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.



10 responses to “Electoral Reform… some logic please!

  1. Do you think there’s an option for a pure bargaining power election, somehow moving away from seats altogether? Say, parties size to some predetermined scale, but what people actually vote on is solely how many chits their party gets to put in the jar so to speak?

    • Sure, this could be done: i) enforce strict party discipline so that basically each party has just one vote; ii) compute bargaining power on basis of seat shares; then iii) attach weights equal to parties’ respective bargaining power to their votes. Voila – proportionality in bargaining power! But weighted voting schemes like this are replete with their own perversities… that’s one of the central points of Arrow’s Theorem: every electoral system that has to choose over more than 2 alternatives must either tolerate some form of dictatorship (i.e., limiting on what or how we vote) or understand that it will generate some perversities (e.g., manufactured majorities or non-monotonic results).

  2. Arvis Pinkletter

    For me, the biggest problems with FPTP are thus:
    – it works best for a two-party system, which we do not have.
    – 40% of the popular vote too often leads to more than 50% of the seats, and 100% of the power, which I consider to be dangerous and exclusive.

    This isn’t to say that I wish for flat-out proportionality either. Our current system attempts to provide local representation for communities and resolve regional disparity in population size…. also, when you vote, you get to vote for/against a specific person and not just a party. What I would like to see is a system that does that, but adds an element of proportionality. Of the popular options, I think I prefer MMP because it tries to mix in the best aspects of FPTP with a proportional element; but I hope for a version of it where the voter has a hand in deciding which candidate fills the “proportional top-up seats”. The tricky part is finding a way to do this that isn’t too overwhelming or confusing for the voter.

  3. Thanks for the rigour behind this.

    I assume there studies on public satisfaction with their various electoral systems?

    I have three concerns about Proportional Representation (PR) that I have seen with Israel and Italy. The first is cronyism. We just saw in Canada that we defeated a number of senior cabinet ministers. Most of these individuals will never return to the House of Commons. Electoral waves can turf really good people, but they can also help create healthy renewal. I can certainly think of one or two MPs this time around whom I feel it was best they were defeated. With the party list system of PR variants, we see individuals who would likely have been gone under First Past the Post (FPTP) returned to office — sometimes for many years. This happened with Prime Minister Benjamin Netanyahu who returned as PM years later, but who likely would have been gone from politics under FPTP. Are there PR systems that somehow term limit those elected from party lists or otherwise prevent party cronyism?

    My second concern is that the party splintering that we see occur under FPTP can give what many would consider fringe parties the balance of power as again seen in Israel. It seems you would call this disproportionate bargaining power. Any thoughts on this? Despite the negatives I have seen, I imagine there are also times when smaller parties have provided a good temper to more dominant parties.

    I assume there are ways to lessen the political instability seen in Italy’s historic electoral system that was fairly pure PR from what I understand. I believe that minority governments and coalitions can be useful and productive. However, I would not want to have to go to the polls every two years or less for years on end — especially when forming coalitions can take so long, and cause such great uncertainty during the power negotiating process. (I know that Italy has also had other problems and is currently undergoing electoral reform.)

    I also have a concern with multi-member systems, such as the Single Transferable Vote system, that elect more than one member (in our case MP) in an electoral district (riding). I believe our system, at least in theory, encourages good constituency work and that the best MPs are strong constituent advocates. Multi-member systems typically require electoral districts that are at least twice as large. This might not be a problem in smaller countries. I also assume it would not be an issue in areas with dense populations and relatively homogeneous issues. It seems to me larger ridings would be an issue in rural areas and areas with great diversity between communities. Are there multi-member systems that could address this issue?

    Currently, I tend to favour a ranked ballot system. However, I recognize I may have a bias as I consider myself to have moderate political views, and ranked ballots can favour middle parties and those that appeal to the widest audience. I find this a strength because you cannot win by only appealing to a motivated base that is more extreme than average. In the short-term, it seems to me that ranked ballots would not make a significant difference for a party such as the Greens. However, ranking them first would no longer feel so futile for people, and I assume that over multiple elections smaller parties could increase their populate vote shares to the point they started electing more members. Is their evidence from other systems, that shows smaller or new parties can have more success with ranked ballots than FPTP? Of course, we have seen new parties such as Reform and the Bloc succeed in Canada, but these grew from regional bases rather than the dispersed support for the Greens.

