Arrow's theorem

Imagine you have a group of friends and you are trying to decide what game to play together. You and your friends each have your own favourite games and you want to make sure everyone is happy with the game you choose.

This is where Arrow's theorem comes in - it is a way of figuring out how to make decisions that everyone can agree on, even when everyone has different opinions.

Arrow's theorem says that it is impossible to have a perfect way of making decisions that satisfies a few simple rules at the same time. These rules are:

1. Every person's opinion should be taken into account when making the decision
2. The group's choice should be consistent, meaning that if everyone's opinions stay the same then the group's decision should also stay the same
3. The group's decision should be fair, meaning that no matter what a person's opinions are, they should have a say in the group's decision

The reason that Arrow's theorem is so important is because it shows that it is impossible to have a decision-making process that always satisfies these rules. This means that people will always have different opinions and sometimes it will be impossible to come to an agreement that everyone is happy with.

But don't worry, even though Arrow's theorem shows us that making decisions that everyone agrees on is tricky, it doesn't mean that we can't try our best to be fair and considerate of everyone's opinions. So next time you and your friends have to make a decision, remember to try to listen to everyone's perspectives and find a compromise that works for everyone, even if it isn't perfect.