The biggest problem with the current debate over electoral reform in Canada is that critics of the existing system are making demands that no voting system could ever satisfy.

One of the most common objections to the first-past-the-post system is that it violates the majority-rule principle, by allowing individuals to be elected, and parties to form government, even when they have received less than 50 percent electoral support.

This sounds like a serious defect, until one considers the fact that no electoral system that permits more than two political parties is able to satisfy this principle.

One can see the problem quite easily by considering recall elections — which allow individuals in a riding to fire their elected representative if a majority votes for a change. The obvious objection is that, with three or more political parties in serious contention, as we have in most ridings in Canada, there is no reason to expect that anyone will be supported by more than 50 percent of voters, so people could theoretically keep recalling and re-electing representatives forever.

This realization is what drives a lot of support for so-called ballot reform (such as ranked-ballot arrangements), which allows voters to not just select their top pick but also to rank all the candidates on the ballot. Then, through some complex procedure (people disagree about which one is best), these preferences can be aggregated and a winner chosen.

“Surely,” the advocates of ballot reform will say, “if you look not just at top picks, but at second and third choices as well, you can find a candidate that has majority support.”

Actually, you can’t. (Or, to put it more precisely, there is no guarantee that you can.)

It may be one of the best-kept secrets in democratic societies, but over 200 years ago the Marquis de Condorcet showed that in many circumstances, in an electoral contest with more than three options, not only will there be no majority preference, but there will also be no way to winnow down the choices to produce a stable majority winner. If you pitch all three against one another, obviously there is no guarantee that any one will get more than 50 percent. If you break it down into a set of pair-wise competitions, however, you can get shifting majorities, such that any option can beat any other, depending on how they are paired off.

Nicolas de Condorcet

Consider the structure of a standard hockey tournament. We all know that there is some luck of the draw in the pairing of the teams, because which team you are matched against early on has a significant impact on your chances of advancing. But imagine a tournament in which everything depended upon luck of the draw, where any team could win, depending on the order in which they had to play one another. Condorcet showed that this is precisely what can happen with democratic voting – you can get one option that “wins” majority support, but any other option could have won had the options been paired off against one another in a different order.

Photo: Robert Nyholm/

Now, in a hockey tournament like this, it wouldn’t really make sense to ask, “which is the best team?” So it is with democratic voting, it simply does not make sense to ask, “what is the will of the majority?” because there often is no majority will — either there are too many options for the majority to favour just one, and if you winnow them down, then the majority preference changes, depending on how the options are presented.

Some people don’t like to be reminded of this result, because it seems to be rather nihilistic, or subversive of the authority of democratic institutions. Yet we have known about this problem with majority decision-making for more than two centuries, and it has not stopped us from developing successful, flourishing democratic societies.

What matters is how the result is interpreted. The correct way to understand Condorcet’s voting paradox, in my view, is that it shows us that every democratic electoral system is going to have an element of arbitrariness in it. Since the legislative process is based on the majority principle, every democratic system will need to do something more than just add up votes, in order to constitute the majority that will make legislative decisions.

This is why the mediating institutions of democracy are so important, and why we will never live in any sort of deep, decentralized democracy, or a techno-utopian “e-democracy,” where the people get to decide directly all major policy questions. Because majority will is often non-existent or indeterminate, we need to do something artificial, in order to create ruling majorities. Thus democratic institutions always include seemingly arbitrary rules, which introduce undemocratic values (such as a concern for “stability”) into the proceedings.

The first-past-the-post voting system illustrates this in a very straightforward way. Since there will often be no majority winner at the riding level, the system instead awards victory to the individual who gets the most votes. The net consequence of doing this in each riding is that it usually results in one party gaining a legislative majority. This may seem like an “artificial” majority, until we stop to consider the fact that, in many circumstances, any majority will be artificial.

We can imagine this element of arbitrariness as something like a bump under the carpet, a bump that can be moved around, but not eliminated. This is in fact that the major lesson learned from formal voting theory over the past few decades. One glance at this literature and it is easy to see that it gets complicated very quickly, with people developing increasingly arcane systems. And yet we know from first principles that each one of these systems is going to have a flaw, or contain an element of arbitrariness. The bump under the carpet can be moved around, but it cannot be eliminated.

One response to this situation is to drop the preference for elections that yield majority governments. This is, in effect, what proponents of proportional representation have been advocating. They take issue not so much with the fact that individuals can be elected with less than 50 percent support but with the fact that a party can win the majority of seats in the legislature with less than 50 percent support. In their view, parliamentary seats should be allocated based strictly on vote share.

The question one should ask, when considering proposals such as this, is “where does it move the bump?” The answer is that it moves it into the legislature — because after all, even if there is no majority government, a majority of votes in the House of Commons is still required to pass legislation. And since the majority will is often non-existent there, something arbitrary is going to have to happen, in order to get legislation passed.

Thus, the best that can be said for proportional representation is that it moves the bump somewhere closer to out of sight. Rather than having a voting system that reliably delivers majority governments it will be left to politicians in the legislature to put together a majority, using whatever backroom horse-trading and negotiation tactics they can come up with. We can rest assured that there will be an enormous amount of arbitrariness in this as well.

Photo: Monkey Business Images /

This article is part of the Electoral Reform special feature.


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Joseph Heath
Joseph Heath is a professor in the Department of Philosophy and the School of Public Policy and Governance at the University of Toronto. He is the author of several books, including début italiqueMorality, Competition and the Firm, and Enlightenment 2.0 début italique, which won the Shaughnessy Cohen Prize for Political Writing in 2015.

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