AHC: Swiss Vorarlberg

Research for a timeline.

So in 1919 there was a referendum in Vorarlberg on whether it should join the Swiss Confederation. The people of Vorarlberg voted 80% in favor of joining the Confederacy, however this was opposed and stopped by the Government of Austria, elements of Swiss Society (Liberals, Franco-Swiss and Italo-Swiss) as well as the recently victorious Allies.

So my question is simple: How could Vorarlberg join the Confederation? What would have needed to happen, and what would the result in Switzerland and abroad be?

EDIT: I forgot to add the AHC into the title, so here it now is.

Don't see it happening. Switzerland doesn't want to piss anybody off.

The biggest problem is Swiss resistance to the idea. It would have added a lot of German speakers and Catholics, upsetting the balance that is part of the Swiss political structire. So while you write elements of the Swiss society, it's basically everyone needed to block it on a political level, even if there never was IIRC a official statement from the Swiss government on the topic.
Austria at the time isn't really able to do anything against Switzerland if it goes through aside from sending sternly worded letters.
And the Allies... The only one I can honestly see doing more than objecting is Italy, because strenthening a country they have irredentist claims on isn't in their interest.