The problem with Maryam Monsef’s contempt for metrics

Monsef’s ‘math is hard’ moment is an odd position for a cabinet minister in a proud science-friendly, evidence-based party to be taking

Maryam Monsef Minister of Democratic Institutions stands in the House of Commons during question period on Parliament Hill, in Ottawa, Thursday, December 1, 2016. THE CANADIAN PRESS/Fred Chartrand

Maryam Monsef Minister of Democratic Institutions stands in the House of Commons during question period on Parliament Hill, in Ottawa, Thursday, December 1, 2016. THE CANADIAN PRESS/Fred Chartrand

On Thursday, Dece. 1, Minister of Democratic Institutions Maryam Monsef addressed the House of Commons to comment on the Special Committee on Electoral Reform’s long-awaited report. Alas, if the committee members expected Monsef to show appreciation—or even recognition—for the culmination of six months of work, they were to be disappointed. “[The committee] did not complete the hard work we had expected them to,” Monsef lamented, drawing boos from the House. She expressed dismay that the report’s authors had failed to provide “a specific alternative system to first past the post”—despite that not being part of the committee’s mandate—and that Canadians were being asked to “choose our own adventure”. And while the report spanned a formidable 348 pages, Monsef devoted nearly half her remarks to a mathematical formula on page 323 called the Gallagher Index, which measures how closely the composition of a government matches the proportion of votes received by each party: “Would Canadians like to take the square root of the sum of the squares of the difference between the percentage of the seats for each party and the percentage of the votes cast?” she asked. Her answer was implied.

MORE: Maryam Monsef’s change in parliamentary tone

Monsef has since walked back some of her remarks, saying that when she said that the committee had not completed the hard work they were expected to, she in no way meant to imply that the committee members had not worked hard. She did not, however, apologize for dismissing the committee’s use of mathematics to compare systems of counting votes. A year and a half ago, the late Jim Prentice, then the premier of Alberta, lost a provincial election to Rachel Notley for sneering, “I know math is hard”. Last week, the youngest female member of Justin Trudeau’s gender-balanced cabinet delivered the same message to the entire country. (Notley’s math, by the way, was correct; Prentice’s was wrong.)

Monsef’s comments on the Gallagher Index – as well as the commentary surrounding them—are telling. Against House rules, Monsef displayed an enlarged printout of the formula to drive home her contempt for its inclusion in the report: what sort of nerd understands that? Seasoned political reporters uncritically described the index as “complicated”. It’s actually simple enough to explain on Twitter, as I did on Thursday night. I can do it again now, with room to spare: for each political party, subtract the percentage of votes received by that party from the percentage of seats it has in the house. Then take the squares of each of those numbers, add up the results, divide the whole thing by two, and take the square root of all that. That’s the Gallagher Index. The reader might have to grab a pen and paper in order to get the full effect; but certainly, this is an easier concept to grasp than any of, say, health care policy, transportation, or environmental regulations, each of which Canadians vote on all the time.

RELATED: The circular logic and mixed messages on electoral reform

But what does it mean? The report explains that as well. “Perfectly proportional” elections—ones where each party receives the same percentage of seats as votes—have Gallagher Indices of zero. The less representative a system of government, the higher the Gallagher Index, to a maximum of 100. The Special Committee on Electoral Reform recommends that Canada adopt a voting system that will give scores of five or less on the Gallagher Index, a position supported by organizations such as Fair Vote Canada and Leadnow.* For comparison, the 2015 federal election gave a score of just under 12.

Of course, proportionality, as measured by the Gallagher Index, is not the only consideration in selecting a voting system; for instance, regional representation can’t be ignored in a country as large as Canada. To their credit, the committee members recognize this. But while Monsef has been upfront about not favouring proportional representation, her beef with the Gallagher Index isn’t that it only measures proportionality. Her beef with the Gallagher Index is that it’s math, with its sums of squares and square roots and symbols that are literally Greek. This is, to be sure, an odd position for a cabinet minister in a proud science-friendly, evidence-based party to be taking.

