We came to Montreal for a talk — Maggie‘s, at a conference I’ll get to next time — and I did what I always do in a city that predates the automobile, which is walk until my feet complain and then walk a little more. Old Montreal rewards the stubborn. The streets in the old quarter still run on their seventeenth-century logic, narrow and cobbled, tilting down toward the river, and on a bright afternoon the crowd thickens into that pleasant shuffle where nobody is quite going anywhere.
Half the pleasure of the place is linguistic. The signage runs French first and English second — not by custom but by law, which is its own small lesson I’ll come back to — and the effect is that you spend the day inside a gentle, continuous act of translation, the focal language flipping block by block depending on who staked the sign first.
And then, on a hoarding around a construction site a few streets up, the city handed me the whole post. A building was being taken apart behind the fence, and the developer had branded the demolition with a single word in enormous letters: PARADOXE. Underneath, smaller: DÉCONSTRUCTION. A thing being unmade, labeled paradox and deconstruction, on a wall, in a photograph, for a blog whose oldest running result is that you cannot make an impossibility disappear. You can only move it somewhere you aren’t looking.
That’s a heavy thing to hang on a construction fence, so let me earn it with a vote.
Thirty years ago this autumn, Québec came within a whisker of leaving Canada. The 1995 referendum finished 50.58 to 49.42 — a margin of roughly fifty-four thousand ballots out of nearly five million, on a turnout of 93.5 percent that still stands as the highest in the province’s history. A whole country’s shape balanced on a knife, and the knife was a question.
Do you agree that Québec should become sovereign, after having made a formal offer to Canada for a new economic and political partnership, within the scope of the bill respecting the future of Québec and of the agreement signed on June 12, 1995?
Read it again and notice what it does not say. It does not say independent. It does not say country, though the premier who wrote it, Jacques Parizeau, told the National Assembly as he tabled it that a Yes meant exactly that: vote Yes and you are effectively giving yourself a country. The word sovereignty had even been struck from the title of the enabling legislation; at Mario Dumont’s urging, Bill 1 stopped being a sovereignty act and became An Act respecting the future of Québec. The operative content lived in that bill and in a partnership agreement signed the previous June, documents mailed to every household precisely so the question could gesture at them without containing them.
What you’re looking at is a binding-looking vote engineered to do the work of a motion to instruct. The lineage is explicit. The 1980 referendum had asked only for a mandate to negotiate sovereignty-association, with a second referendum promised before anything actually changed — an instruction dressed as a decision, and honest about the dressing. 1995 kept the optionality and dropped the candor. It offered the ceremony of final passage while reserving, in the fine print, the escape hatch of mere negotiation. Call it what it is: a poor man’s secession, the costume of a decision worn over the body of an instruction.
You don’t have to infer the ambiguity; it was measured. Three weeks out, pollsters found that 28 percent of undecided voters believed a Yes would simply mean negotiating a better deal inside Canada. One question was carrying two electorates at once — the separatists who wanted out and the soft nationalists who wanted leverage — and it carried them because it declined to make them choose. The vagueness wasn’t a flaw in the instrument. It was the instrument.
Here is where a social-choice reflex kicks in and, for once, earns its keep. A referendum is a two-alternative choice, Yes or No, and over two alternatives the news is unusually good. May’s theorem says simple majority rule is the one method that treats the voters symmetrically, treats the two options symmetrically, and moves in the right direction when someone changes his mind — and, as a bonus, hands no voter any reason to misrepresent his preference. On a straight binary you cannot game your ballot. Sincerity is your best move. A referendum is, at the ballot box, strategy-proof.
But strategy-proofness over two options is cheap, because the hard theorem is about everything else. Gibbard and Satterthwaite proved that the moment the menu holds three or more options (\(k \ge 3\)), every non-dictatorial rule is manipulable somewhere: no procedure exists that makes sincerity always optimal. Set the two results beside each other and a question falls out. If the referendum is strategy-proof, where did the manipulability go? It did not evaporate — conservation forbids that. It went upstream, to the one actor who decides which two options the five million voters are permitted to choose between.
