As it is election season, there is a resurgence of interest in voting systems and their relative fairness. Snazzy animated videos demonstrating behaviors, explanations that call out to Arrow’s Impossibility Theorem, etc.
I want to zoom out a bit and show that voting systems themselves are not a panacea, and also that one’s opinions of voting systems are probably formed by views on certain underlying principles.
First, a voting system is simply an attempt to measure the preferences of a population. It makes no guarantee that the population is fully educated, free of ignorance, or even fully decided. Just as how we can ask one person to make an arbitrary decision before they are ready, we can also ask the same of an electorate.
We then use that measurement to make a decision or choice. In other words, it is not the responsibility of a voting system to arrive at a solid best choice for the electorate. The voting system merely measures the electorate’s preference, as solid or vague or undecided as it might be, at that moment in time. In this sense, all voting systems that seek to declare a final winner are by definition imperfect.
As for which voting system is best, I believe it is important to surface a few assumptions that are often glossed over. These have to do with the very definitions of democracy and fairness, and how they can be expressed through preference measurement. People have different opinions of these definitions, and that is what tends to drive enthusiasm for different voting systems.
For simplicity’s sake, I will boil this down to two questions about single-winner elections:
- If one candidate would defeat all other candidates head-to-head, should that candidate always win?
- If, in a two-candidate election, candidate A has more votes than candidate B, but candidate B’s supporters are much more enthusiastic, should candidate A always win?
For brevity, I will call them the Condorcet criterion, and the Majority criterion respectively. (There are similar names for these criteria in the literature.)
For each question, the answer can be “Yes” or “Not necessarily”, which we’ll define as “No”.
As you can see, this conveniently lays out into a 2x2 grid. Let’s look at each of the quadrants in turn.
- If you believe in both the Condorcet and the Majority criteria, then it implies you would be in favor of voting systems that respect these criteria, and opposed to those that don’t. In general this means you would only support methods that respect the Condorcet Winner Criterion, which tabulate votes in a pairwise fashion.
- Interestingly, it is impossible to be for the Condorcet Criterion and against the Majority Criterion. If you believe in incorporating enthusiasm, it is impossible to guarantee the Condorcet Criterion — they are fundamentally incompatible.
- If you believe in the Majority Criterion but don’t believe in the Condorcet Criterion, then you are likely in support of methods like Instant Runoff Voting. Plurality/First-Past-The-Post voting also fits here.
- If you don’t believe in either, but do believe enthusiasm should be taken into account, then you are likely in favor of various “social utility” voting methods like Range Voting, Score Voting, or Borda.
Most conversations and debates about voting systems go straight towards the merits, demerits, and workings of the voting systems themselves. This glosses over the basic principles defined above. What does it mean to measure preference, at what level do we need to respect the democratic norms of majority decisions?
In an American democracy anyway, these definitions are somewhat axiomatic — the “one person, one vote” phrase has been used in Supreme Court decisions such as Reynolds v. Sims and several follow-up cases. Ranked voting methods such as IRV have been challenged as being incompatible with this doctrine, such as in Ann Arbor Michigan in 1975, but were later decided to be compatible. Range voting methods are more problematic, as enthusiasm is a fuzzy term that can be argued to weigh some ballots/voters more heavily than others. So relaxing the Majority Criterion is problematic. Plus, it is safe to say that the practice of deferring to a louder minority has historically been problematic.
As for relaxing the Condorcet Criterion in favor of just the Majority Criterion, I have not yet found strong arguments for this. The closest example I could find was Fairvote’s Argument against the Condorcet Criterion. The article describes a case in Burlington Vermont where three major candidates — a Progressive, a Republican, and a Democrat — all had wide support. In this election, the Democrat was clearly the Condorcet Winner, defeating all other candidates head-to-head. Under IRV, the Democrat was eliminated early, and the Progressive ended up winning. Fairvote actually uses this case as an example of how IRV is superior to Condorcet. They offer no systematic justification as to why, other than to say that sometimes we may not want the moderate or consensus candidate, and that the Condorcet Winner may not actually be “ready to represent the constituents”. In general, this argument against Condorcet is poorly reasoned.
It’s worth coming back to the idea of the purpose of a voting system. As argued above, the purpose of a voting system is not to come to a final decision — it is to represent an electorate’s preferences. It is usually a law or a policy that then uses the outcome of that voting system to come to a decision.
In that sense, the Condorcet criterion has one additional strength — it can actually represent the times when the electorate is legitimately conflicted or unable to express a clear preference.
This is because a Condorcet vote can yield a rare cycle, where, for example, a majority can prefer A to B, B to C, and C to A.
Unfortunately, this is often described as a flaw with Condorcet methods. Since people tend to conflate the need to “represent a preference” with the need to “pick a winner”, they will often bundle in various “tie-breaking” methods to guarantee that a Condorcet method will always pick a winner. Since these tie-breaking methods are by definition always imperfect, people often then argue that all Condorcet methods are flawed. This view does a huge disservice to the strengths of the Condorcet method.
A better alternative is to consider what it means when the rare cycle is discovered. In these cases, the population has considered a wide selection of candidates, and has identified a smaller or equal set of candidates, from which they cannot clearly express one preference.
This is valuable knowledge. It could indicate a need for additional time to research the candidates, or more transparency from the candidates. It could warrant another debate or another form of exchanging views. It could even justify sending the final set of candidates on to a smaller group of panelists or representative elected officials, who would in turn use their deeper experience to make the final decision.
We already have systems in the US government for these sorts of eventualities. In Louisiana, voters have a chance to elect a majority winner, and if no majority is reached, they hold a runoff — giving voters more time to consider among a smaller set of candidates. In our federal election system, if no Presidential candidate gets 270 Electoral Votes, the election is sent to the House of Representatives to consider the top three candidates as measured by Electoral Votes received.
In Condorcet Methods, the existence of a cycle is valuable information. It indicates a real uncertainty in the population that should be properly addressed. For that reason, it may well be improper to select a single winner at that point, and it is inappropriate to use the cycle as a reason to declare the Condorcet criteria flawed.
The subject of voting systems is challenging because it by definition conflates the very different needs of
- Encouraging an electorate to come to a preference
- Measuring that preference
- Arriving at a decision in accordance with that preference
Before we can have well-thought-out opinions on favorite voting systems, we have to first consider our own views on what it means to be democratic, by considering our answers for the Condorcet and Majority criteria. We also need to consider the best methods for encouraging an informed, decisive electorate, and what we should actually do when that process occasionally fails. Only through answering those questions can we arrive at a healthy solution for the fostering of a society’s self-determination.
