Last evening in Australia, my three children were with me at my place. Often during these evenings together, I try to entertain them with mind games, jokes, stories and the like (not to mention Square Root Marbles competitions). But yesterday I just wasn't the same engaging father that I aspire to be. Instead, I was mostly stuck to the computer screen, closely following the news and analysis of Mr. Trump's success.

Like many other citizens of this planet (but not all), I was disappointed by the result. Prior to the election, I had hoped that on Nov 8, I could empower my two girls with the news of a first female president for the USA. I really envisioned telling them this news, as though I am giving them a gift of a bright and positive world. But as you know, the results turned out to be different. It appeared that America chose Trump! On the positive note, I'm sure that our greater galaxy will survive this event.

Earlier that day, in Australian time, while the key counting action was taking place, I tried to explain the concept of the electoral college to my eldest daughter. Like many other 10 year old children, she was quite interested in the election. Being in an Australian time zone she could follow the counting results live (without having to go to sleep). Like many others of her age, she understands the concept of majority vote well. That is, she understands that if 9 people are voting for either candidate H or candidate T, then if 5 or more vote for H then candidate H wins. Otherwise, it is T that wins.

But also like many of her age, my daughter was not aware of the fact that under the American electoral college system, it is actually possible to have situations where more people vote for H, but still T wins. This has happened last in the year 2000 USA presidential elections in which Al Gore had more people voting for him, but nevertheless George W. Bush won!

Now, a day past since the election, and as final votes are being counted, it appears as though such a situation has occurred again! As I write this, the latest counts are: 59,755,284 votes for Hillary and only 59,535,522 for Trump. This is a difference of 219,762 votes for the benefit of Hillary. So is Hillary the winner? No, obviously not. The rules are the rules and it is the number of electorate votes that determines the winner. Trump leads here by a huge margin.

How can the mathematics of such a phenomena be presented to a child? It is certainly an interesting thing to understand!

I still haven't explained this to my kids (since it is 1:00AM here in Australia). But, after trying out several alternative examples, I believe that it is best to consider a (hypothetical) example with 3 states, each of which has 3 voters.These 9 voters will each select H or T. Then, based on the majority in each state, the whole state will be marked H or T. Here is an example of a possible outcome from such an election:

State A: H, H, H

State B: H, H, T

State C: H, T, T

In the above example, since states A and B each have more H votes than T votes, they are both marked as H. As opposed to that, state C has more T votes so it is counted as T. In such a situation, Hillary wins the election (grabbing 2 out of 3 states) and also has the majority of the popular vote (6 out of 9 votes).

But consider a slightly different example:

State A: H, H, H

State B: H, T, T

State C: H, T, T

How many Hillary supporters are there? Yes, 5 out of 9. So she still leads the popular vote. But what about the states? State A is indeed dominated by H and thus marked as H. But states B and C are both with a (slight) majority of T. Hence Trump gets both states B and C. He then wins the election because he has 2 out of 3 states.

You thus have a simple example where even though Hillary got most votes, Trump wins the election.

I can't wait to try and explain this to my children. I am hoping that the basic mathematical insight that they will gain will also spark thoughts of fairness and correctness. On that front, there is never a clear answer except for perhaps "follow the rules set before the race". Nevertheless, the discussion of the anomaly presented above is insightful.

Did you discuss this with your children? How did it go? Let us know.