# A discussion on probability

In a relatively recent discussion, the topic of applied probability has entered the fray, so I am taking the time to discuss this issue. The discussion is centred around a reflection of the debacle that was the 2016 US presidential election. Vitriolic politics aside, one notes that objectively, the prediction for the outcome of the election was an abject failure. Nearly all news outlets and pundits gave the Democrats a better chance for winning, and of course, they were all ‘wrong’.

There is a lot of contention with use of the word ‘wrong’ in this context. After all, just because there is a 95% chance that something will happen doesn’t mean it’s guaranteed to happen. However, I am claiming that assigning a ‘probability’ to something like a presidential election is fundamentally misapplying the principles of probability to a real world phenomenon.

Probability has been an absolutely invaluable tool in the sciences and economics, because it really helps us understand phenomena at all scales and how to interpret problems where we are only given partial information. But the underlying principle of probability is that events are similar, in the following sense: each time you flip a coin there is no reason to believe that it’s different from any other time you flip a coin, so the behaviour of the outcome should be similar. Therefore, one can concretely say that if you flip a coin a large number of times, that you will expect to see a certain proportion of coins being heads, and that this is the ‘probability’ that after a single coin flip you will get heads. This can be applied in any setting where similar, indistinguishable events happen in large numbers. Even for coin flips we know that not each coin flip is exactly the same (for example, maybe the temperature of the room is slightly different, the fatigue level of your hand is slightly different, etc) but we understand that these extra factors should be negligible. This allows us to apply, for example, probabilistic models on consumer behaviour even though we know that each person is different.

However, this basic principle is violated in models trying to predict large, singular events like elections. There is no reason to expect (the 2016 election of all elections) that a particular presidential election has any parallel in history or in the future. The candidates are completely different, the general political atmosphere is completely different, demographics are changing, etc. Thus the very notion of ‘probability’ is bunk: you can’t repeat it to check if your guess is correct, and models which cannot be repeated usually aren’t valid in science. Thus, one should step away from the pseudo-mathematical (mis)-application of probability in this subject and instead focus on whether one can actually predict the outcome of an election. On that note, this guy seems to have the right idea (see this article).