Two two-round systems, very different results

This month there have been two presidential elections in the Americas under different rules requiring a second round (runoff) under certain conditions. In one, there will almost certainly not be a runoff, while in the other there may be. Yet in the one in which there probably will not be a runoff, the election was extremely close and a runoff could change the outcome. In the one where there may be a runoff, the leading candidate is far ahead, and a runoff almost certainly would be superfluous.

Results from Haiti’s February 6 election remain provisional, but Rene Preval is hovering right around half the votes. BBC (seen on PoliBlog) reports there might be a runoff, with Preval currently at 49.6% of the votes. This result is with 72% of the vote counted. The runner up, Leslie Manigat1, is at 11.6%.

In other words, in Haiti, there could be a runoff between a candidate who very narrowly missed a majority and a candidate trailing him by thirty eight percentage points. Why? Because the Haitian constitution mandates a runoff unless the leading candidate has at least one more than half the votes in the first round.

Meanwhile, Costa Ricans await the results of their presidential election, held the day before Haiti’s. The leading candidate, Oscar Arias Sánchez, has 40.5% of the votes, according to preliminary results posted by the Tribunal Supremo Electoral (via Adam Carr). The runner up, Otton Solís Fallas, has 40.3%. There will not be a runoff if this result holds, even though the leading candidate is nearly ten percentage points short of a majority and leads his main challenger by only two tenths of a percent (3,250 votes). Why? Because under the Costa Rican constitution, a runoff is held only if the winner of a plurality of the vote has less than 40%.

So, the Haitian first-round result is by any standard decisive, and if Preval really is that close to 50% there is almost no chance whatsoever that a runoff could lead to Preval’s defeat. But in Costa Rica, there is a very good chance that a runoff could produce a different result, but there will not be one (unless, of course, the recount puts both candidates below 40%).

There are better ways to determine when a plurality is sufficient and when there should be a top-two runoff. For instance, the double complement rule, first proposed in 1994 by Rein Taagepera and yours truly (in Comparative Political Studies). Under the DCR, in any election in which no candidate obtains over 50%+1, there is a runoff if (and only if) the second candidate’s shortfall from majority is less than double that of the leader.

In other words, if the leader has 44%, he is six percentage points short of 50%. There would be a runoff if the second-place candidate had more than 38%, which is double the leader’s shortfall from majority. If the second candidate is under 38%, the election is over in one round, with the leader’s 44% sufficing. Obviously, the gap required between the top two candidates to avoid a runoff shrinks as the leader approaches 50% and increases as the leading candidate’s plurality decreases–as it should. So with a leading candidate at 40%, there would be a runoff unless the second candidate had less than 30%.

The DCR is not actually used anywhere, but it was the inspiration behind the rule adopted in 1994 in Argentina when that country junked its US-style electoral college. The Argentine rule is a bit more complex. A leading candidate with 45% wins in one round under any circumstances, even if the runner-up is at 44.99%. And less than 40% for the first candidate necessitates a runoff no matter how far the runner-up trails. But in between 40% and 45%, the first round is decisive only if the leading candidate has a ten-percentage-point lead over the runner-up.

The spirit is the same as the DCR, in that the Argentine rule says that what matters is not so much the absolute share of the votes (unless it is over 50% of course), but how successful the leader is at building a majority-approaching coalition relative to the competition. A similar rule is used in Ecuador2, as well as some Argentine provinces and for Uruguayan presidential primaries.

The DCR or any of the existing “qualified plurality” rules would be better than the majority-runoff rule, which may still give Haiti a runoff it does not need, or the 40% rule, which will not give Costa Rica a runoff it arguably should have.

1. Don’t feel to bad for Manigat if he does not get to play in a runoff. In 1988, he narrowly averted a runoff with 50.2% and a runner up at 19.7%. So he’s been on both sides of this wide-first-round-lead thing. (Of course, about six months after his decisive win he was sent off into exile.)

2. In Ecuador, the leading candidate must have at least 40% and a ten-point lead; unlike in Argentina, 45% with a smaller lead is not good enough. There is a similar provision in the Nicaraguan constitution, where the president needs 40% or 35% with a lead of at least five percentage points.

