Why Democracy Might Be Mathematically Impossible: Insights from Arrow's Impossibility Theorem

Democracy might be mathematically impossible – here’s why. The concept that democratic systems are fundamentally irrational is not a reflection of human nature or a critique of democratic societies' historical stability. Instead, it is a mathematically established fact proven by the renowned Arrow's Impossibility Theorem, which even earned a Nobel Prize.

This video delves into the mathematical underpinnings that challenge the rationality of our voting systems. One of the most prevalent electoral methods is "first past the post" voting, where the candidate with the most votes wins. This system dates back to antiquity and has been used in England since the 14th century. Today, 44 countries, including many former British colonies, still utilize this method.

However, first past the post has significant flaws. For instance, in parliamentary elections, it often results in a party holding a majority of seats despite receiving only a minority of the total votes. In the past century, this occurred 21 times in the British Parliament, but only twice did the majority of voters support the ruling party.

Massive thanks go to Prof. Eric Maskin for his invaluable assistance with the script and to Chris D*** for the inspiration behind this video. Special acknowledgments to Latif Nasser, Curtis Gilberts, and Radiolab for their contributions. For those interested in deeper dives, check out Radiolab's episode on voting systems.

For a detailed exploration of Arrow's Impossibility Theorem, refer to these great proofs:

- Yu, N. N. (2012). A one-shot proof of Arrow's impossibility theorem. Economic Theory, 523-525.

- Geanakoplos, J. (2005). Three brief proofs of Arrow’s impossibility theorem. Economic Theory, 26(1), 211-215.

Arrow, K. J.'s theorem remains a cornerstone in understanding the complexities and inherent contradictions in group decision-making processes.

Watch the full video to uncover why democracy, as currently practiced, might be mathematically impossible. Dive deeper into the fascinating world of voting systems and their inherent flaws.