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Question: What are the mathematical probabilities of the US Presidential Election
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Nathan Turner answered on 9 Nov 2020:
Given that the election has now been decided, the probabilities are less relevant!! However, in trying to predict the results, lots of probability and statistics are essential. You may hear in the news that ‘the polls were wrong’ in predicting certain results. The reality is that the polling results rely on a set of assumptions, some of which could be right and some could be wrong!
When polling a population on opinions, polling companies have to investigate a sample (small proportion) of the population. If this sample is not representative enough, then the poll can be skewed by certain variables. This could involve biases from geography, ethnicity, gender etc. One good example from this election could be postal votes (a big talking point!!) – perhaps some polls didn’t conider their impact sufficiently. I should add, this is purely speculation and I don’t have any experience working in election polls!

Eduard CampilloFunollet answered on 9 Nov 2020:
I cannot tell you the probabilities, but here is something to think about the US presidential election. The election was close, with many states deciding by a margin of a few thousand votes. Most of the predictions about the election result use (among other things!) polls from the days before the election. But you only ask a few people in those polls. Statistics help us understand how many people we should ask to get precise predictions, but the simple answer is that to predict the result down to a few thousand votes, we would need to ask to many people!
Sometimes this is summarised as “gargage in, garbage out”: if you have bad data, it does not matter how good your model is, the results are bad.

Chris Budd answered on 9 Nov 2020:
The main prediction is that at the end of the day someone will be annoyed about the result. This is because it is possible to prove that NO voting system is completely fair. For example in the last US election the democrats got the most votes, but the Republicans got the most seats. The same can happen in the UK elections, and even on Strictly Come Dancing. The maths of fair voting is really complicated and lots of fun.

Tom Ranner answered on 9 Nov 2020:
The probabilities that you need to know to guess who will win an election come under the area of statistical inference. You need to combine different sources of data such as directly asking a small number of people which way they will vote (it’s complicated how to design a fair questionnaire and how to pick which people to ask) in a clever way that makes a final prediction. There is often a lot of uncertainties involved – will people change their minds? are the people who you ask good representatives of all voters? These uncertainties are put into this combination as well. In the you may well end of with a prediction of who you will think will win but also a probability of them winning or maybe probability distribution depending on many different parameters or variables.

Christos Klerides answered on 9 Nov 2020:
Very hard to predict exactly! A representative sample of all groups voting in an election is essential to make good predictions. However, there will always be a certain amount of error.

Sophie Carr answered on 9 Nov 2020:
I think now the race has been won the statistics aren’t that useful – but what is important when you look at predicting the election is ensuring you’ve got a representative sample. Getting one of those is really hard and often one of the main reasons that predicting the outcome of an election is so hard.
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