Speaking of democracy, now I speak of Arrow’s theorem.
Suppose we want a democratic system that meets the following conditions:
- There will not be a dictator: a single person will not decide for everyone.
- We can order all the preferences of voters.
- The overall preference of the total of voters is supported, indeed, by people who have voted.
- For every single vote to allow or promote positive value an option to vote against another, the whole system will allow that option valuation also get a positive.
- The preference of all voters to choose between option A or option B only depends on the choices of voters who have to do with those options.
- There is no dictator.
- All votes cast for the different options can be ordered.
- When someone votes one option, the total system takes this into account.
- When someone votes for one option, at the global level has also improved this option.
- The votes from one option or the other depend only on voters who voted.
This democratic system seems good, right?
Okay, now think that there is:
- Two or more people voting. For example, Antonio and Juan, or all citizens of a country.
- Three or more options on which to vote. For example, something “I don’t like”, “I do not care,” “I like it” or the political party 1, 2 or 3, etc.
It’s normal, right?
Then come the math and say us… oh, surprise!… there is no voting system that meets these conditions.