This is an old and well-modeled move. Romer and Rosenthal called it the setter model: give a single agent the power to put one alternative against a fixed fallback, and by tuning her proposal she can walk the pivotal voter across a line he would never cross if the fallback were named plainly. The referendum voter faces a clean, unmanipulable binary — which is exactly why the entire manipulation budget gets spent one level up, in the writing of the binary. The ballot is strategy-proof because the question is maximally strategic. That is conservation of impossibility in its most civic form: the procedure looks innocent at precisely the point where all the guilt has been moved elsewhere.
So I could stop here, brand the 1995 question a manipulation, and take a bow.
(Ed here. You’ve spent four paragraphs proving nobody can pose a clean question, and your triumphant finish is to pose a clean question about the people who posed the question. Just making sure you can hear yourself.)
Except the bow would be a cheat, and the reason it would be a cheat is the entire point. There is no unframed question. A referendum written from nowhere, in a neutral language accessible from a view that occupies no position, is itself one of the impossibilities; chase it and you find that May’s benevolence and Gibbard’s mischief were never two separate facts. The complaint therefore cannot be that the 1995 question was framed. Every question is framed. The honest object of suspicion is narrower and sharper: who held the framing power, and were they accountable for holding it?
Canada’s answer to that is the most interesting thing the episode produced, and it confirms the theme rather than escaping it. After 1995, Ottawa went to the Supreme Court, obtained the Secession Reference, and passed the Clarity Act — a law declaring that any future secession vote must put a “clear question” and win a “clear majority.” As a fix it fails on its own terms, because the Act pointedly declines to define either phrase, leaving Parliament to decide, after the vote, whether the question was clear enough and the majority large enough. As a relocation it succeeds completely. The framing power wasn’t abolished; it was moved from Québec’s legislature to a federal standard, and the fight over who writes the question became a constitutional fight over who gets to grade it. Chrétien wanted to foreclose what he called a mandate through the back door, and he did — by installing a new back door and keeping the key in Ottawa.
And it isn’t behind us. The same week I was in Canada, a few time zones west, the identical law was running in reverse: a court named a rights constraint on Alberta’s proposed separation vote, the legislature deleted the constraint from the statute days later — retroactively — and when a second court found the government had skipped its duty to consult the First Nations whose treaties predate the province, the premier reworded the ballot to ask whether Albertans wanted to begin the legal process of one day holding the real vote. A referendum to authorize a referendum, cut small enough to duck the very Clarity Act I just described. Ottawa spent 2000 adding a constraint; Alberta is spending 2026 taking them away. Same theorem, opposite sign — and the impossibility no better solved in Edmonton than in Québec, only moved again into the fight over who holds the pen.
I thought about none of this at the time, to be clear. At the time I was eating. Somewhere between the monument and the argument, Maggie and I stopped at a deli that has been stacking smoked meat since 1927, and I’m pleased to report the sandwich is not a metaphor for anything. It is a great deal of cured beef on rye, with a pickle and a bowl of poutine standing by as a second, unnecessary, entirely correct opinion.
We came for a talk, though, and the talk is where this two-parter is going. Next time, from the same city, a different room: a hotel hall where the thing being framed is not a country but a person, and the setter is not a premier but an algorithm. Maggie’s paper asks what becomes of the famous fairness-impossibility results once the people being classified are allowed to respond to the classifier — once behavior stops holding still. It’s the same theorem-shaped hole I spent the afternoon circling, relocated into a room with worse carpet. The impossibility doesn’t get solved there either. It only finds a new place to live.
With that, I leave you with this.
Notes
The ballot question, the 50.58/49.42 result, and the 93.5 percent turnout are from Elections Québec and the Canadian Encyclopedia. Parizeau’s characterization of a Yes as giving oneself a country was reported in Maclean’s at the time he tabled the question in September 1995. The renaming of Bill 1 from a sovereignty act to an act respecting the “future” of Québec, and the mailing of the bill and the June 12 agreement to every household, are documented in the same sources. The figure that roughly a quarter of undecided voters read a Yes as a mandate to renegotiate rather than to leave comes from contemporaneous polling in the final weeks of the campaign.
May’s theorem is Kenneth May, “A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision” (1952). The manipulability result is Allan Gibbard (1973) and Mark Satterthwaite (1975), independently. The setter model is Thomas Romer and Howard Rosenthal (1978). The relocation of framing authority I describe at the end runs through the Supreme Court’s Reference re Secession of Quebec (1998) and the Clarity Act (2000).