For at least the last 18 years (as long as I've been in the industry), the proposition box on a brief has been labelled 'Single-Minded Proposition'.
And just compiling (off the top of my head) a list of recent successful ad campaigns, they're all based on a single prop:
Sony - colour
Canal+ "wardrobe" - storytelling
Cadburys - joy
Toyota "border security" - tough
Chrysler - from Detroit
So you'd think people would know by now.
But they don't.
I still regularly see double-headed propositions
Even triple-headers. (A triple that I remember fondly from my time at Saatchi's was a prop for scratchcards: "The fun way to win lots of money in an instant." Three concepts - fun, wealth, speed. Oh dear.)
An especially tricky customer is the disguised double-header. For example, "Value." It's a single word, so on the face of it, shouldn't that be a single-minded proposition? Actually, no. "Value" doesn't mean "Cheap". It means "Product that is better quality than you can usually find at this price." So "Value" is really a double-headed prop, because you need to say something about both price and quality to fulfill it.
The cause of these doubles is clients who don't quite know what they want to say, and agency planners and account teams who fail to convince them to choose a direction. Of course, picking a position is stressful - you're giving up something that you could say. But the effect of not doing so is usually to end up with an ad that is perfect as breakfast for a dog.
Unless... the creatives can successfully decapitate one of the heads on that double-headed prop.
There are two ways to do it.
Option One is to decide which of the two props is best, and work to that. Be honest - tell everyone that's what you've done, and why. Often they're relieved that someone is prepared to make a decision. If the authorities kick up a fuss that part of the prop isn't included, put a passing reference to it in the endline, the voiceover, or a line of dialogue. Then say "Look - there it is!"
Option Two is to find a single concept that can link the two propositions. That's what Andrew Fraser did - brilliantly - in this Volkswagen campaign out of DDB London known as 'Surprisingly ordinary prices.'
The concept of "Surprise" is a single thought, which links the two props of "High quality" and "Low price" embedded within the Value brief.
Good luck, and happy decapitating.