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.
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?
Who’s buying the popcorn?
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. 😦
>>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.
>>Who’s buying the popcorn?
They don’t like popcorn.
LOL
Don’t like popcorn????? 😦
That would save you a few bucks or euros or whatever. 🙂
They had to pay their popcorn themselves, anyway.
These are very practical questions. 😉
Interesting! Why do you think?
The answer is that under the given preferences of the three friends there is no Condorcet Winner. Hence the vote can be manipulated by choosing the pair of options in round 1.
Where’s Ted? – http://en.wikipedia.org/wiki/Bob_%26_Carol_%26_Ted_%26_Alice
LOL
But I did not need Ted in this example.
Reblogged this on Lagrangian Republican Association and commented:
I have updated this post by including tables, I hope the tale is now much more understandable.
After all the work you did making the chart, I hate to tell you……….. 😦
Perhaps if you mention the name of the movie, all would be made clear. 🙂
X: The X-man
Y: The young Victoria
Z: Zorro
lol