Page 45 - 36-1

NTU Management Review Vol. 36 No. 1 Apr. 2026

Finally, we explain the determining conditions in the two cases of the proposition. The
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definition of an increase in ambiguity and Assumption 3 imply that, for >0, )≤
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) ≤ )≤ )≤ ) for all , with strict inequality holding for some .
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That means that Condition (D3) holds at an equality for all 0 ]. Thus, )= )
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for all 0 ]. Based on this result, to satisfy Assumption 2, we must have )=
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) for all 0 ] to keep the center unchanged, which makes Condition (D4) hold at an
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equality. Thus, we have the determining conditions of Case 1, which means that = . Other
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things being equal, if we allow for the center to be changed after the ambiguity increase, then it
can happen that )≠ ) for some 0 ]. Accordingly, Condition (D4) holds for
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all 0 ], with strict inequality for some . We now have the determining conditions of Case
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2, which means that ≤ .
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Q.E.D.

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