That's exactly why politics is a mind killer. The sad thing is, you either have to join this idiocy or accept that your opinions will have negligible impact, because asking people to think in probabilities for half a second loses the competition with strongly-worded soundbites.

This is also why "every statistician/expert is wrong for predicting Hillary would win".

In a binary mind, a 70% likelyhood of an outcome (more than 50%) means that if the opposite happens, everything that went into the prediction was wrong.

In case anyone was curious to review what election "expert" predictions were: they were Hillary to win with 85% chance (NYT), 71% (538), 98% (HuffPost), 89% (PW), >99% (PEC), and 92% (DK).

But all of these sources made more detailed predictions than a simple binary winner. For example, the probability that Hillary received <=232 electoral votes (as was her pledged total) was ~4.3% according to the New York Times.

How big were the error bounds on the predictions? These things tend to be +-5 or 10%-points, considering the statistical model is even sound, which it is only assumed to be "approximately" however much uncertainty that adds.

Do you have any articles where the statisticians analyze what happened?

Probabilities are "error bounds", of a sort, on a binary prediction (in that they express the degree of uncertainty in the prediction.) Error bounds on a probability don't make a lot of sense.

It can easily make sense.

Consider a very simple model, where each person in the country has a probability `p_i` of the chance that they vote for party A, and `1-p_i` that they vote for party B.

Now if we have access to the values `p_i` of all `n` people in the population, then probability that party A wins can be calculated as

    P = sum_{a \in {0,1}^n with |a| > n/2} product_{i = 1 to n} {p_i if a_i = 0 else 1-p_i}

(The precise formula doesn't matter, but clearly it can be computed.) Now assume that we don't have all the values `p_i`, but only the values of `k` people randomly sampled from the population. Then we can calculate `P` on these values to get an estimate of the probability that A will win the election. Our result clearly won't be exact, but we can use statistics to find values `P_1` and `P_2` such that the real value of `P` is in the range `P_1 <= P <= P_2` with high probability over the random sampling of people.

Here we have assumed an underlying random model, which has a probability, and we can estimate that probability within error bounds. We could try to calculate

    P* = sum_{way of sampling k people} (probability of sampling this way) * (probability A wins in this case)

But then we don't know how likely a certain set of `p` values is to be sampled, so we have to guess. Hence we are mixing uncertency and probability. Real statistical models have many different levels of uncertainties and probabilities like that.

Probabilities don't usually have error bounds. Some (most?) people even think that the concept is meaningless.

If I give you a coin with probability `1/3` of heads, I can tell you that it is `1/2` with error bounds `+- 1/4`. How is that meaningless?