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"70% is an election landslide, but I'm not sure it tells you that one kind of staircase is preferred over another." I think 70% definitely tells you what kind

"70% is an election landslide, but I'm not sure it tells you that one kind of staircase is preferred over another." I think 70% definitely tells you what kind of staircase was preferred assuming there are enough staircases (and assuming that that clockwise (CW) and counter-clockwise staircases had equal probability of surviving and being counted). Assume there are 40 staircases, and that 70% (28) are CW. The binomial distribution tells us that the probability of there being more than 27 staircases that run CW is less than 0.83% if staircase direction is chosen at random. Thus, the binomial distribution suggests that it is highly unlikely (<1%) that staircase direction was determined at random. If you want to play around with the binomial distribution: https://www.wolframalpha.com/input/?i=binomial+distribution+n%3D50+p%3D0.5+ https://www.wolframalpha.com/input/?i=binomial+distribution+...

lordnacho 5y ago
I actually thought about this exact thing before I wrote my comment. What you forget is this is an adversarial situation you're dealing with. If it really mattered, nobody would leave it to a coin toss as to which way the staircases have to be. Much like in sports, every little edge counts. Yeah, it isn't chance that 70% of them are CW, but it also doesn't make sense that it's only 70%. The proper comparison is not a 50% cointoss, which is how you might think about some elections, it's a 100% world where every castle maker would tell their apprentices about this important CW swordfighting idea, and people who forget this are castigated for building an obvious weakness into their design. The only reason it would be somewhat lopsided, but not decisively, is if there was some mild reason why people preferred one over the other, which is what your numbers actually suggest. Something like the "easier to walk down" hypothesis might make sense here, where for instance the CCW staircases are accounted for by aesthetic considerations like symmetry.

lordnacho 5y ago

I actually thought about this exact thing before I wrote my comment. What you forget is this is an adversarial situation you're dealing with. If it really mattered, nobody would leave it to a coin toss as to which way the staircases have to be. Much like in sports, every little edge counts. Yeah, it isn't chance that 70% of them are CW, but it also doesn't make sense that it's only 70%. The proper comparison is not a 50% cointoss, which is how you might think about some elections, it's a 100% world where every castle maker would tell their apprentices about this important CW swordfighting idea, and people who forget this are castigated for building an obvious weakness into their design. The only reason it would be somewhat lopsided, but not decisively, is if there was some mild reason why people preferred one over the other, which is what your numbers actually suggest. Something like the "easier to walk down" hypothesis might make sense here, where for instance the CCW staircases are accounted for by aesthetic considerations like symmetry.