10 January 2024

One person, one vote. Simple enough, right?

Not exactly. It turns out that everyone putting a cross in the box next to their favourite candidate’s name is a pretty blunt instrument for measuring the preferences of a group.

Luckily, there is a whole range of options available that produce more democratic results than a “first past the post” poll. And while some of these options make hand-counting extremely complicated, e-voting solutions mean that results can be inexpensively and quickly tabulated.

In recent years, there has been a host of new methods explored for voting in primaries and candidate selection contests. In both Europe and the USA, ranked choice voting and “top-two” approaches have been employed; while the Pirate Parties of several countries have experimented with the “Schulze method“, a special variation of Condorcet voting, which stages a vote as a series of head-to-head contests between each pair of candidates.

Experts claim these approaches can help reduce polarisation, and prevent extreme candidates from pulling parties in directions a majority of members don’t support.

What’s wrong with plurality voting?

Plurality voting, also known as “first past the post”, is the name for a poll where voters indicate a preference for a single candidate, usually by putting a cross in a box next to their name. The winner is the candidate who attracts the most votes, even if they do not receive a majority.

In a two-candidate race, plurality voting is unproblematic — whoever receives more than 50% of the vote wins. Yet political primaries typically involve multiple candidates, and the vote can be spread very evenly among the candidates. This makes getting an accurate picture of voters’ preferences far more complicated.

Imagine a scenario where 70 percent of the vote is split evenly between four moderate candidates, while the remaining 30 percent goes to an extreme candidate whose values put them at odds with most party members. 70 percent of the party would prefer “anyone but” this extreme candidate, but they have no way of making this clear. They split their vote evenly among the moderate candidates, and the extreme candidate emerges victorious.

Playing into the hands of extreme candidates

This is what some believe happened in the early stages of the 2016 Republican primaries. Indeed, Donald Trump failed to win any of his first 17 primary victories by a majority. In Vermont, for example, he attracted only 32% of the vote, yet the “anti-Trump” vote was split across multiple candidates, meaning he emerged as the winner.

In times of increasing polarisation, this scenario is becoming more and more common, especially in open primaries. Which is why some believe that plurality voting plays into the hands of extremists.

Fear of outcomes like these can end up leading people to engage in tactical voting. In this scenario, people are liable to vote for the candidate they believe has the best chance of beating the extreme candidate. This means that the ballots cast don’t really express the true wishes of the voters. The entire contest gets skewed by a single extreme candidate, whom most would “vote out” of the whole contest, if they only had the chance to do so.

Two round / Top-two primaries

One way of overcoming the “split vote” problem is to simply hold an additional round of voting. In a “top two” primary, if no candidate emerges with more than 50% in the first round, a second round is held between the two highest-ranking candidates. 

This method has been used in several French presidential primaries by the Socialist Party, the Republicans, and the green alliance “le pôle écologiste”, mirroring the two-round method of the presidential election itself. It has also been adopted by three US states—California, Louisiana, and Washington—in primaries for both major parties, where some experts claim it has helped to reduce polarisation.

Note that while using this approach, as long as 51% of voters prefer “anyone but” a particular candidate, this candidate cannot win, making it harder for an extremist to cause a major upset.

Ranked-choice and instant runoff voting

Using multiple rounds of voting allows us to get a more accurate picture of the electorate’s preferences. But there are also methods which allow more complex preferences to be expressed on a single ballot.  

In ranked-choice or “ordinal” systems, voters rank the candidates on the ballot paper in order of preference, writing in a “1” next to their first choice, and so on. In some cases, voters are required to rank all of the candidates standing in the election. Others limit the number of preferences they can express. For example, in the 2021 Democratic Party mayoral candidate primaries in New York, voters were allowed to rank up to five of the candidates from the 13 listed on the ballot.

The most common approach to calculating the result in these cases is via Instant Runoff Voting. If your first choice of candidate is eliminated in the first round of counting, your second preference is counted instead. This process is repeated until a candidate receives a majority of votes.

This system allows everyone to vote for their favoured candidate, while also ensuring that preferences among the remaining candidates are clearly reflected in the count. Once again, it is impossible for an extreme outlier to win so long as 51% of voters prefer “anyone but”. A simulation of instant runoff voting suggests that in the 2016 US Presidential Election, Trump would have been defeated in several key primaries. 

The condorcet method

At the start of this article, we saw that things get complicated once multiple candidates are involved. In a head-to-head, by contrast, the winner is simply whoever gets a majority of the votes. What if there were a way to treat a multi-candidate field as a series of head-to-head competitions? 

Enter the Condorcet method—named after the French philosopher and mathematician the Marquis de Condorcet who began advocating its use in the 18th century. 

The idea is simple. Voters rank the candidates in order of preference, just as in ranked-choice voting. The ballots are then counted multiple times, simulating a series of head-to-head contests between each pair of candidates. Whenever one candidate is ranked higher on a ballot paper than their competitor, this counts as one vote for them. 

This is repeated for each pair of candidates. The winner is the candidate who wins all of their head-to-head contests. This provides a comprehensive picture of each and every voters’ preferences, and helps avoid a situation where a large number of voters are deeply unhappy with the results.

Of course, it is possible that no one candidate wins all of their head-to-head competitions. In this scenario, we are left with a “Smith Set” of preferred candidates, and there are different approaches to how to resolve things from this point on. 

One variation of the Condorcet method, the Schulze method, has been employed in primaries by the Pirate Party in Sweden, Germany, Australia and several other countries. The biggest drawback with the method is its sheer complexity, which leaves all but the most inquisitive voters in the dark as to precisely how the final result is calculated. 

The condorcet loser paradox

Let’s consider how the extreme candidate from our example will get on under the Condorcet system. It’s evident that they will not emerge as a winner. Instead, with 70% of voters always preferring another candidate, they will lose every single one of their head-to-head contests. 

That’s why among voting theorists, the extremist’s victory under plurality voting is known as the “Condorcet Loser Paradox”—because plurality voting hands a victory to the candidate who would lose a Condorcet vote.

Reducing Polarisation

This list of methods in this article is by no means exhaustive. For their primaries, the Spanish party Podemos use a variety of the so-called Borda count, a method developed by Condorcet’s rival. And the ill-fated French primaire populaire, a leftist primary to select the candidate for the 2022 French presidential election, used majority judgement

The good news is that all of the alternative voting methods named here avoid the Condorcet Loser Paradox, making them all viable alternatives to first-past-the-post, allowing the members and the public to get involved in selecting candidates, while also reducing the risk of a polarising nominee walking away with the prize. 

An earlier version of this article was published on 29 March 2023.

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