weeks, waiting for CNN International to announce the final results of

the Hillsboro, Oregon school board Seat 1 election. In case you miss

their updates, here is the current count, which will most likely be

certified tomorrow: Janeen Sollman beat me, 3582 votes to 3524, with

the distant 3rd place candidate at 2096 votes. Yes, that's right, I

lost by a margin of only 58 votes out of over 9000 cast. Now I know

how Al Gore felt nine years ago.

It seems like we've been hearing a lot about close elections

lately: aside from the Hillsboro school board, some less significant

races like the Minessota senate seat and the 2000 US presidential

election have been even closer percentage-wise. Why does this keep

happening? One theory is that on most important issues, the majority

of the people are very evenly split, and it just happens that we're in

a society divided nearly 50-50. However, some would subscribe to a

more cynical theory. People are so confused by politics these days

that they just randomly vote for one of the two front-runners whose

names they recognize. Of course, for the sake of good government, I

hope this one's wrong, but let's examine the mathematical effects of

this hypothesis for the moment.

Assuming the theory is correct, then in the close elections we are

really observing a statistical theorem in action, the Law of Large

Numbers. This is the law that states essentially that if you sample a

random variable a large number of times, then the average number of

times you see each possible value will correspond to its actual

probability. On in simpler terms, if you flip a fair coin enough

times, the total number of heads vs the number of tails will approach

a 50-50 ratio. We've all probably noticed that if we flip a coin a

few times, we might get lucky and get a bunch of heads or a bunch of

tails, but in the long run the ratio will even out. This law seems

intutitively obvious when you think about it-- in fact it was stated

without proof by Indian mathematician and astronomer Brahmagupta as

early as the 7th century AD. But it was not until the early 18th

century that Swiss mathematician Jacob Bernoulli proved it

rigorously. According to this law, if you flip thousands of coins,

you will expect the total numbers of heads and tails to get pretty

close. In the show notes is a link to a website where you can

simulate large numbers of coin flips, and see results comparable to

Hillsboro's election.

But you need to be cautious when using the Law of Large Numbers--

a common misuse is what is known as the Gambler's Fallacy. This is

the belief that somehow, the universe "knows" it is supposed to

approach the proper ratio, and therefore if you have seen a bunch of

improbable events going one way, you are likely to see a bunch of

improbable events going the other way to make up for it. At a casino,

a gambler might see that two people rolled snake-eyes on the dice just

before him, and therefore decide he's virtually guaranteed not to roll

snake-eyes. Or if ten of Hillsboro's random voters in a row happen to

vote for Janeen, someone deceived by this fallacy would then think

that the next ten random voters should disproportionately favor me.

But that's not how randomness works: if people are truly deciding

their vote by a coin flip, then each voter has a 50-50 chance of

choosing either of us, just as each coin has a 50-50 chance of being

heads or tails. The universe doesn't care about prior coin flips, or

temporary islands of improbability: an independent event is an

independent event. There are no divine beings standing over your

shoulder waiting to correct the coin flips in case you get too lucky.

The Law of Large Numbers is simply a statement about the natural

effects of probability, that enough random choices will even out in

the end. So don't get tricked by the Gambler's Fallacy, and make

foolish decisions based on expecting the universe to even itself out.

And next time an election rolls around, try to really think about it

rather than flipping a coin. Unless, that is, your thoughts lead you

to voting for an opponent of mine, in which case I won't mind a coin

flip.

And this has been your math mutation for today.

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