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This is the election system in France and Ukraine. In the first round anyone can run. If no candidate wins an absolute majority, then the top two candidates go to a second round where they face off against each other.

What are the relative disadvantages of this electoral system?

Related: What are the disadvantages of first-past-the-post electoral systems? which deals with the relative disadvantages of the other major electoral system.

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    also politics.stackexchange.com/questions/14582/… on ranked choice voting
    – James K
    Commented Apr 13, 2022 at 8:20
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    Surely not anyone can run? Finland has a similar two-round election president, and the candidates have to be set by political parties or associations that can collect at least 20 000 supporters for their candidate.
    – ilkkachu
    Commented Apr 13, 2022 at 18:57
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    I sure went down a rabbit hole with this question. Now that James K provided the terms to search for, there's a veritable mass of voting systems (& literature for their problems) out there for me to check out.
    – Allure
    Commented Apr 14, 2022 at 8:57
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    @Allure You may want to check aceproject.org/ace-en/topics/es/default out
    – Relaxed
    Commented Apr 14, 2022 at 10:12
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    @ilkkachu For the French presidential election, candidates need to obtain 500 nominations by elected officials, with some conditions in the way these elected officials are spread in the country. See also this question.
    – Arnaud D.
    Commented Apr 14, 2022 at 10:58

8 Answers 8

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In no particular order:

  • Cost. Elections cost in time and money. Having a run-off election means that you have to pay twice.
  • Not Condorcet. A candidate who would win in a head to head against every other candidate can be eliminated in round 1. Indeed this system also fails the "independence of irrelevant alternatives" criteria.
  • Voting for the least bad. In the second round, there may be one candidate supported by 40% of the electorate, and a second candidate supported by 20%, but if the 40% of voters who don't support either feel that the second candidate is marginally less awful than the first candidate, then the second candidate can be elected. Being elected for being "marginally less awful" seems a weak mandate! The candidate with the most supporters doesn't always win.
  • Tactical effects. In the first round, voters may choose to vote dishonestly or tactically to get a candidate that they perceive as having a greater chance of making the top two. Then the results of the first round can have a significant tactical effect on the second. For example a candidate may have a significant lead in round 1, so their voters don't bother to turn out in round 2.
  • Voter fatigue. "I've already voted once... Why do I need to do it again?" This can lead to low turnout in the second round, and a reduced mandate.

And, as with all democratic systems, the winner is based on popularity, and not on competence.

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    Voting for the marginally less awful candidate doesn't seem like a disadvantage specific to this type of election. Run off elections seem like a halfway house between the very common first past the post system where this is a big problem and one of the ranked voting systems where people can vote for who they think is the best candidate without worrying (much) that they are effectively voting for the candidate they dislike the most.
    – Eric Nolan
    Commented Apr 13, 2022 at 11:07
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    @EricNolan That's exactly the most serious issue with 2-round FPTP elections IMHO. It's a very expensive and time consuming way to get a half-arsed improvement over single-round FPTP elections. If you care about the issues with FPTP, why not just use a different system? And if you don't think those are problems why bother with 2 rounds?
    – Ben
    Commented Apr 13, 2022 at 11:47
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    Any actual example of low turnout in the second round? In France, for example, turnout is often higher in the run-off because the decision is very clear and that's what decides the final outcome (all features of the system). The opposite also happens but certainly not in a systematic way. If there is an effect on voter fatigue, it would be through long-term decrease of interest in elections in general.
    – Relaxed
    Commented Apr 13, 2022 at 15:52
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    I'm not dismissing it. A run off system (or any ranked voting system, in fact) can't distinguish between. "This candidate is great, that one is lousy" and "These two candidates are roughly equal, but that one has a crooked smile" Only a score based system can do that, but score based systems are prone to dishonest votes... No election system is perfect.
    – James K
    Commented Apr 14, 2022 at 8:35
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    It's worth noting that having a candidate who would win any head-to-head be eliminated in the first round applies to a single-round first-past-the-post as well, so that may be a disadvantage of this system compared to other systems, but it's not a disadvantage compared to the most commonly used voting system.
    – NotThatGuy
    Commented Apr 14, 2022 at 8:42
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This method fails the monotonicity criterion. This disadvantage is somewhat technical in nature, and it's hard to prove that nonmonotonic behavior occurred if you have two rounds rather than an ordinal ballot, but it is a weird and arguably undesirable property.

