Imagine a very small country with 66 citizens. Some time ago, a revolution occurred, and you have become the new president. Initially, every citizen (including you) earns the same amount of money, which is one coin per day.
Now, suppose you are a kind of an evil dictator. You managed that you cannot be voted away by elections, but you don't like the small amount of money you get. You can make laws to change that, but unfortunately, each law needs to pass a poll, and a law is rejected if it doesn't get a majority of votes (more than 50%). Also, the new constitution allows every citizen to vote, except for you, the president.
Luckily, the other citizens are as greedy as you, which makes them very predictable. On a poll, they vote like this:
If the new law increases someones income, he/she votes "yes"
If a new law decreases someones income, he/she votes "no"
If a new law doesn't change someone's income, he/she doesn't vote
You have to know that someone's income can only be an integer number, so it can be 1 coin/day, 2 coins/day etc, but not one coin for every two days. It can be zero.
Now the question is: what is the maximum amount of income you can give yourself by changing the law?
Now, suppose you are a kind of an evil dictator. You managed that you cannot be voted away by elections, but you don't like the small amount of money you get. You can make laws to change that, but unfortunately, each law needs to pass a poll, and a law is rejected if it doesn't get a majority of votes (more than 50%). Also, the new constitution allows every citizen to vote, except for you, the president.
Luckily, the other citizens are as greedy as you, which makes them very predictable. On a poll, they vote like this:
If the new law increases someones income, he/she votes "yes"
If a new law decreases someones income, he/she votes "no"
If a new law doesn't change someone's income, he/she doesn't vote
You have to know that someone's income can only be an integer number, so it can be 1 coin/day, 2 coins/day etc, but not one coin for every two days. It can be zero.
Now the question is: what is the maximum amount of income you can give yourself by changing the law?