Which Voting Rule Will Fix French Politics?
The French political system is based on electing a president via the plurality with runoff rule. The rule requires that each voter votes for the most preferred candidate and the two candidates with the highest number of voters are shortlisted for a second round. In the second round, the candidate that is preferred by a majority of voters is selected. Just like the first past the vote, plurality with runoff is a hugely flawed voting rule that is highly susceptible to the spoiler effect. In simple words, the vote bank of a sizeable group of voters can be easily split up among similar candidates.
The following is a simple example that shows how the rule used in France is flawed. The voters express preferences in decreasing order of preference from left to right.
20%: Y>X1>X2>X3>X4>Z
20% Z>X1>X2>X3>X4>X
15%: X1>X2>X3>X4>Y>Z
15%: X2>X1>X2>X4>Y>Z
15%: X3>X1>X2>X4>Y>Z
15%: X4>X1>X2>X3>Y>Z
The plurality with runoff rule would select Y and Z as the top two candidates for the second round although 60% of the voters prefer one of X1, X2, X3, or X4 to be selected. The reason none of no `X’ candidate is selected is because the votes of the majority are split off between X1, X2, X3, and X4. In the example above, a majority of voters prefers any candidate among X1, X2, X3, and X4 over Y and Z. From this perspective, one would expect a desirable voting rule to select say X1.
New Developments
The type of spoiler effect flaw as described above has had critical consequences in French politics. For example the left’s broad support has been dilapidated because of the spoiler effect, thereby occasionally opening the doors for an extreme right wing politician to squeeze through to the next round. In view of the challenges, this year, the French left decided to take a more proactive and coordinated approach towards ensuring that a representative candidate makes it to the final round. The Primaire Populaire (People’s Primary https://primairepopulaire.fr) is a grassroots initiative with the ambition to unite France’s divided leftist parties behind a representative candidate for the April 2022 presidential elections. The primaries were held in late January and the results were then announced.
Majority Judgement as the Voting Rule for Primaries
The voting rule used for the ‘unofficial’ Left primaries is the Majority Judgment rule. Inspired by the evaluation considerations in wine-tasting, the Majority Judgement rule asks voters to give each candidate a grade according to how well they like them. The rule first finds the median grade of each candidate and then identifies the candidate with the best median grade. The median grade of the candidate is found by ordering the grades given to the candidate by the voters from lowest to highest (the same grade can be repeated) and the median grade of the candidate is in the middle of the list. The candidate with the best median grade is the winning candidate. If multiple candidates have the same best grade, then the unique winner is realised by removing (one-by-one) any grades equal in value to the shared median grade from each tied candidate's list. French academics Michel Balinski and Rida Laraki who made a spirited case for Majority Judgement rule in a paper and then in a book. It is vigorously supported in the slick website mieuxvoter.fr but also has several critiques (see, e.g., one by Steven Brams).
Majority Criterion
One of the reasons why Primaire Populair has emerged is because the current Plurality with runoff is victim to the spoiler effect and does not implicitly coordinate the preferences of the Left. The coordination can be achieved in some sense if a voting rule satisfies a fundamental property that is rooted in majority preferences: if a majority of voters prefer a set of candidates above all others, then one of the supported candidates should be selected. A voting rule that satisfies the property provides a coordination device so that a majority of cohesive voters do not need to make agreements among themselves when expressing their preferences. There are several voting rules that do satisfy this property including the single transferable voting rule used in Australia and the expanding approval rule.
Moving Forward
The emergence of the Primaire Populair is an interesting movement rooted in the observation that the current French voting system is broken and there is a need for innovation and careful deliberation. Typically, status-quo forces are highly resistant to changes in rules of the game. Does the country have the appetite to change the voting rule? Time will tell.
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