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New Voting Rules Could Finally Resolve Brexit

New Voting Rules Could Finally Resolve Brexit

Monday, 11 November, 2019 - 06:30

As the UK prepares for elections on Dec. 12, the outlook for Brexit is as unclear as ever. Among the options before voters are leaving the European Union without a deal (the Brexit Party); leaving with Prime Minister Boris Johnson’s deal (the Tories); hammering out a new deal that would then be subject to a second referendum (Labour); or simply revoking Brexit (the Liberal Democrats).

It’s also possible that no party gets the necessary majority to advance its proposal, and Britain’s political system will continue to block progress altogether.

There are better ways to deal with highly complex and controversial issues in a democracy. The House of Commons, like many legislatures, votes on binary choices: aye or no. This system usually works, and ensures that new bills can pass into law only if they’re backed by a majority. But it may also lead to gridlock, as with Brexit. Faced with an extraordinary situation and a hard deadline, Parliament should adopt alternative voting rules — ones that, by their nature, would force compromise.

Ranked-choice voting, which requires each voter to express a first, second and third choice (or more), helps reach a consensus by aggregating preferences. It has been employed in elections in Australia and Ireland since the 1920s, and more recently in a handful of American cities and in Maine. To use it in legislative voting is less common, but at this point it could be the most viable way to resolve Brexit.

For simplicity, let’s consider only three options: no deal (N); Boris Johnson’s deal (D); and a referendum on Johnson’s deal (R). If lawmakers had to vote for one option only, it’s likely that none would pass and the deadlock would continue, as happened after Parliament rejected former Prime Minister Theresa May’s deal three times.

With ranked-choice voting, a lawmaker who is committed to remaining would mark her first choice as Referendum. But she could indicate that if Referendum didn’t get a majority, then Deal on its own would be far preferable to No-deal. She’d then cast an RDN ballot, in that order. Another legislator might support Deal, then favor Referendum over No-deal, and therefore cast a DRN ballot. Others might prefer anything to Referendum and cast NDR or DNR ballots.

Imagine that among 100 voters, the ballots are distributed as follows: 46 RDN, 10 DRN, 24 DNR, 18 NDR, 1 RND and 1 NRD. Those numbers are made up, but plausible. If we establish that the winner is the option that gets the most first positions, Referendum wins with a score of 47. But only a minority of voters have put Referendum as their first choice. To build a consensus, we’d have to consider second choices as well.

There are plenty of reasonable ways to do so.

Under an instant runoff system, which is used in the Irish presidential election and elsewhere, the option that got the least first preferences — in our example No-deal, with only 19 — would be eliminated. The 18 NDR ballots would now count as first-choice ballots for Deal, while the NRD ballot would count toward Referendum. In this case, Johnson's deal would come out on top with a majority of 52. When more than three options are offered, this process is repeated until a majority emerges.

Another option, known as the Bucklin system, after the American politician James W. Bucklin, stipulates that if no option secured a majority of first choices, then first and second choices would simply be added, resulting in 98 for Deal, 58 for Referendum, and 44 for No-deal. In this case, too, Johnson’s deal would be adopted.

Alternatively, points could be attributed to first, second, and third choices, for example 2, 1, and 0. This is known as the Borda count system, for the French mathematician Jean-Charles de Borda. With 34 first places and 64 second places, Deal would win with a total of 132 points, ahead of Referendum (105) and No-deal (63).

The Marquis de Condorcet opposed the Borda count and instead proposed using pairwise comparisons. There are 52 ballots where D is ranked ahead of R, 57 where R is ranked ahead of N and 80 where D is ranked ahead of N. Consequently, D would be declared the Condorcet winner. However, this system could result in a deadlock. Suppose three voters cast circular ballots, RDN, DNR, and NRD: Two favor R over D, two favor D over N, and two favor N over R. This illustrates the famous Condorcet paradox, later formalized by the American economist Kenneth Arrow in his impossibility theorem, which states that collective preferences can be cyclic even if individual ones aren’t.

In a more traditional variant, called a majoritarian system and used in many presidential elections, voters choose only one option in a first found, then the two options that get the most votes advance to a second round, where the final decision is made. In our example, voters would choose between Referendum and Deal. At this point, another two-round process might be logical: (1) Do you approve Johnson’s deal? (2) If not, should the UK leave with no deal, or remain in the EU?

Most important, all of the above systems would rule out No-deal, the least popular option, and allow a consensus to emerge that a majority could at least live with. In our simplified example, Johnson’s deal would win in many voting systems, as the best overall first or second choice, but a referendum could realistically win as well.

Determining the will of the people is a delicate art. Given the current gridlock, the British Parliament should consider temporarily adopting new voting rules — ones that would force compromise, better reflect the will of the people and help restore their faith in their democratic institutions.


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