a negotiation - pretty much everyone understands by now "first try as many different goods as you can". It's a good default. They'll still gain whatever value there is to be gained by being a skilled negotiator in the later steps when there is something to be logicked out. When little tricks like "I know A wants X, but I don't know what B wants yet of 3 options - so I can offer A one of the things I want to test for B" change whether you have a 67% of success vs 100%.