What makes a voting method good?

What makes a voting method good?

Sep 30, 2018

If you’ve spent much time at The Center for Election Science website, then you probably know what a voting method is. A voting method is the method that voters use to put information on their ballots and how that information is calculated. Right now, the main voting method we use has us choose one candidate, and the candidate with the most votes wins. This is called plurality voting or first-past-the-post. But because those terms are weird and hard to remember, this essay will just call that approach our current choose-one voting method.

 

There are also many other approaches besides the current choose-one voting method. Other methods can have us score, rank, and even approve multiple candidates. That information can then be used in different ways like to calculate average support, simulate sequential runoffs, translate rankings to point values, or run pairwise comparisons between candidates like a round-robin tournament.

 

So given all the possible voting methods with their infinite iterations, how do we know whether a particular one is any good?

 

Here are some guidelines.


 

 

The Winner: Make It A Good One

 

So what’s a good winner? One reasonable definition is electing the candidate who maximizes the electorate’s expected utility—that is, how happy voters are with the winner, on average. You can measure this directly in polls by asking respondents to use an honest assessment scale (basically a Likert scale that has respondents indicate how much they would like to see each specific candidate elected). Then you can take responses from this scale and average them. The distributions from this scale can also be interesting. Some candidates can be outright popular, some being divisive (love them or hate them), some attracting general support in addition to extreme support or opposition, and others just not being popular at all.

 

If you’re short on real-world election data, you might try using computer simulations to evaluate a voting method. Those simulations can generate millions of elections. These elections can have different dynamics—such as tactical voting prevalence and candidate number—to see what kinds of winners a voting method chooses. We can see what the results look like on average and the variability among those winners. Variability can be important because if a voting method fails to elect a good winner in certain conditions, it would be better if it didn’t fail catastrophically.

 

These high-utility winners can be described as consensus candidates who appeal to the largest breadth of voters. These winners hold appeal for the bulk of voters while not marginalizing large electorate segments. That’s a good winner.

 

A candidate who generates the highest utility for voters is always present (keeping in mind that the outcome is still limited by who actually runs and votes). If there’s a tie, then it doesn’t matter which candidate a voting method selects.

 

But there are some other ways for determining the best winner. Unfortunately, however, these other winner types don’t always exist.

 

A good winner might also be someone who is preferred to all other candidates by more than half the voters—called an absolute majority winner. This tends to coincide with the utility winner as well. Like I warned though, the catch is that this “majority winner” may not always exist. Note also that runoffs only artificially create majority winners. Runoffs accomplish this “majority” by eliminating candidates, a process that sometimes eliminates the best candidate. If a runoff is necessary—simulated through rankings or otherwise—then you don’t have a real majority winner.

 

Another example of a good winner is a Condorcet winner. This is a winner who can beat every other candidate head-to-head. Imagine a round-robin tournament with an undefeated winner. That’s the idea. Like a majority winner, this Condorcet winner doesn’t always exist. Condorcet winners (when they exist) also tend to be the high-utility winner as well.

 

Keep in mind that practically any voting method can pick a good winner in easy situations. For instance, if there’s a clear winner with more than fifty percent of the vote, any voting method is likely to get the winner right—including our current choose-one voting method. What we’re really interested in is a voting method that does the job in complex situations. We’re talking about 4-to-5-way races or elections with similar candidates who could potentially split their vote.

 

If you’re celebrating a voting method’s performance in blowout elections, then you’ve set your bar too low. Elections don’t always play out in easy mode. It’s also important to note that if the election is close and with multiple candidates—say under the current choose-one method—then you may not even know who the best candidate was. That’s because that voting method doesn’t capture the information you need to see whether the winner was a high utility or Condorcet winner.

 

So, we obviously want to make sure the voting method picks a good winner, like the examples above. If a voting method fails at this—particularly if it does so badly—then it’s not worth considering. After all, selecting a good winner is a voting method’s core job. But there’s more to look at in practice than whether a voting method is good at electing a strong candidate. That’s particularly true if you’re looking at multiple voting methods that perform well in the winner-selection area.


 

Minimizing Complexity: Keep It Simple, Stupid (If You Can)

 

A voting method should be as simple as possible. If two methods produce similar results, then the simpler one is likely the better path.

 

There are different ways to measure complexity. One is how easy it is to explain how the voting method works. Do people understand not just how to fill out the ballot but also how the voting method calculates that information? Or, at the very least, do people understand the general concept for how the voting method works? Could you get an average grade schooler to explain it back to you, or would it take a high schooler?

 

(If you have a computer science background, another metric you might consider would be how many lines of code it would take to execute the voting method’s algorithm.)

