If democracy leads to bad decisions, should we abandon it? There is a well-documented body of evidence that most voters don't know the scientific and socio-economic facts that are required to make good political decisions. Some believe that in order to reduce the risk of making grave mistakes on important topics such as climate change and economic redistribution, we ought to adopt a political system in which formal political power (typically voting rights) is given to the most knowledgeable citizens. We don't let incompetent people drive vehicles because it would cause a lot of harm, and the same reasoning would apply to incompetent voters (whose behaviour has life-changing consequences for everyone, including future generations). But this kind of system, called epistocracy (from the Ancient Greek "epistḗmē", meaning knowledge), usually encounters objections revolving around rights to equality and self-determination. It seems, then, that we are caught in a tricky dilemma: either we favour democracy at the risk of making catastrophic political mistakes, or we favour epistocracy at the risk of effectively depriving some citizens of their political power. My research in attempting to resolve this problem has led me to consider a little-known alternative, named enfranchisement lottery, where a small number of voters are randomly selected in the population and learn about a specific political topic for a while before choosing policies. I argue that this third way combines the best of democracy and epistocracy without their biggest flaws, making it a promising solution to our dilemma.