It is also a troubling one. Asked repeatedly how the government intends to actually select a new voting system, Monsef offered only vague comments about “enhancing the culture of engagement”. “Engagement” has been a major theme in Monsef’s short tenure. It is also a quality that is notoriously difficult to measure. Perhaps that is a feature rather than a bug: at the intersection of “affinity for engagement” and “contempt for metrics” is fertile breeding ground for leaders who wish to make up their own rules. “I have not yet heard a consensus around one system or another,” wrote Monsef at the end of a summer of engagement, as though she hadn’t anticipated that twenty-five million registered voters would fail to come to an agreement on the subject. Monsef is committed to finding the “best” electoral system to replace first past the post, but she has rejected every systematic method of determining what’s best. The Minister who slammed a committee for inviting Canadians to “choose our own adventure” has been taking us on an adventure whose itinerary she seems to be making up on the fly; it will end when she’s ready, and not a moment before.

Perhaps it was inevitable, then, that we would find ourselves drifting toward the conclusion Monsef had worked so hard to avoid: a referendum on electoral reform. At least that method of determining the best system is simple: you hold a vote, you count the ballots, and the option with the most votes wins. Technically, counting is math, but at least it’s easy math; not a Greek letter or a square root in sight. Surely, even a bunch of Canadians can manage that.


Brenda Fine is a math instructor at the British Columbia Institute of Technology. She can be reached on Twitter at @moebius_strip

* Correction: An earlier version of this article stated that Fair Vote Canada and Leadnow favour a purely proportional system with a score of zero. That is not the case.






The problem with Maryam Monsef’s contempt for metrics

  1. True proportional representation is of every social group. The UK GMC Single Transferable Vote elections proportionally represent women, immigrants and specialists. No parties in sight! A (party) proportionality index is merely a symptom of that partisan monomania that has devoured the electoral reform debate, to the exclusion of other considerations.
    Any such index, like the Gallagher index, does not measure the proportionality of an electoral system. The same proportional electoral system is more proportional, the more seats in the multi-member constituency. The Single Transferable Vote is more proportional in Northern Ireland than in the Republic of Ireland, merely because the Republic uses 3 to 5 members per constituency, whereas Ulster uses six members per constituency.
    The BC Citizens Assembly, which recommended STV, had a man and woman from every riding, rural and urban. They compromised on the number of seats per district. The vastest wilderness was conceded a minimum of two members. The densest city district was entitled to 7 members. The average constituency worked-out at four or five members.
    Google: ERRE>Work>Electoral Reform>Briefs) namely, BC Citizens Assembly on Electoral Reform (September 23).
    Richard Lung.
    Website: Democracy Science; with links to 3 free e-books on election method: Peace-making Power-sharing; Scientific Method of Elections; Science is Ethics as Electics.

  2. There is one misleading statement in this report “A purely proportional system, the kind favoured by organizations such as Fair Vote Canada and Leadnow, would give scores very close to zero”. This is not true. No electoral reformer recommends pure proportionality – it brings its own set of problems.

    FVC has already said that they agree with the recommendations of the #ERRE report. A GI of 5 or less is great.

  3. “At least that method of determining the best system is simple: you hold a vote, you count the ballots, and the option with the most votes wins. Technically, counting is math, but at least it’s easy math; not a Greek letter or a square root in sight.”

    Counting ballots? That sounds like summation to me. Careful, that kind of talk around here will earn you a scary Greek letter: https://en.wikipedia.org/wiki/Summation

  4. Whoa!
    What a putdown.
    Two questions.
    Math aside, why did Justin put out that lamb to be slaughtered?
    Who wrote her script?

  5. One man, one vote. Our leader seems to be going around the world learning from different dictators on how to stay in power forever, rewarding them with our tax dollars. From Africa to Cuba, he is learning.

