If you are a United States citizen and you want to do as much good as possible with your vote, then how should you use it? (These principles apply outside the US as well, but my analysis focuses on US elections.)

Expected Value of Voting

For those who care about maximizing the welfare of society, the importance of voting increases as the population increases. Below is the mathematical justification for this claim. These calculations assume that you know the correct person to vote for. If you wish to avoid math, you can skip to the next section.

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When I took physics, I learned that stars radiate light all throughout the electromagnetic spectrum, and radiate the most at some point in the visible spectrum. Our sun radiates more yellow than any other frequency; blue stars radiate more blue; and red stars radiate more red. Given that visible light falls in such a narrow range (with wavelengths ranging from 400 to 700 nanometers), why do all stars’ peak frequencies occur in this range? It seems like a remarkable coincidence.

I wondered about this question for some time, until yesterday I finally realized the answer.

The sun radiates light mostly in the visible spectrum; when this light hits objects on earth, some of it is absorbed, and some is reflected. Most of the light that gets reflected is in the 400 to 700 nanometer range, so any device that picks up light will be most efficient if it can pick up this range. Our eyes evolved to use light to perceive objects, so they evolved to see light in this range. In other words, the reason we see light in the 400 to 700 nanometer range is because that is the range where the sun emits the most radiation. And we can see other stars because stars’ peak radiations do not vary all that much, so they all fall within the visible spectrum.