Frequently Asked Questions

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What is a good voting system?

An election is a mechanism used to qualitatively measure an opinion, in order to choose, elect or rank. A good voting system must therefore allow each voter to fully express his or her opinion, and then show a consensual and consistent collective preference. Neither traditional majority voting systems nor proportional voting meet these criteria.

How can we improve our voting system?

Voting is the most fundamental act in a democracy. By voting, we decide on how we organise our social life, we resolve crises and build our future. And we often vote: at school, in our companies, in political or professional elections, in sports associations, etc. We vote in full confidence, because of our common trust in our voting systems – and from there derive the legitimacy of the vote’s results and the peaceful acceptance by all of its consequences.

Unfortunately, we vote badly: whether we use simple majority or proportional voting, uninominal or plurinominal systems, our voting methods are outdated and do not account for the opinion of the electorate. They are all based on the same practice: give voters a ballot, ask them to choose a single option, and sum of votes for each option.

These methods are nonsensical and weaken public confidence in our elections:

    • They do not allow voters to truly express themselves: although voters have an opinion – positive or negative – on all candidates, they are only allowed to support a single candidate, and therefore also forced to endorse it fully. These voting systems permit no nuance. By voting for a single candidate, voters say nothing of their opinions about other candidates reveals absolutely nothing about what he thinks of others – while the same “no” to two different candidates can hide extremely diverse opinions.
    • They often put voters in front of an absurd strategic choice: if I do not join any candidate or if I hesitate between several, should I vote “useful”, “against”, “by default”, or blank?
    • They result, in the absence of the real winner supported by a majority, in democratic accidents. The result of an election – and therefore the true choice of the majority – can change simply with the presence of an extra candidate that would syphon votes away from like-minded candidates.

What are the strengths of Majority Judgment?

Majority Judgment satisfies the criteria of a “good voting system”. It measures the opinion of voters, accounting for its complexity, indicates precisely the legitimacy received for each candidate (by separating strongly positive opinion from less positives opinions, for instance), and designates a consensual winner.

    • Voters can express themselves fully: they give an opinion on all candidates;
    • The best candidate wins and his legitimacy, through the “mentions”, is precisely measured;
    • The notion of “strategic” or “useful” vote disappears, as several candidates can be judged positively without impacting each other;
    • “By default” or blank vote no longer exist because it is possible to judge all candidates negatively;
    • Majority Judgment eliminates “Arrow’s paradox”, as adding or removing minor candidates does not impact the opinion given to other candidates, and therefore the winner.
    • Votes is extremely difficult to manipulate: blocks of voters who would try and influence the vote by giving disproportionately positive or negative opinions, with no nuance, can only have minimal influence on the results.
    • The ability to give an opinion on all candidates strengthens consensus, while traditional voting mechanisms quickly eliminate voters’ second choices.
    • Power goes back to the voters: if all the candidates are judged “insufficient” or “rejected”, the election can be carried out anew with new candidates.

Isn’t Majority Judgment more complex than a traditional majority vote?

For voters, it is straightforward and intuitive to have and give their opinion on each candidate running for election, rather than to single out one candidate or classify them from first to last. Using Majority Judgment, each candidate obtains roughly the same number of votes. All it takes to obtain the real winner is to sum the “mentions” received by each candidate: for instance, Candidate A receives 20 “very good” mentions, 15 “fair”, 10 “insufficient”, etc. This gives us each candidate’s “merit profile” and “majority mention”; the majority mention of a candidate is simply the best mention approved by a majority of voters. So, if at least 50% of voters think that Candidate B is “good” or better, his or her majority mention will be “good”.

In case of a draw – when two or more candidates receive the same majority mention – the candidate with the smallest number of voters disagreeing with the majority mention wins. For instance, of Candidate A has a 63% of voters thinking he is “very good” or better, then 27% of voters disagree with that mention. If Candidate B has 58% thinking he is “very good” or better, then 42% disagree with that mention and Candidate A wins.

All around the world, more complex voting methods have been used for decades for political elections, such as the alternative vote in Ireland and Australia. Although these polls sometimes require several days of counting, this has been hampered their use.

Finally, it should be noted that several Swiss cantons have already adopted “bi-proportional” referendums – a system developed by Michel Balinski, one of the inventors of Majority Judgment. This sophisticated proportional system, much more complex than Majority Judgment, requires an algorithm and a computer to calculate the result!

Has Majority Judgment already been tried?

Majority Judgment has been the subject of many experiments and uses at the local level, for instance to elect professors and lecturers at the Universities of Montpellier, in France, and of Santiago, in Chile, at Polytechnique and at the Ecole des Arts et Métiers.

