Weight-of-conflict conjecture

Weight-of-conflict conjecture was proposed by Glenn Shafer in his book on the Dempster–Shafer theory titled A Mathematical Theory of Evidence.

It states that if $$Q_1$$ and $$Q_2$$ are commonality functions for two separable support functions $$S_1$$ and $$S_2$$ defined over $$\Theta$$, and $$Q_1(A) \le Q_2(A)$$, then the corresponding weights of conflict satisfy the condition $$W_{S_1} \ge W_{S_2}$$.


 * $$\forall A \subseteq \Theta : Q_1(A) \le Q_2(A) \implies W_{S_1} \ge W_{S_2}$$