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I don't understand what the probabilities for an election actually mean. I was reading this piece but I still don't get it. What could it possibly mean to say that candidate A has 70% chance of winning while candidate B has 30% chance of winning.

There is no randomness at any point of the election. Votes are not random, people don't usually show up to the voting places and flip a coin, they already know who they are voting for. The counting process is also not random.

The repeating events interpretation also makes no sense. It sort of implies that some people would vote different in each trial, which also makes no sense to me, unless we are talking of non-independent trials.

The only way I can interpret these probabilities is if we are talking about the probabilities of getting those poll results assuming one of the outcomes.

Gelman clearly thinks this view is wrong, so my guess is I must be wrong. What am I missing?

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    $\begingroup$ I don't see where Gelman denies that view in the article. He denies that it makes sense to state the probabilities to many significant figures. But that is a point about our ability to estimate the probabilities, not about the meaning of the probabilities themselves. In fact the view you are talking about is the only one that makes sense to me. $\endgroup$
    – Dave Kielpinski
    Commented Oct 18, 2017 at 23:19
  • $\begingroup$ Re "there is no randomness:" On the contrary, there are myriad events in an election that must be modeled as random because (a) they cannot be predicted and (b) they nevertheless exhibit regular statistical properties. Examples of such events are the turnout, which is determined by who is sick that day, what the weather is like, and so on; and the actual proportion of voter sentiment, which (at least for some voters) is determined by information they might or might not have seen just before election day. $\endgroup$
    – whuber ♦
    Commented Feb 20, 2019 at 19:11

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Try this:

100,000 people will vote. You try to predict the outcome by asking 100 people how they will vote. 48 say candidate 'A' and 52 say candidate 'B'.

They will all show up and vote as they say.

The issue is that, given random chance, your 100 people might not be a perfect representation. Maybe you made 104 calls, but 4 people who would have voted 'A' were not at home. Had they been at home,you would have gotten 52 'A' and 48 'B'.

You are right in this sense: if you called all 100,000, and they showed up, and they didn't lie, then you know the answer for certain. But you tried to estimate the outcome, where random chance on who you called matters. By calling one out of one thousand people, you run the chance of getting a non-representative sample.

How to turn that into the claim "candidate B has a 70% chance of winning" is all of what statistics is about.

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  • $\begingroup$ I understand the probabilities associated to sampling. What I don't get is what a '70%' of winning actually means. I'd understand if they say "candidate A is liklier to win" in the sense of "we have more confidence candidate A will win". $\endgroup$
    – mguzmann
    Commented Oct 19, 2017 at 5:53
  • $\begingroup$ OK...suppose you call 100 people and 49 say 'A', and 51 say 'B'. Now suppose, instead, 25 say 'A' and 75 say 'B'. In the first case, if you do all the math, maybe that means B has a 55% chance of winning. But, I am sure you can see, that in the second case it is more likely that B has maybe a 99% chance of winning. That is what statistics is all about - converting data into chances. $\endgroup$
    – eSurfsnake
    Commented Oct 19, 2017 at 5:56
  • $\begingroup$ You're not answering the question. $\endgroup$
    – mguzmann
    Commented Oct 19, 2017 at 6:01
  • $\begingroup$ I'll try one more way. Suppose you feel sick. There is a blood test to determine if you have a fatal disease. The problem is that it is sometimes wrong. The doctor does 100 tests on you. Suppose, first, that you are told 51 of the tests say you will die, but 49 say you won't. Now suppose that the doctor tells you that 90 of the tests say you will die, and 10 don't. What do you think are the chances of dying in each case? $\endgroup$
    – eSurfsnake
    Commented Oct 19, 2017 at 6:01
  • $\begingroup$ but dying can be viewed as a probabilistic event, either by repeated trials (many people trying), or by comparing to other people who under the same conditions died or didn't die. There is nothing probabilistic about an election. $\endgroup$
    – mguzmann
    Commented Oct 19, 2017 at 6:19

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