  6. Minister Monsef even missed the “take half” part in her description of the Gallagher Index! Our governance suffers when voters, journalists and politicians don’t understand statistics. The government’s committee recommended the government select a PR system with a Gallagher Index of 5 or less. That appears to be for the purpose of eliminating Single Transferable Vote (STV, which would be higher than 5 with the acceptable 3 to 5 seats per district) and for eliminating any watered-down version of Mixed Member Proportional (MMP, which would be greater than 5 if too few seats were used for the regional seats). In simple terms, they recommended a fairly highly proportional system for Canada.

    • @Maxwell Anderson. Agreed. Based on Elizabeth May’s comments in the post-QP scrum, the report’s recommendations, including the usage of the Gallagher Index, were meant to whittle the government’s choices of alternatives to about two or three, which, given the two versions or PR that were purposed by the Green/NDP’s supplemental report, would certainly include an open list MMP. That being said, I’m surprised that STV would therefore be eliminated from contention.

  7. Why is this illegal Muslim immigrant still in this country.

    • Although Maryam Monsef is definitely a twit, your racist, xenophobic comment is worthy of the racist, xenophobic CPC leadership candidate Kellie Trump, of whom you must be a disciple.

  8. It strikes me that most of these “systems” are simply devices to give a voice to candidates who can’t muster enough support to ever get a look-in. It’ simple: the candidate who gets the most votes (has the most supporters) wins. Grossly divisive parliaments e.g. France, Italy) yield poor governments. Period.

  9. This woman is an embarrassment to all women and Trudeau is an embarrassment to Canada and the vast majority of Canadians.

  10. Minister Monsef is most definitely neither a twit nor an embarrassment to anyone, but she may well be over her head as Minister of Democratic Reform. Clearly not happy that the STV (thought to favour the more middle of the road parties) was not recommended by the committee.
    Math is mostly not difficult, statisticians, at least, do understand statistics, and fortunately advanced calculus is not required.
    The majority of those Canadians who favour electoral reform seem to have a clear preference for some form of proportional representation; the question comes down to which system will give the optimum result while still being understandable. Here’s a caution: the BC Citizen’s Assembly may well have chosen the “best” method of giving a fair PR result, but it was so convoluted that most BC voters could not understand, much less support the proposal and it was no surprise that it was soundly rejected.

  11. I share Ms Monsef’s apprehension of this; I’m also somewhat disappointed that a math instructor would state the incorrect wikipedia statement of the limit to Galligher’s index. The Galligher index is merely a measure of the disparity between popular vote gained by a party and the number of seats won: as such, it’s a quick and dirty oddly scaled RSS which is not a particularly good estimator. Also, it is merely a measure of one kind of parity and, as Prof Galligher himself points out, says nothing about whether this is a desirable state. Oddly, the committee interviewed Prof Gallagher and chose not to discuss his index or it’s possible usefulness in selecting a particular electoral system nor what methodology would be applied. Somehow the committee picked an acceptance level without bothering to compute the statistical uncertainty of this particular index which one would avoid if precision was an objective. In any case, assigning PMs based on party affiliation and the average preference of the 37.8 year old man with his 41.2 year old partner with their 1.1 resident childer is first order nonsense. More than anything the suggestion that this index is useful oversimplifies the electoral process to the extreme: voters do not exclusively vote for parties; in fact, the theory is they vote for a candidate who appears to best represent their views and/or will best represent their local concerns – clearly a party platform cannot be a fit to a diverse cohort of voters nor can votes for candidates with party affiliation be considered an endorsement of the party. So far, the CPC driven majority opinion of the committee is not only mathematically incomplete, but ignores constitutional constraints, the role of regional parties, small parties and independent representation; in fact it envisions a monolithic system where party brass dictate to their MP drones (not unlike Harper’s governance) and where the virtues of local candidates are of little importance.
    The most important defect is the complete ignorance of how the current electoral system was established, to what extent constitutional and legislated measures represent the contracts (plural as various provinces engaged on different terms) for confederation and gives short shrift to the basic fact of diversity within the country.

Sign in to comment.