    I don’t necessarily expect answers to all my questions, but I thought there was value is posing them.

    Thanks again for your post, Bill.

  4. I just read about open lists for proportional representation. Open lists would appear to prevent cronyism, but might suffer from a strong incumbency bias. Regardless, wow would that be a big change to physical ballots.

  5. All fair points, but what about some of the other arguments for PR?

    1) FPTP exaggerates regional differences and rewards parties with a narrow geographical focus — the 1993 election gave the Bloc Québécois 54 seats with 13.5% of the vote, but only 2 seats to the PCs with 16% of the vote.

    2) FPTP is poorly suited to contexts where there is more than one axis of political alignment. E.g Québec from roughly 1977-2000, where you had the choice between a left-wing nationalist or a right-wing federalist party, but were basically out of luck if you happened to be a left-wing federalist or right-wing nationalist. (You’re still out of luck today if you’re the former.) Also, the transition from one axis to another is difficult, e.g. the sovereignist-federalist polarization is still the dominant one in the party system, even though it clearly isn’t in most of the public’s mind.

    3) More generally, if you see effective democracy being about different parties forcefully making the case for different policy options and debating them in public so people can make informed choices, FPTP really sucks. E.g. climate change: did Canadians actually debate that in this election? Wouldn’t an electorally viable, single-issue environmental party hammering away at that (and forcing the larger parties to explain their positions) have helped? Etc. Instead we had an election full of largely empty rhetoric about “the middle class”, whatever that is.

    It would also be interesting to hear your views on what impact (if any) the particular Canadian constellation (FPTP with multiple parties) has on the quality of parliamentary work — the rubber-stamp Parliament effect.

  6. This call for more sophistication – merited to some extent – is overkill. Evidence is, most people who could vote strategically, don’t. Most people are not rational calculators. Change the system, and a sophisticated minority will indeed continue to cast strategic votes. Most people won’t.
    Therefore, electoral system change need not transform party systems dramatically, at least as far as voters are concerned. New Zealand is a good case in point. It more or less has the parties it had prior to change. Despite elite-driven efforts, fragmentation of the larger parties was relatively limited and they continue to be the major players. More often than not, electoral systems get chosen to fit party systems, not the other way about – at least that’s my reading. And FPTP doesn’t seem to fit Canada very well, now.

  7. Beyond PR – FPTP debate, is there any thought about ranked choice to avoid vote splitting? Voters would not have to rank every candidates, only those that they don’t oppose. It is simple to implement and explain, doesn’t require different seating arrangements.

  8. I’ve invented a system to deal with that first loser and second loser problem refered to above in connection with Cox.
    Namely by getting rid of premature exclusion of candidates in an election count and replacing it with a rational exclusion count to complement the rational election count of transferable voting.
    This was made possible by extending the key concept of the re-adjustable keep value, introduced by Brian Meek computer count of Single Transferable Vote.
    This extension, in my system, (called Binomial STV) counts candidates keep values, not only in surplus of a quota, but in deficit of a quota.
    It may not matter that a candidate has a deficit keep value, in one round, because there are systematic recounts (according to the binomial theorem of prefered candidates in the election count and unprefered candidates in an exclusion count. For example, the election keep values and the (inverted) exclusion keep values are averaged to give a final keep value per candidate. This most simple version is first order Binomial STV.
    A more complete title is: Abstentions-inclusive keep value averaged Binomial STV.
    All preferences including abstentions are counted, so as not to give undue importance to the exclusion count, as voters don’t generally fill in preferences to the bitter end.
    Please see my free Smashwords ebooks:
    Scientific Method of Elections.
    Peace-making Power-sharing.
    These books are more complete than my original Democracy Science web-pages. But the web-site contains examples of the system, including a new example, showing how counting the abstentions works.

    • Sorry it took so long to approve your comment. Your system strikes me as being quite relevant to the recent debate and amendments to the Australian Senate elections system (STV), as it focused on the extent of voters’ preferences on the ballot. I’ll have to take a look at what you’ve come up with more closely.

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