 

The way a voting method calculates voter data comprises most of its complexity. That’s particularly true with multi-winner proportional methods. There, voting methods tend to use complicated reweighting and partial ballot transfer schemes. While some of these calculations are easier than others, this complexity is often just a price we pay for good proportional methods.

 

Ballot complexity can directly interact with the voting method and the number of candidates running. For instance, ranking candidates can be mentally demanding when you have a candidate list of, say, 10-20 candidates. You could sometimes see ten candidates in a highly competitive election with only one winner. But for a multi-winner election with five or more winners (like a city council), a voter could easily see dozens of candidates. At that point, ranking becomes impractical and an alternative like proportional approval voting (this lets you select candidates rather than rank them) becomes more appealing.

 

Ballot complexity can also present itself through ballots that are filled out incorrectly, called spoiled ballots. Ranking methods in particular tend to have more spoiled ballots, for instance, and can be an indicator of voter confusion. There, voters may improperly give some candidates the same ranking or another mistake causing the ballot not to count.

 

One complexity factor will be the electorate itself. Has the electorate experienced other voting methods before? Has it been educated on the method in question? Does it understand how the calculation works? If the calculation method is complex, is there at least trust that the method is fair or that a trusted third party organization can verify the results?

 

 


 

Gauging Candidate Support & Encouraging Competition: Let’s Get It On!

 

A voting method should act as a temperature gauge for all the candidates, not just the winner. For the voting method to succeed here, the following factors need to be fulfilled:

(1) voters must have some degree of expressiveness on their ballot,

(2) voters must be encouraged to honestly express key information on their ballot without fearing tactical blowback, and

(3) the voting method must actually use all the information that voters provide.

 

If a voting method fails on these three factors, then it will do a bad job at gauging candidate support. And that causes all kinds of problems, like missing out when novel candidates have good ideas.

 

Factor one: expressiveness. If a voting method doesn’t allow the voters to express any information, then you don’t even have a starting point. Forcing voters to choose only one candidate, for example, is the least information a voter can provide. Unsurprisingly, this doesn’t provide sufficient information to assess all the candidates. That’s because the voter was never given a real opportunity to say anything about the candidates to begin with.

 

An exception to the expression element could be a list-based proportional method. There, a voter would choose a party and that party would get seats in proportion to their vote. Because list-based systems do so well on the other two factors (tactical voting and using all the ballot information), they also do a good job overall in gauging support for alternative candidates.

 

This isn’t the case, however, for the traditional choose-one voting method we see in single-winner elections. That method unambiguously fails all the factors, which is why it so abysmally gauges support for candidates in its elections.

 

Factor two: tactical voting. Tactical voting is when voters purposefully put down inaccurate information on their ballot to maximize their ballot’s likelihood of having a personally favorable impact on the outcome. Tactical voting is an unavoidable aspect of voting methods. There’s even a proof called the Gibbard–Satterthwaite theorem that explicitly proves this susceptibility for any voting method. But even if we can’t eliminate tactical voting, we’d still like to minimize it. After all, if too much tactical voting is present, we—by definition—get bad information.

 

Continuing to tear down the current choose-one voting method, it’s extremely vulnerable to tactical voting. There, if your favorite candidate is unlikely to win, then you may not vote for them. Instead, you may choose exclusively among the front-runners—whom you may not even like. This favorite betrayal issue particularly hurts new candidates who may not be considered viable—even when they have good ideas. This problem means that under our choose-one method not all candidates get a fair shake, and they don’t get a reasonable opportunity to grow.

 

Factor three: using the information. Just because a voting method takes in ballot information from the voter doesn’t necessarily mean that information is actually used. For instance, instant runoff voting, a ranking method, only uses first choice preferences at any one point and only counts next-choice preferences if the candidate being ranked is eliminated for having the fewest first-choice preferences. If the next-preferred candidate on a ballot has already been eliminated, then support for that candidate doesn’t appear on any tally. And if a candidate isn’t eliminated, then the support for the other ranked candidates on that ballot also don’t appear on any tally. This means the support for other candidates can go unmeasured and remain invisible.

 

Some of these voting method dynamics like inexpressiveness or haphazard ballot data use can cause a voting method to be susceptible to vote splitting. Vote splitting means that support divides between similar candidates so that candidates are shown with less support than they actually have. Some methods—again, like our current choose-one voting method—are quite sensitive to this. In fact, vote splitting can cause candidates not to run for fear of being labeled a “spoiler”. This was actually Michael Bloomberg’s rationale for why he didn’t run in the 2016 US Presidential election.

 

Here we see that how candidate support is gauged can affect how candidates are perceived. It can even determine whether certain candidates run. And the last thing we want to do is create a barrier to entry for candidates that is too high. In democracy, competition is good, and a good voting method should encourage it.