In national elections, Majority Judgment was experimented with and used in the following cases:

    • In 2007, in the French city of Orsay, an experiment was carried out in three of the city’s twelve polling stations for the presidential election;
    • In 2011, a primary was carried out by the French Socialist Party in polling stations in Fresnes and Alfortville;
    • In 2016, an open primary was organised by [ADD LINK], involving over 50,000 online voters;
    • In 2017, over 52,000 online voters used Majority Judgment to assess the candidates of the first round of the French presidential election, in an experiment by the CNRS, Paris-Dauphine University and Polytechnique.

Mieux Voter seeks to replicate and expand experiments using Majority Judgment, especially with local communities, for which it can be a powerful vector for local democracy, such as for citizen consultations, local referendums, or participative budgets.

Why not grade candidates?

Grade voting requires voters to give a numerical score for each candidate. The winner is the candidate with the highest average grade. It has been experimented with a number of different grade: -1, 0 and 1; 0 and 1; 0, 1 and 2; from 0 to 10; from 0 to 20; from 0 to 100, etc. This system is studied in depth in chapter 17 of Michel Balinski’s and Rida Laraki’s book Michel Balinski’s and Rida Laraki’s book at chapter 17.

Grade voting has both advantages, such as people’s habit of giving grades, making the process easy to grasp. However, it also suffers from grave disadvantages. First of all, support for a candidate is not a measurable physical quantity. When measuring a temperature, for instance, the difference between 0°C and 1°C is exactly the same as between 99°C and 100°C; this makes it possible to calculate average temperatures. However, in the case of votes, we cannot ascertain that the difference between a 4/10 and a 5/10 is the same as between a 7/10 and 8/10. The exact meaning of grades would first need to be defined and, even then, people’s interpretation of grades will vary. Because of this uncertainty, the average of these grades would not mean anything.

Even more problematic, voting systems based on an average of grades are the most susceptible to manipulation of all the voting methods. Indeed, it is sufficient for a small number of voters to exaggerate their grades (by giving the top grade to their number one choice and 0 to everyone else) to directly affect the winner or ranking. By contrast, Majority Judgment is the voting system least susceptible to manipulation, as it does not rely on averages (see above).

In order to properly use grades, as is the case for diving, figure skating or wine ranking, one must draw up mentions and then associate a grade to each mention. For example, since 2006, Denmark has been using a numerical and verbal scale to evaluate students: 12 (A, Excellent), 10 (B, Very Good), 7 (C, Good), 4 (D, Fairly Good), 2 (E, Fair), 0 (Fx, Insufficient), -3 (F, Very Unsatisfactory). This amounts to using the very mentions proposed by Majority Judgment.

Why not ranking candidates?

Ranking candidates also seems like an obvious and easy solution but, likewise, the flaws of this method are numerous and sometimes serious:

    • Ranking candidates (in order: the favourite, the second-best, all the way down to the least preferred) is actually very complex as soon as you reach more than a handful of candidates;
    • Ranking candidates does not allow voters to fully express themselves, as it is impossible to give the same ranking to two candidates, let alone to express the intensity of a preference;
    • As all rank-based methods, it suffers from the Arrow’s paradox: adding or removing a candidate, even a minor one, can drastically impact the ranking and the winner.

For decades and until recently, figure skating panels used a method based on rankings. In 1997, Candeloro was ranking 3rd before the performance of a skater who placed last. Because of Arrow’s paradox, that low-ranking skater impacted the ranking, bumping Candeloro to 2nd place, with no better performance or effort on his part. The following uproar and scandal led to the adoption of a new method.

A similar scenario happened in France in 2002, when Lionel Jospin, leader of the major left-wing party and a favourite of the election, was eliminated in the first round (placing third) because of the presence of several minor left-wing candidates who syphoned votes away from him. Despite being the second choice of many left-wing voters, Jospin and all other left-wing candidates were eliminated. France still uses the same two-round majority voting system. The problem with this election was not the presence of several candidates but the voting system itself: democracy should allow for the presence of different opinions, even similar to each other.

Will Majority Judgment not favour the centre?

Majority Judgment does not favour any political tendency a priori. It gives an equal chance to all candidates. A mathematical demonstration proves this and various practical experiences confirm it (see Chapter 19 of Michel Balinski’s and Rida Laraki’s book).

This recurring criticism comes from a confusion between Majority Judgment and grade voting. In order to understand this, imagine that candidates are graded on a scale from 0 to 10. Candidate A receives the top grade (10/10) from 51% of voters and the lowest grade (0/10) from 49% of voters. The majority grade of this candidate is 10/10, as more than a majority of voters (51%) have given him this grade; however, his average score is 5.1/10. Candidate A has a chance to win with his majority score (similar to Majority Judgment), but much less so with his average score (similar to grade voting).

