Arrow's impossibility theorem
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If there are two or more people participating in a majority vote and there are three or more options, there is no fair voting system" As a premise, the following conditions are necessary to conduct a fair majority vote:
2. When everyone wants A, the overall intention also becomes A (unanimity). 4. If the options are A and B, an individual's opinion is either "A>B" or "B>A". Also, if the options are ABC and "A>B" or "B>C", then "A>C" (completeness). However, according to Arrow, it has been mathematically proven that "it is impossible to create a voting system that satisfies all conditions". Famous voting paradoxes
As a premise, there are options A, B, and C, and there are three voters.
Each voter is trying to vote as follows:
A: A>B>C
B: B>C>A
C: C>A>B
Let's compare the options two by two (A and C).
Only A is A>C.
The others are C>A.
However, when applied two by two, it becomes circular, How can we create better voting rules?
This theorem only proves that it is impossible to satisfy the four conditions, and does not deny democracy.
Vote by assigning points to the options.
https://gyazo.com/9c7664ded64fd698fff328490ab2ae8d
If there are three or more independent options for voters, no preference voting system can simultaneously satisfy specific evaluation criteria when converting individual preference rankings into community-wide rankings.
Here, "specific evaluation" means the following: