## Bayesian voting 101

Now that we have described how quadratic voting works (see my blog post dated 23 Feb. 2020) and have presented several salient objections to this complicated method of voting (see my previous blog post), in this post I shall present a simpler alternative procedure of collective decision-making, one that I have described on many previous occasions (see here and here, for example, via The Journal of Brief Ideas). For the record, my alternative method of voting is inspired by the work of Dr. Warren Smith and goes by various names, including cardinal voting, range voting, score voting, and utilitarian voting, just to name a few. But in my case, because I wish to make an explicit connection between intensity of preferences and degrees of belief, I prefer to call this technique “Bayesian voting.” In brief, under this method of collective decision-making voters are allowed express the intensity of their preferences on every issue or candidate on the ballot. The winner is the candidate that receives the highest cumulative score.

That’s it! That’s all there is to it. There is no need to distribute a set number of “voice credits” to the voters beforehand or to any crunch any obscure mathematical equations beyond simple addition. To see for yourself how Bayesian voting might work in practice, in a real-world election, check out the sample Bayesian ballot pictured below and which I have borrowed from this helpful website:

Image credit:

Or, better yet, let’s return to the very same example that we already used in one of our previous posts to illustrate how quadratic voting works: the upcoming South Carolina presidential primary. Assuming once again (for the sake of simplicity) that only five candidates are competing in this early primary, a Bayesian ballot might thus look like this:

Under the traditional one-man, one-vote rule, each voter is allowed to choose only one candidate from this five-person slate of candidates. Under Bayesian voting, by contrast, each voter would be allowed to rank or score every candidate along some uniform scale, such as the familiar 0 to 10 scale. (I have used a five-point scale in my sample South Carolina ballot above, since many voters will already be familiar with the five-star rating system of yore used by Netflix to rank films.) As I mentioned above, the winner would be the candidate that receives the highest cumulative score. Bayesian voting thus combines the best of both worlds: it captures the simplicity of the “one-man, one-vote” rule, and it also allows voters to express the intensity of their beliefs and preferences. Furthermore, as Warren Smith and others have shown, in addition to its simplicity and intuitive appeal, Bayesian voting has many additional virtues. I will identify and describe these virtues in my next blog post.