Ben Abramowitz, Ehud Shapiro, and Nimrod Talmon cite “Gödel’s Loophole” in their excellent 2020 research article “How to Amend a Constitution? Model, Axioms, and Supermajority Rules” (via arXiv). Their formal paper is mathematical in nature, but here are the first few sentences of their abstract:

“A self-governed [group] must have rules by which group decisions are made. These rules are often codified by a written constitution that specifies not only the rules by which decisions are made, but also the means by which these rules can be changed, or amended. One of the defining characteristics of constitutions is entrenchment, or the difficulty of enacting changes. Too little entrenchment means a constitution has little force behind it and can change frequently. Excessive entrenchment can be similarly destabilizing if it frustrates too many of its constituents, and can undermine the collective will.”

The last two statements above (in bold) captures perfectly the problem of constitutional decision rules. Abramowitz, Shaprio, & Talmon then cite my Godel paper in Part 3.1 of their research article, where they write (emphasis in the original):

“Since agent preferences are over decision rules themselves, we assume that these preferences reflect some properties agents desire in any group decision, i.e. level of consensus required for change. Ideally, these same principles should be reflected by the amendment rule itself. If the status quo has special status, say for purposes of entrenchment, then perhaps any change to it should not violate the principles behind the status quo. For example if 2/3rds of the agents are required to accept proposals, but they only need a simple majority to change this decision rule, then the 2/3rds threshold is only entrenched in a very limited sense, since a smaller majority can undermine it. We codify this sense of internal coherence as anterior consistency. (The example above relates to Godel’s loophole [Guerra-Pujol, 2013] of the US constitution.)”

In reply, I wish to make one point of clarification. To borrow their own example of a 2/3rds threshold versus a simple majority, Godel’s loophole would apply even if a 2/3rds super-majority, and not just a simple majority, were required to change a group’s decision rule. I won’t repeat my argument here (see part 3 of my paper), except to say that that is Godel’s loophole, i.e any decision rule can be amended, even entrenched or unamendable ones!