With the traditional single-candidate ballot, candidates “share” the electorate. As a result, depending on the number of candidates, it is possible to win (if there is no second round) or move to the second round with only 15% or 20% of the vote. This means that candidates have no incentive to seek the support of at least 50% of voters. The functioning of the two-round single-candidate ballot ensures a so-called “majority” to the candidate placing first in the second round, while this by no means guarantees the actual support of a majority of the electorate. For instance, in the same 2002 presidential election, Jacques Chirac obtained over 82% in the second round; however, this score did not indicate a broad support for his ideas among the electorate (he had received less than 20% in the first round) but a rejection of his extreme-right opponent.

This functioning of single-member voting encourages candidates to choose one of two strategies – or strike a balance between the two:

    • adopting a divisive posture to capture a small, but faithful, segment of the electorate; or
    • “make everyone happy”, to gather a few voices from everywhere – the so-called “soft consensus” candidate.

By contrast, Majority Judgment results in a mention given by a majority of voters. A divisive candidate may get strong support from 20% of the electorate but be rejected by a majority of voters. Likewise, the “soft consensus” candidate may obtain 20% of favourable mentions from those he has seduced, but fail to gather support from the rest of the electorate.

We must not confuse a “true consensus” with a “soft consensus”. Majority Judgment gives no reward for either divisive or falsely unifying candidates. It does, however, reward obtaining the best mention by a true majority of the electorate – meaning the support of a majority.

With Majority Judgment, can we vote blank?

Blank ballots usually mean: “I do not approve of any of the candidates.”

With the traditional single-candidate system, blank ballots are managed as a “special case” and treated separately.

With Majority Judgment, however, there is no need for exceptions and it is entirely possible to express dissatisfaction with all candidates. In order to “vote blank” with Majority Judgment, one simply needs to assign the “rejected” mention to all candidates. This opinion will be taken into account alongside all and therefore counted for what it really means.

Wouldn’t voters be tempted to cheat with Majority Judgment?

Why would they be? Because they are asked to express the support they give to all candidates instead of choosing one? Because they would “exaggerate” the mention they assign to their first choice and “reject” all others? This is dubious at best, since the overwhelming majority of voters specifically want to express themselves when they vote.

By attributing “rejected” to all but one candidate, a voter would actually deprive himself of providing nuances about his second or third choices. If he cheats, it is because he thinks his favourite candidate does not have a solid chance; so why lose the possibility to indicate which of the other candidates would be his “second favourite” or “third favourite”.

Moreover, by attributing an exaggerated “excellent” to his favourite candidate instead of a mention more in line with his true convictions, a voter does not actually affect the result of the vote; at least, unless a full 50% of all voters have a better opinion about the candidate than he does. Likewise, by attributing an exaggerated “rejected” mention to an unpopular candidate instead of a mention more in line with his true convictions, a voter does not affect the outcome of the vote; unless a full 50% of all voters have a worse opinion about this candidate than he does. For these reasons and because Majority Judgment does not rely on averages, even if voters did cheat by exaggerating their opinions, the actual impact would be minimal.

Let’s imagine a classic case with two candidates, A and B, both receiving “good” as their majority mention. Imagine that a voter, Theo, prefers A over B. Theo may be tempted to give A an “excellent” mention and “reject” B. In most cases, this will have no impact on the outcome. Indeed, there are two possibilities:

    • Case 1: Theo thinks that A deserves “good” or more and that B deserves “fair” or less. This will be the case for the vast majority of voters preferring A over B. In this case, Theo’s exaggeration would have no impact using Majority Judgment.
    • Case 2: Theo gives both candidates (1) “fair” or less or (2) “good” or more. But then, Theo does not have a strong enough motivation to exaggerate and will probably prefer to vote honestly. Indeed, in case 1, he does not like either candidates and, in case 2, he actually likes both candidates. Finally, even if he is convinced to cheat, lowering B’s mention in case 1 or increasing A’s mention in case 2 will not change anything. This further limits voters’ ability to cheat.

This reasoning is generic. A theorem (ADD LINK to the MIT Press Book) further shows that, in the rare cases where a voter may actually have influenced the outcome of the election by cheating, the scope of this influence is very limited: if the voter can help his favourite candidate, he cannot hurt his competitors, and if he hurts the competitors, he cannot help his favourite candidate.

Conversely, with the grading vote, exaggerating always has an effect and a potentially potent one. Increasing Candidate A’s grade from 7 to 10 directly increases his average, and lowering B’s grade from 5 to 0 lowers his average. This explains why, in all simulations, grading vote is the most susceptible to manipulation and Majority Judgment is the least (see chapter 19 of the book [ADD LINK]).

With Majority Judgment, the optimal strategy for the vast majority of voters is simply to vote honestly because it gives them a better voice in the election and because exaggerating will not change the winner anyway.

This post is also available in: French