Electoral reform… logic, please REDUX

Right after the election, the rumbling for electoral reform began.  The impetus was 1) the Liberals’ manufactured majority, and 2) their promise to replace Canada’s electoral system from First-Past-the-Post to … well, something else.  I wrote a blog post noting that a great deal of nonsense on electoral systems and electoral reform would follow.  Well, here we are:

Andrew Coyne: Electoral reform wouldn’t end majority governments — only the phoney ones

Andrew Coyne: What problem is electoral reform supposed to solve? Here are a couple, to start

Andrew Coyne: Our deeply flawed winner-take-all voting system

I have a great deal of respect for Coyne, who I think is the country’s best columnist right now, but – Ay Carumba! – these columns are exactly the sort of thing that I was complaining about (e.g., “false majorities”… there are no true majorities!). For that reason, I am reposting my “Logic, please!” post….

Let’s correct several misconceptions about electoral reform:

  1. FPTP produces “false majorities.”  This chestnut gets dragged out after the election of every majority government. A less pejorative term is “manufactured majority,” but that’s actually tangential to a more fundamental point:  there are no “true” majorities in the sense that a majority necessarily reflects a transitive social ordering (save in the case of majority rule over 2 alternatives).  That’s one implication of Arrow’s Theorem.  What do I mean by that?  Well, imagine three options, say, Liberal, Conservative, and NDP.  It may well be that if we constructed a pairwise competition we’d have L>C, C>N, and N > L.  So each option is majority-preferred at some stage.  Which of these majorities is false?  Well, in a sense none and all. To even label majorities “true” or “false” is utterly jejune.  Look, any time we have more than 2 options and are voting over more than 2 dimensions (e.g., economic and social policy), we cannot rule out that there exists a voting cycle, and that the majority that emerges is pretty much a function of the agenda / voting system.  And even if the majority were independent of the electoral system we used, we’d never know it. A byproduct of this line of argument is that claims about electoral mandates (“the election showed voters want us to effect policy X”) are claptrap. Indeed, I doubt on the basis of the theoretical work of Arrow, McKelvey, and Riker whether it makes any sense to talk of electoral representation  (in the sense of a systematic link between the preferences of voters and the outcome of the election) at all – no matter what electoral system is employed.
  2. “Under FPTP, many people’s votes don’t count / are wasted”.  This is another bromide.  A vote is said to be “wasted” when it does not elect a winner.  So you’ll often hear advocates of electoral reform talk about adopting voting systems under which all votes count. they’ll say.  I can only infer from such claims that the speaker thinks that every vote cast under their preferred system will go toward electing a candidate, ergo, no votes will be cast for losers.  But here’s the thing:  Logically, we could only achieve this if we guaranteed ex ante that every candidate who ran would win.  I can see only two ways to achieve this: a) ensure that only as many candidates are nominated as there are seats in the House of Commons, with all candidates elected by acclamation; or b) expand the House of Commons so that everyone who wants to be an MP gets to be one. (It would be even better, right, to have winners who did not even need votes?) Seriously, the first option (dictatorial control of the menu of options) is normatively undesirable, and the second is infeasible.  Any time you have more candidates than seats, it will be that case… hold tight here… that some candidates will lose!  I know, it’s shocking, but it gets worse: some people may actually vote for those losing candidates.  This is true under any electoral system.  It’s just that by layering on tiers and effecting panachage, various quotas, etc. some electoral systems obscure this fact.  But, really, you can’t escape the plain fact that if you have more candidates than seats, some candidates will lose…(really, they don’t all get seats, no, no, not even in the Netherlands), and that is, in fact, healthy for representative democracy.
