While I largely consider myself a mathematician, people are far more passionate about their politics than they are about their math skills, and I need readers, so I’m going to push your political hot-button ever so slightly and see what falls out. But yes, I’m going to use mathematics for the stick I poke you with. I’ve probably lost half my readers right there.

For the sake of simplicity I’m going to assume that if you are reading this you are a conscientious individual that meticulously votes at every opportunity, federal, state and local. Put another way, I’m going to presume you care and want your vote to count for something. Well, you’d be correct: your vote does count. Not very much, but it does count. I’m not trying to disparage your vote, it counted as much as anyone else’s vote. There were 131,257,328 votes cast in the 2008 federal election[i], meaning your vote accounted for 1/131,257,328, or about 7.619 x 10^{-7}% of the total popular vote. (If you’re rusty on scientific notation, move the decimal point seven places to the left to get the numerical percent, or nine places to the left to get the actual decimal fraction.)

Okay, now that you’re feeling insignificant and wounded, let me finish you off: The number of representatives in Congress, the Executive, or Judicial branches has not changed since . . . 1960. And that was only in the Senate with the addition Hawaii. The number of representatives in The House of Representatives hasn’t changed since 1912! So, in one-hundred years, exactly, the population has increased while your number of representatives has not.

Welcome to the Rules of Exponentiation. Let’s say that population growth is 1% on average, which is relatively close to the actual number in the preceding decade. I am going to spare you the logarithmic explanation of why this works, but it means that if you divide the growth rate by roughly 70 you end up with the amount of time it takes something to double. Assuming our 1% population growth number, that means the population doubles every seventy years. (Historically over a longer period of time the population growth rate has actually been much higher than 1%, but using the last decade seems reasonable here.)

So, for those of you celebrating your one-hundredth birthday, when you were born your Representative was responsible for just over 212,000 of you, and today, you are one of about 722,000 represented by that same one Representative. Which means that, roughly, you have only 30% the representation in government that you had a hundred years ago. For those of us a little younger the math is relatively simple, but looks pretty ugly to the uninitiated, because it is not simply a matter that your representation gets diluted 4% over four years (assuming a 1% population growth), but actually slightly more, roughly 5.7% due to exponential population growth in one presidential election cycle, and 11.4% in just two cycles.

So with each passing year, or with each passing election, your vote counts for less, and your representation becomes also less. **What’s the solution?** (I’m expecting some comments in the comments area below.) Given the voluminous amount of derogatory rhetoric thrown around about our congress, I am guessing that there won’t be a large faction pressing for tripling the number of representatives in the House of Representatives, but that’s just a guess. There exists, conceivably, some legitimate mathematical arguments for doing exactly that. I suspect there may even be some reasonable legal arguments for doing exactly that. But still, I will be extremely surprised if anyone presents them in anything approaching a lucid form. Now there is a correct mathematical solution, but again, I doubt very much it will appear in the comments.

Go.

[i] Results according to the Federal Elections Commission, http://www.fec.gov/pubrec/fe2008/2008presgeresults.pdf

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