The tale of three friends in a cinema

Once upon a time Alice, Bob and Carol wanted to see a movie together, as they were close friends. In their local cinema they could choose out of three different movies, X, Y or Z. So the three friends had to make a choice.

But each of them wanted to see a different movie. Alice preferred to go to X, with Y as second preference and Z as third. Bob’s preferences were Y>Z>X, while Carol preferences were Z>X>Y. Because of this, the friends decide to vote.

 name first choice second choice third choice Alice X Y Z Bob Y Z X Carol Z X Y

First, they have a vote between X an Y. Alice and Carol vote in favor of X and Bob in favor of Y. So X wins the first round. Subsequently they vote between X and Z, with Bob and Carol voting for Z and Alice for X. Hence the friends go to movie Z.

 round X Y Z winner 1st 2 1 NA X 2nd 1 NA 2 Z

However, in a parallel universe these same friends are facing exactly the same problem. But in this case the first round is between Y and Z. Alice and Bob are voting for Y and Carol for Z. The next round is between Y and X, with Alice and Carol voting for X and Bob for Y. Hence the friends go to movie X.

 round X Y Z winner 1st NA 2 1 Y 2nd 2 1 NA X

In yet another parallel universe, we have again the same situation. Only now the first round is between X and Z. Bob and Carol are voting for Z and Alice for X. Next round is between Z and Y, with Alice and Bob voting for Y and Carol for Z. Hence the friends go to movie Y.

 round X Y Z winner 1st 1 NA 2 Z 2nd NA 2 1 Y

In three almost identical parallel universes three friends, Alice, Bob and Carol, where facing the exact same question: which movie will we watch? Though each friend had the same preferences in each universe, the friends decided to watch a different movie in each universe.

13 thoughts on “The tale of three friends in a cinema”

1. I am a visual learner. Could you please make a diagram?
Who is Bob’s date? Alice or Carol? Who is paying for the tickets?
I haven’t been to a movie in a theater for over 35 years. The last time I stepped in a used piece of chewing gum. 😦

1. >>The last time I stepped in a used piece of chewing gum.

That’s nasty, really.

>>Could you please make a diagram?

That would be difficult, but I will think about it.

>>Who is Bob’s date? Alice or Carol?

Alice, Carol is Alice’s best friend as well Bob’s little sister.

>>Who is paying for the tickets?

I do.