Did Monsef actually read the report?

In t he stormy Thursday press conference in which mealy- mouthed Democratic Institutions Minister Maryam Monsef somehow managed to unify election reform opponents and supporters in a grand coalition against her, she at one point held up a sign with an intimidating mathematical expression on it. I think “intimidating” is a fair description. I am reasonably sure that no full- time journalist in the country knows more math than I do, but I still get a touch of nausea at the sight of a Greek letter sigma in an equation.

Despite having an undergraduate degree in science, Monsef complained that the equation she was waving around was “an incomprehensible formula” that her electoral reform committee was trying to foist on the public as a new ultimate basis for Canadian government. The Liberal committee members themselves accused their colleagues of “recommending that Canada’s electoral system be determined by the ... formula.”

You may have two questions about this scary assertion. Is it true? ( Hint: no.) And what does the formula mean?

One of the goals a lot of people have for election reform is to make House of Commons representation “more proportional” to vote totals when it comes to party affiliation. We all have different ideas about how important this feature should be. Some of us feel strongly that MPs ought to be elected as individuals, and the wishes of voters in the riding next door, or in another time zone, should not matter. But most citizens and experts who talked to the committee thought overall proportionality was a highly desirable feature of an electoral system.

And yet ... after all, the current system usually leads to mostly- sorta- kinda proportional outcomes. Regionally strong parties are sometimes overrepresented in the House, and a party might occasionally win a national election with slightly fewer votes than another, but there is usually a loose connection between the nationwide party support and the seat outcome. Moreover, alternative systems differ in their relative emphasis on proportionality.

What we need is some way of scoring systems for how proportional they are. If we care about proportionality at all, we cannot do without such a method.

This is where the dreaded “Gallagher index,” the formula on Monsef ’s placard, comes i n. The Gallagher index does not assign proportionality scores to electoral systems. What it does is to score election OUTCOMES for proportionality. You can plug our 2015 election into the formula yourself: you just need the vote shares and the resulting seat counts for every party. Since the Liberals got 54 per cent of the seats with just 39 per cent of the vote, and t he Bloc Quebecois won 10 times as many seats as the Greens with only 36 per cent more votes, this election does not score too “well”: it’s a 12.

That is a typical score for a Canadian federal election. A higher score indicates a less proportional outcome: our regionally fraught 1993 election was a 17.6, and the 1984 Tory landslide hit 20.9, but sometimes we dip into single digits. U. K. elections, structured like ours but with added international and interregional lumpiness, typically score from 13 to 18. Elections to the U. S. House of Representatives, quite proportional by conscious design, have Gallagher scores ranging from 2 to 5. Scores for Israel’s Knesset, often cited as an exemplar of strict proportionality, hung around 2 in the 1980s; they are rising as Israeli election law cuts out smaller, zanier parties by means of increasing minimum thresholds for Knesset representation.

There are alternatives to the Gallagher index, but they all score proportionality in about the same way. The index’s key feature is that it implements the “least squares” approach to j udging the agreement of two sets of numbers, where one set is a guess, an ideal, or a prediction from theory, and the other set is what is actually observed. The method of least squares is ubiquitous in all sciences, from the ultrahard to the positively gooey.

The point that the Gal- lagher index does not score electoral systems, as such, is important. The House electoral committee recommended that whatever system the Liberals put to a referendum should be one which is likely to yield low Gallagher-score outcomes — which is just another way of saying “more proportionality.” Knowing which systems will do that requires extra inference, and, indeed, guesswork. The likely Gallagher-qualities of various systems were discussed in a document that the committee issued in November, without inducing a public flipout from Monsef.

But this committee’s use of the Gallagher formula does not mean that it is sayi ng the electoral system should be based entirely on one calculation. Its report says exactly the opposite. The committee merely set out an upper bound for desirable Gallagher scores; within the defined range, it did not specify that lower scores are better. Moreover, the committee observed specifically that the lowest possible Gallagher scores would be generated by a system of pure party lists — and it then categorically rejected such a system, because it would fracture the voter- to- MP relationship that is a more important feature of our politics. Maybe the minister just missed that part of the report.

THIS IS WHERE THE DREADED ‘GALLAGHER INDEX’ COMES IN.