  3.  Strategic voting occurs only under FPTP. Uh… no, that’s just not true.  All voting systems save majority vote under two alternatives admit strategic behaviour.  This is the central message of the Gibbard-Satterthwaite Theorem.  This is not merely a theoretical proposition: Gary Cox (1997) demonstrated that desertion from “2nd loser” to the “1st loser” (consistent with people ditching their most preferred but hopeless option to defeat their least preferred option) under a wide variety of electoral formulas.  The limiting factor appears to be district magnitude (i.e., seats per district): after M>5 this behaviour becomes harder to effect.  BUT there other forms of strategic voting nonetheless emerge under various forms of PR even when M>5.  For example, voters try to gauge if they should stick with their preferred party and risk it falling under the threshold or defecting to a viable coalition partner. Or voters may try to balance coalitional blocs (as Kedar suggested). Why one form of strategic voting (e.g., trying obtain a certain coalition) is normatively better than the sophisticated voting we observe under FPTP is beyond me.
  4. “Proportional representation is fair.”  I guess if you equate fairness to proportionality that’s true in a tautological sense. To me proportional representation implies no more or less than  proportionality between parties’ vote shares and seat shares.  Nothing wrong with that. Equally, nothing special about it.  Here’s my issue with focussing disproportionately (ha!) on votes-seats proportionality:  what we actually care about in Parliament are majorities, mainly on the floor – because that determines if the cabinet has the confidence of the House or not – but also in committee where many rules and policies are fine-tuned.  Majorities (neither true nor false, note) are constructed by and reflect parties’ bargaining power.  So if we have a single-party majority, one party has all the bargaining power; if we have a minority situation, then bargaining power is distributed among the parties – which could construct majority coalitions, allow a minority government to operate, etc.  The point being it’s all about bargaining power.  If you are truly committed to the idea of proportionality, it strikes me that consistency requires you to advocate for proportionality in bargaining power… because that’s what really counts. A few elementary examples show that the mapping from seat shares to bargaining power is incredibly erratic. E.g., let A have 40% of the seats; B have 35%, & C have 25% — and let’s assume this is all perfectly proportional to the parties’ respective vote shares: all 3 parties have equal (normalized Banzhaf) power  of 1/3. Now add a fourth party that draws seats about proportionally from A, B, & C: A=31%, B=28%, C=22%; D=19%:  the (normalized Banzhaf) power scores are .417, .25, .25, and .083, respectively. So A lost seats but gained power; whereas C and B lost seats and power, and D’s power is nowhere near proportional to its seat share! Let’s not even discuss parties’ ideological positions and how that might compress or expand the uncovered set. No magic here, just some elementary math and game theory, but it suffices to show that votes-seats proportionality doesn’t guarantee any sort of proportionality in bargaining power. (I am sure that some crazy mathematician genius has a voting system to ensure bargaining power proportionality.  Bring it on, I say.) You might retort that, regardless of disproportionality in bargaining power, anything is an improvement on concentrating all power in one party.  Perhaps, but not only does that exaggerate the situation (recall all those SC cases Harper lost – that was the court effectively checking the executive, no?), but it comes at the cost of some obvious off-setting perversities, e.g. non-monotonicity in power (lose votes, lose seats, gain power! I’m looking at you, Party A).  (P.S.  If A & B formed a coalition, it’s no “truer” or “falser” a majority than if B, C, and D got together.)
  5. FPTP generates regional tensions:  Ah, the old Cairns’ thesis.  Let me make three observations on this point: 1) we don’t know whether Canada’s regional tensions are a function of FPTP or deeper socio-economic / spatial forces; 2) PR is hardly sufficient to undercut regional tensions:  see Belgium, Spain and Italy for counter-examples; and 3) so any argument that PR would resolve Canada’s simmering regional tensions strikes me as incomplete;  it’s not necessarily wrong, but such an argument cannot IMO be brought home on first principles.

None of the above is an argument in favour of FPTP as such.  It’s a plea for some coherent arguments predicated on logic that can withstand some cursory examination. After studying institutions for a long time, I am confident predicting that electoral reform will certainly change the identity of winners and losers and alter which political strategies are dominant; it may also have policy effects. But these effects are unpredictable; the effect of institutions will interact with the country’s social and economic context; and some of these effects will be negative.

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