Intuitively, this means that rating a candidate higher can cause that candidate to lose.

A voting method satisfies the monotonicity if the following property holds. In order to define it, I need a few other definitions first. Note that we can define this property without talking about agents/rational actors at all; it can be defined using just collections of ballots.

In order to define this property, I'll introduce the nonstandard notion of X-superiority.

Let A and B be ballots. Let X be a candidate. A is X-superior to B if and only if, for all pairs of distinct candidates (Y, Z), A and B have the same ranking of Y, Z when neither Y nor Z is X, and for any pairwise comparison involving X, A ranks X higher than B does or A and B have the same ranking.

Following Wikipedia's example, X > Z > Y is X-superior to Z > X > Y, but X > Y > Z is NOT X-superior to Z > X > Y because the order of Y and Z is reversed.

Let A and B be I-indexed sets of ballots. A is X-superior to B if and only if, for all i in I, it holds that A[i] is X-superior to B[i].

A voting method fails the monotonicity criterion if and only if, there exist I-indexed sets of ballots C and D such that the candidate X wins in C, the candidate X does not win in D and D is X-superior to C.

Here's the nonmonotonicity example from Wikipedia with an explanation.

C > B > A   28
C > A > B    5
A > B > C   30
A > C > B    5
B > A > C   16
B > C > A   16

In this election, B is eliminated first and A wins in the next round.

Next consider the election below

C > B > A   28
C > A > B    3
A > B > C   30
A > C > B    7
B > A > C   16
B > C > A   16

Now, C is eliminated first and B subsequently wins.

Two C > A > B were shifted to A > C > B ballots in this example, increasing candidate A's votes, and that caused candidate A to lose.

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    This effect can be summarized as one of the 'Tactical effects' from the accepted answer. If a candidate is projected to make it to the second round with certainty ('A' in this example), then it becomes advantageous for remaining voters to switch their first round votes to the candidate that they feel would be easiest to defeat.
    – Brady Gilg
    Commented Apr 14, 2022 at 19:01
  • @BradyGilg that isn't what happened in the example though. Votes were actually move to the candidate certain to make the 2nd round. Who then lost. This feels like an edge case that would be impossible to produce in real life though because it requires similar size vote piles for most combinations of candidates.
    – Jontia
    Commented Apr 15, 2022 at 6:25
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    @Jontia The situations are mathematically equivalent. 'Moving votes to A -> A loses' and 'moving votes away from A -> A wins' are identical, it's only a difference in your perspective.
    – Brady Gilg
    Commented Apr 15, 2022 at 16:15
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The main problem is that it uses a single-mark ballot, so that voters can only express an opinion about one candidate.

In a two-candidate general election, this is fine, but in a multi-candidate election, it results in vote-splitting and unrepresentative winners.

Imagine an election in which there are dozens of very good, representative candidates, and two unrepresentative extremists on opposite ends of the spectrum. The majority of voters prefer the representative candidates, but which one? Their votes are split between them, and each only gets a small fraction of the vote. The unrepresentative extremists, on the other hand, are unique, and have no nearby competitors in the ideological space, so they get solid pluralities of the vote, and advance to the next round.

In this round, one of those two remaining candidates will get "majority support", but this is an illusion created by eliminating everyone else. Any of the representative candidates would have received a majority of support over one of the two extremists, but they aren't in the race anymore because of vote-splitting.

Here is an illustration on a one-dimensional political spectrum:

A bell curve political spectrum is colored by voter preference, with orange and green candidates as left and right extremists, and red, blue and yellow as moderates who lose because of vote-splitting

Red, Blue, and Yellow are good representatives of the voters, but votes are split between them, leaving Orange and Green to get the most votes and proceed as finalists to the runoff. Green, an unrepresentative extremist, will win the election, despite Blue being preferred over Green by 70% of voters. (Here's a 2D version.)

