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What postulates or models have been proposed to fix the number of particle generations?

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I understand that the question of the number of generations, while practically settled experimentally, is an open issue from the point of view of theoretical models. I can only think of two theoretical arguments to set bounds in this number:

to get some CP violation, we need at least 3 generations in the CKM matrix.
to keep the sign of the beta function of QCD under control, we can not have more than 16.5 flavours, so 8 generations.

Are there more arguments in the theoretical/phenomenology market, bounding the number of generations in some way? And, is there any that fixes it exactly to three?

asked Aug 29, 2014 in Phenomenology by - (260 points) [ no revision ]

Slightly related: http://www.physicsoverflow.org/7671/gut-that-includes-all-3-particle-families-into-a-large-group

commented Aug 29, 2014 by Dilaton (6,240 points) [ no revision ]

yep, feel free to upvote my old answer there :-D.

I guess that arguments to select a family of models also match the answer here, if they are able to provide at least a bound in the number of generations.

commented Aug 29, 2014 by - (260 points) [ no revision ]

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