I am confused, because, looking at the timeline for the question are statistic results of these two questions equal?, it was reopened by @AliceD, yet it was closed by @ArnonWeinberg even though votes to close were invalidated in 2016, a month after AliceD's comment voting to close the question as off-topic as it would have a better fit in Cross Validated SE (https://stats.stackexchange.com/).
The motivation for the question is user experience
I am trying to make the better user experience for my poll application and one of the ideas I have for this is breaking multi choices polls into binary polls.
so User Experience SE (https://ux.stackexchange.com/) may be a better fit for that, but the bulk of the question surrounds statistics, and Cross Validated could be a better fit for that.
The edit before reopening included
In fact, what I wish to know from this community is: "Does anybody do statistical research on how results of these two types of questionnaires are different?" The problem with this research is that when you ask any of these question types from someone it affects the result of the second one (people want to show themselves rationally. and if we do not ask questions with the same items for example (a or b), (a or c) (a or b or c) from the same person we do not certain about the complete answer of this particular person and the data is insufficient for comparing)
But, this edit hasn't made the question more psychology related than before apart from the rationality part in my view, so I am confused.
Stats.SE or UX.SE may still be a better fit for this as I would have thought that rationality will play their part in their answers.
My thoughts would be that while it us too old to migrate now, it should still be closed as it can be reposted in UX.SE or Stats.SE
Or am I wrong with that view and the rationality portion makes this question on topic?