We used the same information as that used by Manski, but we managed to derive the tight bounds. As I state in my book (page 269) Manski's bounds happen to be tight under certain conditions, e.g., no contrarians. This means that one can get narrower bounds ONLY when there are contrarians in the population, as in the examples discussed in reference (Pearl 1995b). It is shown there how data representing the presence of contrarians can provide enough information to make the bounds collapse even to a point. This reference (R-203-AIM) also gives intuitive explanation of how this can happen.
Best wishes,

========Judea Pearl

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