I am trying to prove the Arrow's Impossibility Theorem. I was searching on the internet but there is lots of different versions. I want to prove it for this statement:
Arrow's Theorem:
Consider a set of alternatives with at least 3 elements and assume that the number of voters is finite. Then, it cannot be established a demotratic voting system satisfying the Pareto and IIA properties.
Where:
Pareto: When every voter prefers A to B, the system must also prefer A to B.
IIA: If the system choose A and not B, and one or more voters change their preferences without changing the relationship between A and B. Then, the system must not change A for B.
I tried to understand some of the proofs I found on the internet but I can't get any insight of how this works.
- Could you give me a proof for this statement along with a simple and brief intuition?
- Could you include some bibliography that may be helpful?
from Hot Weekly Questions - Mathematics Stack Exchange
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