Barry's Beef

It certainly isn't a Bi-election.

Unless you were referring to Simon Hughes there.
 

I would be careful about posting such items - the grammar police are, in my humble estimation, nutters and will try to recruit you to the purist school of linguistic happiness.

Where two word are joined together to describe a third a hyphen is used to connect them: a well-resourced area, the 24-hour clock etc.

So yes to Parliamentary Under-Secretary of State but no to by-election
 

Was the typo done on purpose ?
 

Parliamentary Under-Secretary of State?
- and -
By-election or Bye-election (I prefer the latter).