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 The justification for the second type of transitivity (which is based on Score voting) can be seen colloquially: if the voter indicates they "somewhat" prefer A to B, and "strongly" prefer B to C, then it'd seem that they ought to "very strongly" prefer A to C.
-If using Score-based transitivity, there are two situations where constraints must be applied, supposing the voter's preference is A>B>C: if the voter votes A>B 30% and A>C 35%, then they can at most vote B>C 5%. This is because A>B + B>C ought to provide the minimum margin for A>C. And if the voter votes A>B 40% and B>C 20%, then they must give A>C at least 60% support. Also note that with Score transitivity, there is an implication the voter's marginal strength of preference for a candidate must increase as they are pitted in matchups against other candidates, the less and less preferred they are i.e. a voter's marginal support for 1st choice>3rd choice must be greater than 1st>2nd. This is because in order to indicate a 2nd>3rd preference, the voter has to put some kind of margin there, which then factors into the minimum margin required for 1st>3rd. To some extent, this makes this type of transitivity easier to work with than the other type of transitivity, because there will be more matchups where the voter is required to give 100% support, which means less matchups where the ratings can change the result. For a scale of 0 to 5, for example, the voter is guaranteed to give 1st>6th 100% support, as well as to 1st>7th, etc. In general, if there are n possible scores (evenly spaced apart, and including the min score), then a candidate in the j-th rank will have 100% support against someone at the (j+n-1)-th slot and below.
+If using Score-based transitivity, there are two situations where constraints must be applied, supposing the voter's preference is A>B>C: if the voter votes A>B 30% and A>C 35%, then they can at most vote B>C 5%. This is because A>B + B>C ought to provide the minimum margin for A>C. And if the voter votes A>B 40% and B>C 20%, then they must give A>C at least 60% support. Also note that with Score transitivity, there is an implication the voter's marginal strength of preference for a candidate must increase as they are pitted in matchups against other candidates, the less and less preferred they are i.e. a voter's marginal support for 1st choice>3rd choice must be greater than 1st>2nd. This is because in order to indicate a 2nd>3rd preference, the voter has to put some kind of margin there, which then factors into the minimum margin required for 1st>3rd. To some extent, this makes this type of transitivity easier to work with than the other type of transitivity, because there will be more matchups where the voter is required to give 100% support, which means less matchups where the ratings can change the result. For a scale of 0 to 5, for example, the voter is guaranteed to give 1st>6th 100% support, as well as to 1st>7th, etc. In general, if there are n possible scores (evenly spaced apart, and including the min score), then a candidate in the j-th rank will have 100% support against someone at the (j+n-1)-th slot and below. To generalize further, if there is a certain % of spacing between two consecutive evenly spaced scores, then two candidates who are n ranks apart will have the more-preferred candidate getting at least n*the % support, and at most 100% support. For example, 2nd>4th must be at least 40% strong with a scale of 0 to 5. Thus, if printing a ballot where the voter is asked to give rated pairwise support to candidates between each rank, it would make sense to actually omit certain scoring options in some cases which would be prohibited by this constraint i.e. for the 2nd>6th matchup, the voter shouldn't be allowed to give either candidate a 3 out of 5, since that would prevent them from creating the minimal 80% margin required for the matchup (3 out of 5 is 60% support; if you add or subtract 80%, you get 140% and - 20% respectively, which are not allowed vote values).
 The use of the rated pairwise ballot may increase the likelihood of a transitive result (i.e. having a Condorcet winner) relative to the use of a ranked ballot in Condorcet methods.