How do the Alternative Voting Methods Compare?

There are various ways to compare different single-winner voting methods with each one focusing on different criterion. Despite this, there are some really good metrics that show the relative quality of each method.

Bayesian Regret

According to the folks at rangevoting.org, Bayesian Regret is "the expected avoidable human unhappiness" caused by using a given voting method. In simpler terms, it measures the average voter satisfaction of an election using a given voting method.

In the graph below you can see that the Y-axis shows voting method simplicity, with the most simple methods (plurality, approval) at the top, and the most complex methods (condorcet, IRV/RCV) at the bottom. The X-axis shows the range of voter satisfaction from the most strategic to the most honest voting.

The big take-aways from this graph are the following:

1. While plurality is simple, it is unequivocally the worst voting method with regard to voter satisfaction of the outcomes.

2. At its best, Instant Runoff Voting (aka Ranked-Choice Voting) can be a big improvement over plurality, but at its worst (its most strategic) it is no better than plurality.

3. The voting method with the highest potential satisfaction while being only slightly more complex is Score Voting (STAR voting is a form of Score Voting).

4. Approval Voting is the simplest method (it's literally plurality voting with fewer rules) and still results in very high voter satisfaction.

Voter Satisfaction Efficiency

Another measure of voting method quality is called Voter Satisfaction Efficiency. This metric, developed in 2016 by Harvard PhD Dr. Jameson Quinn, provides a more detailed look at how often each voting method elected the best candidate, with the best candidate defined as the one "that would make as many voters as possible, as satisfied as possible with the election outcome."

In the graph below you can see how each voting method performs based on various levels of strategic voting.

The big take-aways from this graph are the following:

1. As with every other analysis of voting methods, plurality is overall the worst performer with regard to Voter Satisfaction Efficiency.

2. Like the Bayesian Regret graph above, this analysis confirms that scored voting methods (STAR, Score, Approval) perform the best.

3. At its best, IRV/RCV performs as well as scoring methods, but when voters are strategic (which they frequently are) IRV/RCV can actually be worse on average than plurality (comparing the 100% strategic red dots).