Epilogue: I might also note that today happens to be the birthday of the man who won the US presidency with the smallest plurality in history. Lincon had only 39.9% of the popular vote in 1860. The runner-up, Stephen Douglas had 29.5%. Lincoln’s plurality would have just barely sufficed under the DCR, but obviosuly not under Haitian rules and would have been just barely insufficient under Costa Rican rules.

19 thoughts on “Two two-round systems, very different results

  1. Looks like no runoff in Haiti. This morning NPR reported that the OAS steped in to broker an arrangement by which blank ballots would not be counted. By excluding these ballots, Preval gets a clean 51% and a runoff will be avoided. I can’t help but wonder if the mass demonstrations by Preval supporters had any bearing on the arrangement that was reached.

  2. Lincoln, in every state he won but California and Oregon, received more than 50% of the vote. California and Oregon represented 7 electoral votes then, so Lincoln would have still won. Lincoln won 180 EVs, representing 59% of the total.

    Ergo, neither IRV, nor any ranked ballot system, would have changed the outcome without there having been, in addition, a change in the rules of the Electoral College.

    The real trick was the way Lincoln’s Chicago pals rigged his nomination. Seward would not have done nearly as well nationally.

    Another neat thing to remember is that Missouri had its slave status forced on it, and it was the only State that produced a full slate of Electors for the only State’s Rights candidate, Stephen Douglas. The South voted for Breckenridge, who was certainly not for State’s Rights, but instead for the Federal Slave Code.

  3. Of course, I agree that Lincoln probably would have won under almost any imaginable direct-vote rules, which is why there is no serious problem with a rule like the double complement rule, even though it might sometimes allow a candidate with under 40% to win. It will do so only when the rest of the field is very fragmented (i.e. when the next highest percent is under 30), and in that case, the plurality winner is probably majority-preferred over any alternative, anyway. No need for a second round, or to take into account second choices.

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  7. > “Obviously, the gap required between the top two candidates to avoid a runoff shrinks as the leader approaches 50%”

    DCR also means (if I get the math[s] right) that the absolute minimum plurality that can win, regardless how fragmented the opposition, is 33.33% (ie, if the lead candidate has 30%, this is 20% below a majority – twice this is 40% – and no other candidate can possibly poll lower than [30% – 40%], except maybe Dick Cheney in Illinois in 2008).

    Of course, if one were counting single-round preferential votes, or in a one-place assembly that can re-ballot, it would make no sense to accept any threshold below 50%. But when counting second and third preferences involves a whole nother election, double complement does make sense.

  8. Sure. I’d prefer Alternative Vote. But there is a lot of resistance to ranked-choice ballots, whereas there is a lot of interest in moving towards runoffs in jurisdictions that use plurality (for executive office, but logically the concept could be extended to single-seat legislative races). So my argument for DCR is really: if you are looking at two-round options, consider this, rather than majority runoff (or 40% or 45% as a first-round threshold).

  9. Tom, either you or I are confused about DCR. Letting A be the vote share of the leader, and B be the share of the second place candidate, you seem to be saying there’s no runoff if 2 * (50 – A) < A – B . In this case the minimum share to avoid a runoff is indeed 33.3…%.

    I’m under the impression that DCR would mean no runoff if 2 * (50 – A) < 50 – B . Perhaps more clearly, this means no runoff if A is closer to 50% than to B. The minimum vote share to avoid a runoff would then be 25%.

  10. Vasi, my reading of DCR is that if the lead candidate polls, say 43% (and thus falls short of an absolute majority by 7%), then s/he needs to outpoll the second-highest contender by over twice that – ie, by over 14% – ie, 43% wins if no other candidate has over 29%.

    I seem to recall (and MSS and co-author may have spelled this out explicitly) that the rationale for DCR is that the likelihood of a runoff actually changing the first-round order of candidates (and therefore justifying the time and cost) is empirically related to (a) how many undecideds the first-place candidate needs to win over, to win an absolute majority (here, 7%) vis-a-vis (b) how many undecideds the second-place candidate needs to win over, to win a simple plurality (here, 43.001%).

