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Conditions for a fair democratic voting system

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.

That is:

  • 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.

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