This same vote-splitting problem also affects every other voting system that only counts first preferences in rounds, such as FPTP, exhaustive ballot, supplementary vote, contingent vote, and instant-runoff voting (called "ranked choice voting" in the US, or "alternative vote" in the UK).

A much better solution is an approval voting primary, like the one adopted in St Louis recently. Voters can select as many candidates as they approve of, which makes this vote-splitting much less likely.

Alternatively, a system that considers all voters' preferences simultaneously can be used to eliminate the primary altogether, such as a Condorcet ranked-choice system or STAR voting.

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The main drawback has already been mentioned (but not emphasized enough in my opinion): It costs a lot to organise two rounds of voting for every election. That's also what you will find in guidance from international organisations.

The other objections are mostly theoretical and hard to support empirically. For example, it does not seem obvious at all that countries with a two-round system have a much higher level of voter fatigue or non-voting than others, in general.

The advantages of a two-round system over a simple first-past-the-post system should not be underestimated. Being able to vote for the least bad choice while keeping the system transparent and simple to understand for the voters is a feature not a bug. Ranked voting systems fail in that respect and even if their proponents tend to dismiss this as a non-issue, it is in fact an important trade-off.

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    'guidance from international organisations' where can I find this guidance?
    – Jontia
    Commented Apr 13, 2022 at 19:06
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    It seems odd that you dismiss certain concerns as being "theoretical", but include no sources or data to back up your own claims. Is there any evidence besides your personal opinion that voters are confused by ranked voting and not fptp? Commented Apr 14, 2022 at 1:43
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    I also think there is an inherent complexity and risk of confusion regarding the ballot itself, which is often noted as requiring a higher level of literacy and numeracy to be used effectively but that wasn't my point.
    – Relaxed
    Commented Apr 14, 2022 at 5:59
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    People who like FPTP like to claim that ranked systems are confusing. People who actually use those systems don't seem to be confused. The apparent simplicity of FPTP is shown to be misleading in elections where dark red is telling potential voters that a vote for light red or yellow is really a vote for blue.
    – Eric Nolan
    Commented Apr 14, 2022 at 9:19
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    @EricNolan To retirate my earlier comment and hopefully make all this clearer: Do you any ranking system where the counting is done at the polling place, by any voter, without prior training? In France, a group of 4 voters will count 100-300 ballots in an hour, with the connection between what's on the ballot and the final tally immediately visible to all. It's then aggregated with similar counts from other groups of 4 voters present in the same room, publicly displayed at the town hall, in newspapers and now on a website. That's the simplicity and transparency I am talking about.
    – Relaxed
    Commented Apr 14, 2022 at 10:07
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This is a variation of STV, except instead of Instant Runoff, it's Separate Election Runoff, and votes gets transferred only once. As such, many of the advantages and disadvantages are similar to that of STV. Perhaps the most infamous case of this was when Louisiana had a runoff between Edwin Edwards, who was widely considered corrupt, and David Duke, a former KKK grand wizard, leading to the bumper sticker slogan "Vote for the crook: It's important."

As James K said, inclusion on the next round depends only on first-place preferences, and ignores lower preferences. So you could theoretically have a candidate that is ranked as first or second place preference by all the voters, but doesn't make it to the runoff. Thus, candidates who appeal to a broad base, but only moderately, can be at a disadvantage to candidates who are strongly supported by a minority. For instance, suppose one candidate is running on a platform of tax breaks for Republicans, one on tax breaks for Democrats, and one on no partisan-based tax breaks. If there's broad support for no tax breaks, but everyone mildly supports tax breaks for their side over no tax breaks, while strongly opposing tax breaks for the other side, then the runoff will be between the two tax breaks candidates, even though almost everyone supports the "no tax breaks for anyone" compromise.

And with a large field, a candidate needs only a few people to have that candidate as their top choice to get into the runoff, and voting blocs getting their preferred candidate largely comes down to which ones can build coalitions and coalesce around single candidates.

Another issue is that this can result in both candidates being from the same party. This can be an advantage or disadvantage depending on one's point of view. On the one hand, if most people support one party, then arguably it makes more sense for the voters to choose between candidates in that party than to have an election with a foregone conclusion. On the other hand, this can make people in the minority party feel disenfranchised. Moreover, depending on how the votes are split, it's possible for both of the final candidates to be from the minority party.