    The debate over what is a sufficient plurality to win without a runoff, in presidential systems, has some interesting analogies to the debate over what is a suffficient plurality to win an absolute majority of parliamentary seats, in parliamentary systems. In the latter, the variables to tinker with are not so much at the 50% or 45% end for the major parties, as at the 4% or 5% or 10% end for the minor parties.

    I used to argue that, in an STV-PR system with optional preferences, a plurality of votes (after preferences are counted, not on first preference votes alone) should be sufficient if it was greater than 47.5%, ie, if the plurality party/ coalition was outpolled by its combined opponents by less than 5%. If by more than 5%, the electoral system should give the combined opponents more opportunity to get their act together and try to defeat the plurality bloc on the floor of the legislature. Empirically, STV with 3, 5, or 7-seaters usually conforms roughly to this model, even in multi-bloc elections, as Ireland, Tasmania and the Aust Capital Territory suggest – somewhere around 47-48% is the point where a disciplined plurality bloc can win an absolute majority against a divided majority.

  11. Glad you guys are debating what the DCR is. Let’s go to the original. The criterion for plurality victory is defined as:

    50% – v2 > 2 (50% – v1)

    It’s just an arithmetic average of plurality rule (v1>v2) and majority rule (v1>50%). (v1 and v2 here should have the numbers sub-scripted, and simply refer to the votes of the first and second-ranked candidates.)

    Tom’s recollection (2d paragraph of comment #10) is basically correct. The basis of the DCR is a pragmatic one: When is a plurality “good enough” and a runoff “not needed.” Of course, one does not have to accept the DCR’s answer to that question. Those interested in this debate might also be interested in Jeffrey O’Neill’s extended look at the question.

  12. Rather than gloating about being right, I ought to correct my earlier statement to make it consistent:

    “(a) how many undecideds the first-place candidate needs to win over, to win an absolute majority (here, 7%) vis-a-vis (b) how many undecideds the second-place candidate needs to win over, to win a simple plurality (here, 14.001% to turn 29% into 43.001%).”

  13. ie, 43% wins if no other candidate has over 29%.

    I don’t want to be a pedant, but that seems inaccurate. We have v1 = 43%, let’s propose v2 = 35%, higher than 29%. Plug into the equation MSS just gave:

    50% – v2 > 2 (50% – v1)
    => 50% – 35% > 2 (50% – 43%)
    => 15% > 2 (7%)
    => 15% > 14%, which is true. So an immediate win, with no runoff.

    Maybe I’m still just not getting it, please point out where I’m wrong.

  14. Okay, maybe Vasi’s right after all, and I was wrong.

    MSS, please resolve this authoritatively:

    “DCR means that a leading candidate with 43% can win on the first round if no other candidate polls over…”

    A. 29% (= 43% – 14%)


    B. 36% (= 50% – 14%)


    C. Neither of the above?

  15. Under the DCR, if the leading candidate had 43%, the second candidate would have to have at least 36% to force a second round.

  16. Thanks, MSS. I stand corrected. So that still leaves the absolute minimum plurality as 33.334%…?

    (for an electoral systems junkie, my maths lobe is sometimes problematic!)

  17. So that still leaves the absolute minimum plurality as 33.334%…?

    Keep in mind that if the plurality leader gets 34 votes out of 100, then at least 4 other candidates have to get 17 or fewer votes each in order to avoid a runoff. In other words, the theoretical lower bound isn’t much of a practical concern.

    What is an interesting question to me is whether the administrative and cost advantages of DCR are worth the increased chance (relative to conventional top-two runoff) of failing to elect a candidate supported by a majority coalition. For an example, see this comment.

  18. It occurred to me that one criterion for fixing the “runoff cutoff” might be to empirically find the threshold that, in practice, regularly elects candidates with large first-round pluralities. No cutoff, or too low, and you have a South Korea 1988 (or Lincoln 1860, or PNG…) situation where the winner has only 39% support or less.

    On the other hand, requiring 50% could lead to a situation like Georgia (US not Urals) where a front-runner with, say, 48% on the first round might be narrowly beaten on the runoff by a rival who had only, say, 38% on the first round.

    If one is a strict majoritarian, the latter result is quite legitimate – but if one supports plurality rule, one might still want to avoid producing a “38% President”, whether on the first round or the second.

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