 

 

Administration: Somebody’s Gotta Do It

 

For whatever reason, the software behind voting machines in many states is inadequate. This means more complicated voting methods require new software and new machines. If modern software isn’t an option, then you’ll have to stick with a simpler system. Some cities experience years’ long delays implementing alternative voting methods due to not having proper software. At a certain point, however, those delays become inexcusable. As an aside, any voting method can and should have a paper record even if software is used.

 

If hand counts are preferred, then a voting method’s complexity will become an issue. That’s particularly true for a voting method that requires ballot transfers over rounds. This kind of complicated voting method is certainly not impossible to run by hand, but the labor involved is significantly more compared to other methods.

 

If a voting method’s administration requires tallies at the local precinct level rather than a central location, then this can also create problems. Not all voting methods are precinct summable due to how votes are tallied. Instant runoff voting, for instance, requires all votes be tallied in a central location since it requires ballot transfers.

 

Other methods may technically be precinct summable but require more labor. For instance, STAR voting uses scores with a single runoff between the two candidates with the highest scores. This means that to get precinct summable tallies, administrators must compile both scores and pairwise comparison tallies between all candidates (translated from scores). And this must done in every precinct. While possible, this may be a tall order for some areas where the administration has limited sophistication with alternative voting methods.

 

As shown in San Francisco elections, some voting methods can take a long time to calculate in practice. Instant runoff voting, for example, has proven itself to be just such a method that can result in delays over multiple days or more. Those delays can be problematic for an impatient electorate.

 

Risk-limiting audits should really be the standard for elections to ensure their integrity. But they aren’t. Risk-limiting audits use statistical sampling techniques to determine whether to do a recount. If these audits were the norm, then different forms of data such as that found in ranking methods could create complications. This becomes particularly challenging with instant runoff voting. That’s because the multiple rounds create additional opportunities for different outcomes. The situation is even worse in instant runoff voting elections where which candidate is eliminated in each round is close.

 

Ideally, we’d like to think we can just throw software at the problem. But in the real world, this doesn’t always work out.

 

 


 

Representation: Come Get Ya Some

 

In executive offices like mayor or governor, representation is more straightforward. In other conditions, this can be more complicated. For instance, if you have a legislative body or council, then you may wish to have that body be more diverse. One way to deal with that is to use a multi-winner proportional voting method. That is, you’re electing multiple candidates simultaneously. The voting method then elects candidates in proportion to the number of people that supported them. For example, if one segment of candidates’ ideology has 20% of the electorate's support, then the candidates representing that ideology would get about 20% of the seats. That’s what proportional means here.

 

Electing councils or legislative bodies only makes up a portion of situations, but it shouldn’t be ignored. Ignoring these types of elections can inadvertently have us exclude key groups. For instance, using a bloc-style method (ex// choosing as many candidates as there are seats to be filled) can exclude entire segments of the electorate. Additionally, ignoring how multi-person bodies are elected opens us up to gerrymandering. Here, we could (and currently do) blunder the situation by splitting legislative bodies into single-member districts.

 

When we’re thinking about these types of multi-winner elections, we’ll also want to consider how proportional we want the outcome. We can get high proportionality if we elect lots of people (say a 50-100 person legislature) at once. If we think that proportionality is too high and creates parties that are too small, then we can always artificially raise the threshold for electing candidates (say 2-5%).

 

When using district-based proportional voting methods, we want to consider how many people are elected at once. If too few people are simultaneously elected (say 3-4), it could be too hard for sizeable parts of the community to be heard. That’s because electing too few people simultaneously sets the threshold for election too high.

 

The idea here is that if we want a legislative part of our government to cover broad ideas, then we need to have a voting method that elects a diverse enough body that can actually generate those broad ideas. That kind of diversity goal is fundamentally different than the goal with single-winner elections since there what a “best” candidate looks like is relatively more straightforward. Still, of course, we need to make sure a multi-winner voting method doesn’t give any group more than their fair share of seats.

 

 

 

Some Things Just Don’t Matter

 

A voting method isn’t good or successful merely because it’s been around a long time. For instance, we don’t give bloodletting extra props because it was used for almost two millennia. Keep in mind that sound ideas that we take for granted today—like randomized controlled trials in science—were slow to catch on.

 

Saying that an election completed “without a “hitch” is also poor evidence. In uncompetitive scenarios with only two candidates which voting method was used won’t matter. (Sadly, this uncompetitiveness describes most US elections.) What does matter is how a voting method performs under tighter elections with many candidates and whether the voting method encourages that competition to begin with.

 

In the end, a voting method must be good at electing good winners when electing executive offices, and it must provide fair representation to multi-person governing bodies. But it must also consider practical elements like the sophistication of software, administrators, and the electorate itself. Finally, a good voting method must accurately gauge candidate support so that it can foster the type of competition currently devoid in our elections.

 

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