I'm not sure how my brother got this idea, but at one point he made an app, just for fun, which would choose two random presidents and have the player choose which was more attractive. I really liked the idea and when he shut the app down I asked if I could make a website version of the same thing.
The site is completely for fun. It uses an ELO ranking, which is fairly common when dealing with contestants of different skill levels (or in this case beauty levels). I wasn't entirely sure what values I should be using, so I just made up some numbers which seemed to work. The end result is that there has been no definitive answer and the results will change a bit if more people come and vote.
I decided to track each vote, along with a timestamp and the matchup, which would allow me to re-run the numbers and recalculate the ELO if I ever wanted to do so. One thing I wanted to ensure is that all contestants get fairly even playtime. To ensure this, I'm randomly selecting possible candidates and then prioritizing ones that have lower total matches. This has kept things pretty even.
It has been pointed out to me that one president has two portraits that do seem quite a bit different. This was originally on purpose, though I have wondered since if it was a mistake since the president can now face off against himself... either way, I haven't felt the need to try to fix it, since it might involve redoing all the voting.
I've done my best to update the site with each new presidential election. When MidJourney was making its debut online someone made all the US Presidents in the style of Pixar. I reached out to them for permission to make a "Pixar" version of the voting. I have no plans to update this with future presidents, I just thought it was kind of fun and silly.