Suppose I have 6 vignettes and the possible responses to all those vignettes are 1 (YES) or 0 (NO). If participants answered (YES) to all six vignettes, they would get a tally score of 6. If they answered (NO) to all six vignettes, they would get a tally score of 0. In other words, this method of 'tallying' the total number of vignettes the participant says (YES) to would create a single item with a 7-point scale from 0 to 6.
Because not all vignettes are considered the same (they were purposefully made to vary to capture different aspects of social context), one cannot assume that the counts will be psychologically equidistant from another. Thus, the Cronbach's alpha is relatively low (~0.4) since they weren't meant to be measuring the exact same thing six times.
Can I run an Ordered Logit Model with the tally scores, or would that be violating an assumption since it's showing low reliability to begin with?