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Structural convergence is a framework for the convergence of graphs by Nešetřil and Ossona de Mendez that unifies the dense (left) graph convergence and Benjamini-Schramm convergence. They posed a problem asking whether for a given sequence of graphs $(G_n)$ converging to a limit $L$ and a vertex $r$ of $L$, it is possible to find a sequence of vertices $(r_n)$ such that $L$ rooted at $r$ is the limit of the graphs $G_n$ rooted at $r_n$. A counterexample was found by Christofides and Král’, but they showed that the statement holds for almost all vertices $r$ of $L$. We offer another perspective on the original problem by considering the size of definable sets to which the root $r$ belongs. We prove that if $r$ is an algebraic vertex (i.e. belongs to a finite definable set), the sequence of roots $(r_n)$ always exists.
This chapter focuses on the first stage in which some level of convergence between the adjudication of trade and investment disputes might be observed: treaty design. After an analysis of 144 PTAs the authors conclude that there is a rising trend of including investment chapters with ISDS mechanisms into PTAs. However, this trend is not uniform around the world. Therefore, if structural convergence is to occur between the two adjudicatory mechanisms, such convergence will not be global, but regional or local. The chapter then continues with a discussion of the potential implications of this phenomenon and argues that some level of convergence can be expected in two areas. First, the broader context and objectives of PTAs with investment chapters can have an influence on the reasoning of investment tribunals. Second, some level of converge might occur due to the interpretive functions of treaty committees. Nonetheless, convergence might be minimal due to: different epistemic communities; investment chapters often look like stand-alone BITs within a trade agreement; and the recent PTIAs require different qualifications for trade and investment dispute settlement decision makers.
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