Axe-man ‘Arry and Burglar Bill

This is one of those maths problems that has people with names in alphabetical problems.
Axe-man ‘Arry and Burglar Bill have been captured fora theft they both did, both are in separate rooms in the police station, they have two choices in getting off: They can either say they know nothing about it, or that the other person did it. Neither has any idea of what the other is saying.

The outcome is that as the police have no direct evidence conviction relies entirely on what the prisoners say. If they both deny any knowledge they both go free, if they both say the other one did it they both go down. If only one says the other one did it, then he goes free, does not have to share the swag, and the other goes down. Both the know that the other is untrustworthy. What would the outcome be?

This is a logic puzzle, so my answer when I saw it, that they both go free because police procedure has not been followed is not allowed. Only use information from the puzzle. Answer after the picture.

Burglar Bill has no idea what Axe-man ‘Arry will say, but knows that ‘Arry cannot be trusted. There is no honour amongst thieves and it would be consistent of ‘Arry to want to keep all the swag to himself and grass on Bill. Knowing this and also wanting the swag for himself Bill decides to grass ‘Arry up.

‘Arry knows that if Bill grasses him up there is nothing he can do. But if Bill has kept quiet then ‘Arry will get the double share of the loot. Being selfish he decides to grass on Bill. In the end both go down. Which is good news for society, but the worst possible news for ‘Arry and Bill.

The tragedy of the commons

The above is an example of what is called the tragedy of the commons, originally about the rights to graze common land. If everyone has the right to graze common land then they will not want anyone else to get a better share, everyone will graze their livestock there as much as possible and the common land will be overgrazed. Everyone loses out, it is the worst case scenario. But if someone takes the need of others into account and uses the common land less in order that it does not get overgrazed then he is the only one who loses out: The other farmers win despite being selfish.

It looks bad for COP26, the climate change conference which starts on Friday. That is if the theory is correct.

The good news is that although the tragedy of the commons has actually happened in a few places, people tend to cooperate. One farmer will only graze the common land on a Monday, another on a Tuesday and so on and the common land is preserved. The farmers form cooperatives to have a better chance of selling their produce. Even where there is no common land farmers will hire out their expensive machinery like combine harvesters to other farms and the crops are got in collectively. Humans are social creatures who cooperate. When people put forward theories such as the tragedy of the commons which relies on non cooperation to be true it says more about those people, people who think everyone is as greedy and uncooperative as they themselves are.

That is why I am optimistic about COP26. People are cooperative at a deep level, selfishness, and political ideals based on it, are shallow and the worst choice.