Hello Konstantin,
No, there is no official order as to which criterion gets chosen when picking one for single attribution. So, from your perspective, it would look completely random.
Over the years, we've seen how confusing it can be to some of our API users. So, in our next generation Google Ads API that is currently in beta, we no longer use single attribution. We've set it up such that we don't report things in that way anymore. Questions like yours really do improve our API because we listen and make changes accordingly. Unfortunately, for the AdWords API, it will continue to appear random as to which one gets chosen.
Best,
Nadine Wang, Google Ads API Team

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