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For a more mathematical analysis of how this process plays out in terms of representation, I found this article to be very helpful: https://www.hpl.hp.com/techreports/2007/HPL-2007-28R1.pdf

*It is also worth noting that the main article simplifies the process a little, since a certain threshold approval is required

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"Electing the Doge of Venice: Analysis of a 13th Century Protocol", https://doi.org/10.1109/CSF.2007.21

"This paper discusses the protocol used for electing the Doge of Venice between 1268 and the end of the Republic in 1797. We will show that it has some useful properties that in addition to being interesting in themselves, also suggest that its fundamental design principle is worth investigating for application to leader election protocols in computer science."

Thanks for the link. My first thought when reading the article was there had to be a more simplistic mathematical equivalent.

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