insert one dash where needed. the trade unions president was voted into office by a resounding majority at…

Brief Explanations:

The dash is used to add an after - thought or an interruption. Here, "at least that's the story they gave" is an after - thought to the main statement about the trade union's president being voted in. So the dash should be placed after "majority".

Answer:

The trade union's president was voted into office by a resounding majority - at least that's the story they gave.