As one of his first policy proposals, Prime Minister Justin Trudeau pledged to replace Canada’s first-past-the-post electoral system with a system that “[better] reflects and represents” Canadians and makes “every vote count.”

Underlying Trudeau’s claim—that first-past-the-post results in electoral outcomes that are in some fundamental sense “unfair” or “undemocratic”—is the undeniable fact that under the current winner-take-all system, representation in Parliament is only weakly related to popular vote. With just under 40 per cent of the popular vote in the most recent election, Trudeau’s Liberals won 55 per cent of seats in the House of Commons. In contrast, the Green Party won three per cent of the popular vote but only a single seat, or 0.3 per cent of the House.

Before rushing to replace first-past-the-post with some other system (perhaps European-style proportional representation), Trudeau and his advisors should spend some time pondering the classics of social choice theory, the branch of economic theory that analyzes the properties of various social decision rules (for instance, different voting systems).

The most central insight of social choice theory is Arrow’s Impossibility Theorem, named for Kenneth Arrow, the Nobel Prize-winning economist who is widely recognized as the founder of social choice theory. The basic question that Arrow set out to answer was whether it’s theoretically possible to construct a social decision rule (i.e. voting system) that aggregates individual preferences into a rational social preference ordering that satisfies certain unobjectionable criteria. Arrow’s conclusion, as the name of the theorem would indicate, is that it’s impossible; there is no social decision rule that aggregates individual preferences into well-behaved social preferences that does not involve making one individual a dictator.

The political scientist William Riker argued that Arrow’s theorem implies that democracy, conceived as an expression of the “will of the people,” is an incoherent illusion. For Arrow’s Theorem refutes the notion that the will of the people can be discovered through any voting mechanism without the outcome being either irrational or dictatorial. Stated differently, since there is no voting system that will generate a well-behaved social preference ordering without making one person a dictator, the notion that replacing first-past-the-post with any other electoral system will somehow allow our democracy to “better reflect and represent Canadians” makes little sense.

Accordingly, if other voting systems are compared to first-past-the-post, they should not be evaluated in terms of whether they result in a better reflection and representation of preferences of Canadians, but instead, in terms of other properties, for instance, whether they produce stable governments. In this respect, first-past-the-post does unusually well relative to other systems (for instance, proportional representation). Given the long history of at least three parties in Canadian national politics, Canada would have had far fewer majority governments under a proportional representation system than under first-past-the-post.

On this note, Trudeau’s desire to ditch first-past-the-post is especially bizarre. After all, the Liberal Party would not have just won a majority government if the last election were conducted under a proportional representation system. As retired UBC political scientist Kenneth Carty observes, big tent political parties like the Liberals are particularly well-served by first-past-the-post.

One wonders if political self-interest will eventually trump Trudeau’s desire for electoral reform.