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It is very simple. All one has to do is imagine the election being repeated an infinity number of times under a stationary-non-changing distribution.

by platz 10y ago

chimeracoder 10y ago
> It is very simple. It's actually not simple at all! This has been one of the most contentious questions of statistics for over a century. > All one has to do is imagine the election being repeated an infinity number of times under a stationary-non-changing distribution. That's using a frequentist interpretation of probability, which is not the only interpretation. (Nor is it, in fact, the interpretation used by e.g. Nate Silver, who is one of the statisticians mentioned in the article). (The frequentist interpretation, incidentally, has been shown to be self-contradictory, for reasons that involve continuous mathematics that I won't get into. In other words, you can construct situations that have nonsensical interpretations under the frequentist approach. That doesn't mean frequentist statistics aren't useful, but - like any model - the approach has limitations.)
- platz 10y ago
  Yes, my hope was to point out the absurdity of this situation for an event that only happens once. It would be nice if all polls calculated a CI or probability distribution of their results (i know 538 does). But even 538 doesn't display their priors. But this would confuse the public even more.. e... asking them to interpret a 95% chance to win with low confidence
deleted 10y ago
[deleted]
defen 10y ago
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.

It is very simple. All one has to do is imagine the election being repeated an infinity number of times under a stationary-non-changing distribution.

by platz 10y ago

It is very simple. All one has to do is imagine the election being repeated an infinity number of times under a stationary-non-changing distribution.

chimeracoder 10y ago

> It is very simple. It's actually not simple at all! This has been one of the most contentious questions of statistics for over a century. > All one has to do is imagine the election being repeated an infinity number of times under a stationary-non-changing distribution. That's using a frequentist interpretation of probability, which is not the only interpretation. (Nor is it, in fact, the interpretation used by e.g. Nate Silver, who is one of the statisticians mentioned in the article). (The frequentist interpretation, incidentally, has been shown to be self-contradictory, for reasons that involve continuous mathematics that I won't get into. In other words, you can construct situations that have nonsensical interpretations under the frequentist approach. That doesn't mean frequentist statistics aren't useful, but - like any model - the approach has limitations.)

platz 10y ago
Yes, my hope was to point out the absurdity of this situation for an event that only happens once. It would be nice if all polls calculated a CI or probability distribution of their results (i know 538 does). But even 538 doesn't display their priors. But this would confuse the public even more.. e... asking them to interpret a 95% chance to win with low confidence

deleted 10y ago

[deleted]

defen 10y ago

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.