deletions | additions       diff --git a/This_example_shows_that_direction__.tex b/This_example_shows_that_direction__.tex  index 6458c60..85011a0 100644  --- a/This_example_shows_that_direction__.tex  +++ b/This_example_shows_that_direction__.tex 
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Beyond this simple example, we want to find out what happens with more complex constraints. What are the conditions for resistant BDPs to converge? This is what we will investigate next.   Let us first show that that direction $2)\Rightarrow 1)$ of Theorem \ref{theorem:opinion} does hold for resistant BDPs, that is, resistant BDPs without disagreement in their cycles will always  stabilize: \begin{theorem}\label{theorem:resistantsufficient}  Let $\G$ be an influence profile, $\O$ be an opinion profile, and $\C$ a set of constraints. 
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  \end{proof}  Note that the following questions still need to be answered:  What is the upper bound on how long stabilization can take (at in resistant BDPs? At  worst, the number of possible opinion distributions?). distributions which are consistent with the constraints, can be taken as bound, but can we find a tighter upper bound? And what are the necessary conditions for resistant BDPs to converge?