Electoral Reform… some logic please!

It takes about 15 minutes after the outcome of an election held under FPTP for the rumblings for electoral reform to start.  A great deal of nonsense follows, much of it from my putative colleagues in the discipline who ought to know better. (I’m sure The Spaniel will contribute his share of this nonsense in due course.)  I am going to write extensively on the topic in a day or two. (Indeed, I’ll make this a topic for my POLI 310 students.)  But before I do that let’s correct several misconceptions:

1.  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. Strategic behaviour is simply part of human nature IMO – ever notice how even young kids try to play one parent off against another?  Heck, even chimps are strategic! We are strategic, folks… deal with it because there’s no getting rid of it.
2. FPTP produces “false majorities.”  That’s another old chestnut that 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.
3. “If we’d held the election under PR, this is what the result would have been…”  These sorts of simulations drive me nuts: they are beyond naive. Look, voters’ preferences are endogeneous to the voting system in place; so too are politicians’ actions.   What do I mean by this?  If we adopted medium-to-large-M PR, for example, our larger existing parties would quickly splinter as ambitious politicians defected to start their own parties (see New Zealand for a case study).  Then, given the new options and availability of new voting strategies, people would vote differently.  So the idea that you can hold voters’ revealed preferences (i.e., their votes) constant while you simulate outcomes under different voting systems is naive to the extreme. The confidence bounds on any such exercise are essentially unbounded, and the assumptions, unfounded.
4. “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.  (Aside: Are these the arguments you get, when people grow up having won participation trophies for everything? No losers here, we’re all winners!  Even my 6-year old knows this is a charade.)
5. “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.)

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. This is evidently a high bar. Sigh.

Follow