4 ms·

I realize you're joking, but if the election were repeated an infinity number of times, wouldn't the same candidate win each time?

• platz 10y ago
  The distribution for the roll of a die doesn't change, but the individual outcomes do. It all boils down to how this random variable is defined.
  • defen 10y ago
    Right, but what mechanism would change the outcome of the election if it were re-run? Are you suggesting that some percentage of people randomly choose their candidate while they are in the voting booth?
    • platz 10y ago
      I know I do!
• chimeracoder 10y ago
  > if the election were repeated an infinity number of times, wouldn't the same candidate win each time? It depends on what you mean by "repeated an infinite number of times". First, there's a problem with the framing of that statement, because you can't literally repeat something an infinite number of times. You can repeat something indefinitely, and observe the behavior as the number of repetitions increases without bound, but that's not quite the same thing. (I realize this sounds pedantic, but if you want to understand the underlying interpretation of probability, it's an important distinction to be aware of). So, let's say you asked, "if the election were repeated over and over again, without bound, what would the outcomes be?" And the answer to that is... well, it depends on who you ask. Setting aside the "fate vs. free will" philosophical question, different statisticians would answer that question differently, depending on which interpretation of probability they use. There are three main interpretations of probability, though these days, people pretty much only ever use two (frequentist and Bayesian). And you could construct either a frequentist or a Bayesian argument that the same candidate would always win, or that a different candidate could win each time. Think of the election as a function - some unknown inputs go in, and an outcome goes out. What are the inputs to that function? (That's a rhetorical question - we're not really sure what makes every individual voter vote, and what disruptions could happen to nudge each person to vote a different way, or to not make it to the polls that day, or for their ballot to get lost in the mail, etc.). Congratulations, you have a random variable[0]! Now all you have to do is decompose it to determine the underlying components and the true distribution they draw from[1]. I realize that's not a very satisfying answer, but the underlying issue ("what does probability mean") is not a simple question, and statisticians have been debating it for over a century. [0] which is, confusingly, neither random nor a variable. [1] Which is itself controversial way of putting it, because some statisticians would argue that there is no "true" distribution, or that, if there is, we can never actually know it.
• inimino 10y ago
  A (very) slightly more practical way to look at: what happens over a hundred elections where Nate Silver reports a 80% lead for one candidate three weeks out? If that candidate wins about 80 times then the model is good. What you want is infinite (or many) actual historical elections and then just look at the ones where the model gives 80%. A good weekend project if you have a universe simulator lying around. Edit: this is what "under a stationary distribution" means. It means holding everything that goes into the model, such as the polls, constant, while allowing everything else to vary, then you run the experiment many times. The easy way to do that is just let Nate Silver keep doing his thing for a few centuries.