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60-30-10: Nothing fishy

I have been following the supposed 60-30-10 pattern that several people (including an Ateneo professor) have "uncovered." The pattern was, in essence, that every canvass released by Comelec during election week was nearly identical in that Team PNOY got 60%, UNA got 30% and the others got 10%. Every canvass was within a percentage point of this number.
It was the talk of social networks, made the headlines of a national daily, and was the subject of interviews and TV news reports. They all suggested that something fishy was going on, and that it cast doubt on the results of the last elections. Even Comelec is now investigating
Nothing fishy is going on. It is just poor math education. Anyone with a basic knowledge of mathematics can tell you what is happening.
Let us say the true national average is indeed 60-30-10 – that is, when all the votes are counted, this is the result. Now from what I understand, each canvass released by Comelec does not reflect any particular region or province – they put together all the results from around the country that they have COCs from, and release the result as a canvass. And each time they release a canvass, it represents millions of votes from around the country.
So what does mathematics tell us? That if the election was really 60-30-10, then each canvass represents a very large sample from the total votes. And therefore each canvass would give a result that would be very, very close to the 60-30-10 national average.
This is because each canvass is sampling a very large number of votes. In fact, it is a mathematical law – it is called the Law of Large Numbers, which says that the larger your sample size is for an event, the closer your result from that sample will reflect the entire population.
Now if you look at specific precincts, or maybe even specific regions, you will definitely find that each precinct or region will show more differences between each other. Each will have a different number that is further away from the 60-30-10 pattern. That is because they reflect local voting results. But if each time the Comelec released a national canvass it was reporting results that came in from all over the country, and each canvass was from a large chunk of voters, then each canvass would be very similar to each other and close to the national result.
So I will make a public bet. I will wager 10,000 pesos that when people look at results from different precincts or even regions, they will find that there is more variability in the averages between precincts or regions than the 60-30-10 averages reported from each Comelec  canvass.
Any takers? I will accept the first ten bets – contact the GMA News Online Science and Technology editor and he will take the bets. I am not worried – mathematics (or rather probability theory) is on my side.
And it would be great if people were better educated in mathematics so they don’t see patterns where none exist. – GMA News

Dr. Michael Purugganan is Dean for Science at New York University.