Measuring Election Accuracy
One of the most important criteria we use to evaluate voting systems is "Accuracy", but how do we determine if a voting system is accurate? Does it elect the candidates who should win? Is it fair and representative?
There are a number of tools that voting scientists use to answer these questions and like all good science lovers we advocate taking a close look from multiple perspectives. Looking at the "Condorcet Winner" is one method, "Bayesian Regret" is another. These methods can be an invaluable addition to the data we can collect from real world elections. One of the most exciting and thorough is "Voter Satisfaction Efficiency" (VSE) which analyzes voting systems using thousands of simulated elections. VSE looks at what can happen under a wide variety of scenarios and factors in variables like strategic voters, voters blocks who cluster on issues, and much more.
Voter Satisfaction Efficiency
Voter Satisfaction Efficiency makes a strong case for STAR Voting. In VSE, STAR out preformed all the other voting systems that are being seriously advocated for, many of them by large margins. The only voting system that was close to on par was a Condorcet Method called Ranked Pairs which had previously set the bar for accuracy but which is too complex to be viable in real world elections.
Here are some of the findings that we can extrapolate from the VSE graphs:
- STAR is among the very best of the best. When voters are honest STAR delivers it's best results with a VSE of over 98%.
- Under less than ideal circumstances, such as elections where a large portion of voters are strategic STAR was still highly accurate with a VSE of over 90%. The worst case scenario STAR Voting was basically just as accurate as the best case for Ranked Choice Voting and much better than Plurality Voting (our current system) under any circumstances.
- Compared to other systems STAR showed a higher resiliency against strategic voters. This means that voter tactics has a smaller impact on overall election accuracy so that even if many people try and game the system we still come out in good shape. The exception was 3-2-1 Voting which was slightly less accurate than STAR and slightly more resilient to strategic voters.
- VSE strategy simulations also showed that STAR doesn't incentivize strategic voting for voters overall. Strategic and dishonest voting is just as likely to backfire as it is to help the individual voter so why bother?
You can learn more about Voter Satisfaction Efficiency here.
Why not just skip the simulations and go straight to real world data?
Real world, empirical election data is a critical source of information, but it can only go so far. Where it comes up short is when ballots are not expressive enough to collect the voters' full opinions, and when we have no way of knowing if the votes cast were honest or dishonest. For example if our current system elected the candidate with the most votes, that is generally considered a fair and accurate election according the the available information, but that still doesn't mean that the candidate with the most support won. The problem is that in some elections if voters could have showed a degree of support for multiple candidates or if voters had not voted strategically for a "lesser evil" a different candidate may have won.
For assessing voting systems with less expressive ballots, pre voting day polling, and exit polls can be a valuable addition to election results and ballot data. In many cases ratings are used in this kind of polling because a rating is able to collect the kind of data needed to asses less expressive ballot data and election results.
Real world data is particularly insightful when we are looking at election results from voting systems that do use more expressive ballots. For example Instant Runoff Voting uses an expressive ballot, but also uses a multi-round, tournament style elimination process which doesn't count all the rankings. When we go back and look at the ballot data again, sometimes we find elections where the candidate who won wasn't actually preferred by the voters... according to the ballots cast.
Condorcet Winner as a Measure of Accuracy
The Condorcet winner is the candidate that was preferred over all others head-to-head. When there is a Condorcet winner there's a good case to be made that that candidate should have won. Unfortunately Condorcet can be limited because there isn't always a single winner that was preferred over all others. Sometimes preferences are cyclical.
A ranked ballot is all that is needed to find the Condorcet winner if one exists, but a score ballot also shows preferences and so will also find the Condorcet Winner if one exists.
There are a few situations where some people may argue that the Condorcet winner didn't actually have the most support. Advocates of Instant Runoff Voting (IRV) often argue this to defend the results of a recent Burlington Vermont IRV election which didn't elect the candidate who was preferred over all others. In order to make that argument convincingly we would need to know more than just voters' preference orders, we would need to know how much each voter liked each candidate.
In ranked ballot systems there's no way to know if a voter actually liked their second choice. Second choice could mean full support if a voter really loves more than one candidate. Conversely a voter's second choice may be a candidate who they strongly dislike, but who is better than their worst case scenario.
In a 2009 Burlington Mayor's race there were three viable candidates, a Democrat, Republican, and a Progressive, and all three had significant support. The Democrat was preferred over all others (the Condorcet Winner) but came in third place after voters first choice votes were counted. The Progressive won.
Many Republican voters had ranked the Democrat as their second choice to show that they preferred the Democrat to the Progressive candidate. If these voters would have actually been significantly more satisfied if the Democrat had won, then the Condorcet winner did deserve to win after all. On the other hand if Republicans would have been almost equally dissatisfied with either the Democrat or the Progressive then the Progressive was probably the candidate with the most support after all. To learn more about Burlington read more from Equal Vote here and more from The Center for Election Science here, and the Center for Range Voting here.
The point is that in these kinds of close three way ties it's critical to have enough ballot data to determine if the candidate who won had the most support or not. For that we need a ballot that allows us to show degree of support as well as vote no preference if desired. In Burlington the ballots clearly showed that the Democrat was preferred over all others and was the Condorcet winner and so he clearly deserved to win according to the ballots cast. Instant Runoff Voting was repealed the following election.
STAR Voting would almost always elect the Condorcet winner, but if it doesn't, there is a convincing case to be made for why another candidate actually had more support and better represented the people.