Arrow's impossibility theorem simple proof and explanation 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.

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*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?

 A: The shortest proof I know of is from Yu (2012)
The idea is as follows. Say that an individual is pivotal for a decision if his preference between two alternatives determines the social preference given the preference of the other members of society. Unanimity and universal domain imply that there must exist a pivotal individual for some decision. Using transitivity and independence of irrelevant alternatives you can show that the pivotal individual is always pivotal for any decision. Hence, they must be a dictator. 
A: You may find this paper useful: Geanakoplos, John. "Three brief proofs of Arrow’s impossibility theorem." Economic Theory 26.1 (2005): 211-215, currently available as a pdf at https://cpb-us-w2.wpmucdn.com/campuspress.yale.edu/dist/4/1744/files/2017/07/53.-Three-Brief-Proofs-of-Arrows-Impossibility-Theorem-2005-1el9mnc.pdf.
Also have a look at Fey, Mark. "A straightforward proof of Arrow’s theorem." Economics Bulletin 34.3 (2014): 1792-1797, currently available as a pdf at https://www.rochester.edu/college/faculty/markfey/papers/ArrowProof2.pdf
