Is that ^ acceptably punctuated?

User2~pi is correct. A significant majority means not just a majority (anything greater than 50%), but a majority that's large (above 50%) enough to be "sufficiently great or important to be worthy of attention; noteworthy". That's from Google's definition of significant. You can have a small majority, a tiny one, large, vast, overwhelming, etc.

Exercise: How large is your majority?

Word of the day: futtock

@JimReynolds Yes.

@JimReynolds By the way, Google hasn't published its own dictionary; rather, it uses (some version of) the ODE/NOAD, whose entries can be accessed at en.oxforddictionaries.com.

I'm not sure why they've decided to keep that information private because I'd imagine it'd help their credibility. Perhaps there are some legal facts we don't know, but... yeah – peculiar situation, by my lights.