A group of (possibly over-polite) people have just finished their meal at a restaurant. One of them asks, "Does anyone want dessert?" The table goes quiet.

Some of the people might want dessert. But nobody wants to say "yes" first, in case they are the only one, and look like a pig while making everyone else wait for them to eat alone. Equally, though, nobody wants to say "no" first, because it might put one or more people who haven't spoken yet off from saying a truthful "yes".

So the question is - is there any blind ballot system that has the property that:

• During the voting process, nobody knows what anyone has voted.
• If the vote is unanimously yes, everyone knows that.
• If the vote is not unanimously yes, everyone knows that, but nobody knows who voted what or how many yes votes there were (or even if there were any or not)

And does not require an external arbiter or programmed device?

The classic "black balling" method doesn't work, because although the presence of a black ball in the bag shows that the vote is not unanimously yes, when the bag is revealed it is still possible to see if there are white balls present (ie, someone did vote yes)

A group of (possibly over-polite) people have just finished their meal at a restaurant. One of them asks, "Does anyone want dessert?" The table goes quiet.

Some of the people might want dessert. But nobody wants to say "yes" first, in case they are the only one, and look like a pig while making everyone else wait for them to eat alone. Equally, though, nobody wants to say "no" first, because it might put one or more people who haven't spoken yet off from saying a truthful "yes".

So the question is - is there any blind ballot system that has the property that:

• During the voting process, nobody knows what anyone has voted,
• If the vote is unanimously yes, everyone knows that,
• If the vote is not unanimously yes, everyone knows that, but nobody knows who voted what or how many yes votes there were (or even if there were any or not)

and does not require an external arbiter or programmed device?

The classic "black balling" method doesn't work, because although the presence of a black ball in the bag shows that the vote is not unanimously yes, when the bag is revealed it is still possible to see if there are white balls present (ie, someone did vote yes).