I would like to draw your attention to the second paper by Sergei Gukov, Kirill Saraikin, and - last but not least :-) - Cumrun Vafa.
- lead to asymptotically free low-energy effective field theories
- and, consequently, for which a maximal number of lines of marginal stability are intersecting in/near a given point
Even if there is an element of randomness in the vacuum selection in the real world, we must study the rules of this randomness. We must be trying to find the right probability distribution; this tells us not only something about the qualitative properties of the real world, but it is also a guide showing where we should look for the exact right vacuum that describes the real world. The probaility measure has probably nothing to do with the "exact democracy between different vacua" because the latter is completely unjustified (being perhaps related to the infinite temperature) and hard to define; only colleagues with extreme far left wing preconceptions can be convinced that this egalitarianism is necessarily a good zeroth approximation. ;-)
The actual distribution is more likely to be related to the Hartle-Hawking wavefunction, which is why it may be a good idea to follow the path of Sergei, Kirill, and Cumrun.