Does this sentence make sense?

No.
Say
eg Younger people are more likely to vote left than do older people.
eg Younger people vote left more often than older people do.

Thanks!

Do you know what this "grammar rule" is called?

"Some political scientists argue the political plays a less-important role than does the corporate, relative to other countries."

I have only seen this in extremely formal scientific articles but never in newspaper articles.

It's an inversion of the normal word order.

. . . than the corporate does, relative to other countries.

CliveIt's an inversion of the normal word order. . . . than the corporate does, relative to other countries.

Huh. I don't understand why you considered my sentence incorrect. I applied the same rule didn't I?

Younger people more likely to vote left than do older people.

The error here is that you need 'are' .
eg Younger people are more likely to vote left than older people.
eg Younger people are more likely to vote left than are older people.