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James K gave a good answer, but I would add one more issue:

The system is subject to gaming by organized factions or parties using stalking-horse candidates.

It is possible, under this system, for a clever and organized group to introduce candidates who appear to be members of ethnic or class voting blocs, or who campaign on slightly altered variations of a given ideology, in order to split the vote from those groups and influence who the top two final candidates are. In first-past-the-post systems, you can't afford to do this, because it might lead to a first-place finisher from outside your faction winning the race outright with a very small percentage of the vote. But in multi-round voting this can be an effective strategy.

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    Any stalking horse strategy that works to influence who the top two finishers are should be even more effective at locking down the top 1. If you can split off Red voters into light red/dark red then that's even more effective for blue if the election is FPTP than if it is subject to a run-off where light-red and dark-red can come back together. You absolutely can afford this in a FPTP election, because the point is not to split your vote at all.
    – Jontia
    Commented Apr 13, 2022 at 14:53
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    To add to that, we had a famous one, where Republicans recruited a "legalize Weed" candidate to run for congress to split the Democratic vote. The trick works just fine, now. apnews.com/article/… Commented Apr 14, 2022 at 0:58
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@Acccumulation's last paragraph approaches what is IMO the most important flaw, but understates the problem.

Imagine a country which is 45% blue-ish and 55% reddish, but where the blue parties are more united so there's two blue candidates and five red candidates. Unless one of the red candidates does much better than the others, the runoff will be between the blues so blue would win. If you instead had a full runoff system (instant, or as many rounds of voting as it took) you would expect most of the red votes to accumulate on the remaining red candidate (some light reds might prefer light blue to dark red), so the final round would be red versus blue and red would win.

Sure, it's better than FPTP, but the extra cost and time would be way more than enough to do IRV.

(You could say "why don't the red parties unite?" but that just gets back to the main problem of FPTP, and, bringing it down to real politics, there's a lot more room for disagreement among those who want the state to do more than there is among those who want it to do less.)

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    Note that the instant-runoff system still suffers from the same flaw, just to a lesser extent. It handles two groups of identical clone candidates fine, but can't handle 3 or more strong candidates with differing ideologies.
    – endolith
    Commented Apr 14, 2022 at 15:29
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    +1, but agree with endolith. The problem you describe is very real, but IRV does not address it meaningfully better. Your scenario exactly demonstrates how IRV encourages two party duopoly. Sure fringe parties are welcome to participate, but the pressures at play create 2 major parties on opposing sides of a political spectrum, while remaining hostile to centrists (who cannot make it past the early elimination rounds)
    – eclipz905
    Commented Apr 14, 2022 at 17:08
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Here is an example: in a 3-candidate election there is a centrist candidate that everybody could live with but is not a popular first choice (as it is often the case). Not having many first choices the centrist candidate gets eliminated on the first round. The run-off is among two extremists, both supported by a minority, so more than half of the population gets stuck with an extremist they really dislike.

From a theoretical point of view, IRV has all problems that STV has, only worse. This question has an answer that is a good analysis that focuses on a three-candidate election, which is a case where IRV and STV are in theory equivalent (you don't call to the polls twice in IRV and eliminated candidates don't have the time to endorse the runner-ups but mathematically it's the same).

IRV is coarser than STV, because it discards all 1st round results except who are the first two candidates. As such, it suffers more from random-like effects on the performance of the losing candidates and is more prone to the spoiler effect.

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    Isn't that how it works now, in US single-round plurality elections? With a 2nd round at least the centrist voters have a chance to revote. Commented Apr 14, 2022 at 1:13
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    There are a lot of voting systems. US-style first-past-the-post is arguably the worse of them all (to its defense, it predates most modern theory on the matter), and so is also worse than IRV. It's about the only "serious" voting system that is worse than IRV though.
    – Rad80
    Commented Apr 15, 2022 at 15:52
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    @Rad80 Top-two runoff, supplementary vote and contingent vote are worse than IRV, and used in the real world. I think it's important to mention them as a sort of progression for all these people who think that FPTP and "RCV" are the only two options.
    – endolith
    Commented Apr 16, 2022 at 4:23

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