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Cosmic.vote #1: Introducing Majority Judgment

Mister Ticot
Jul 14 · 7 min read

The ambition of Cosmic.vote is to bring decentralized organizations to Stellar. No wonder that Majority Judgment has been chosen for its first contract: when it comes to decentralized governance, having a well-designed, robust voting system is an absolute game-changer. Let’s see why Majority Judgement is superior in this matter.

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Origin

Majority Judgment is a voting system invented in 2007 by Michel Balinski & Rida Laraki. Those scientists based their design on decades of studies regarding voting systems — a field known as social choice theory.

The point of Majority Judgment is to combine the advantages of previous voting systems while avoiding as many flaws as possible. While a perfect voting system has been proven impossible to achieve, Majority Judgment appears to be the closest to an ideal solution.

A First Vote

With Majority Judgment, voters give a grade to each candidate. The votes are then combined to determine candidates’ ranking. This process determines the winner in a single round of voting.

As Majority Judgement contracts are now available on Stellar, why not giving it a try:

  1. Use the poll widget below, or open the poll page on Cosmic.vote.
  2. Pick a grade for each option, then click on Cast Your Vote!.
  3. Within the signing side-frame, select a wallet to sign with.
  4. Browse to your wallet by using either Go to (wallet) or the QR Code.
  5. Sign the transaction.
  6. Close the signing side-frame & enjoy the results. :)
  7. Congratulations! You just participated in your first Majority Judgement election!

Counting Votes

Grades received by the candidates are sorted from the worst to the best. We take the candidate median grade, which we call the “majority grade”, to be the result of that candidate. To break ties, we join the completion of the grade to the result.

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The majority grade & its completion

Worth noting, each candidate has a score that has a meaning of its own. This is different from most voting systems, where candidates’ scores are relatives to each other.

Advantages

While studying voting systems, scientists came up with several “qualities” those may have or may not have. Let’s check a few of those, and see how Majority Judgment behave compared to habitual voting systems.

This will give show how we compare voting systems together, and why Majority Judgment is the better candidate for community governance.

Independence to Irrelevant Alternatives

A group of friends decides to vote for which food they’ll eat tonight. All agreed that something unhealthy has to be ingested, but the exact format remains subject to debate. We’re facing the classical alternative: Pizzas, Hamburgers, or Hot-Dogs.

In the Alpha universe, our friends decide to rely on Majority Judgement to take the decision. They end up with these results:

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In the Beta universe, they’ll go with an ordinary voting system, Plurality Voting. Here’s what they got:

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However, the tricky Alice points out that Pizzas with a creamy base are a meal of its their own sort & deserve a dedicated entry. Our friends decide to take her point & to vote a second time:

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So what happened here? As you can see, adding a new candidate moved Pizzas out of the winning place. While a majority of our friends are pizza lovers, adding a second kind of pizza divided the votes and led to the victory of hamburgers.

In social choice theory, this flaw is known as “Weakness to Irrelevant Alternatives” and describes a voting system in which adding a non-winning candidate can nonetheless change the election outcome.

This is considered as one of the nastiest flaw voting systems can have. Indeed, a documented electoral strategy consists of funding oppositions to multiply the alternatives & erode the voting base of a main opponent.

Majority Judgment dodges this issue elegantly: as each candidate has a score of its own, adding or removing entries won’t change the order of the other candidates:

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Superb example of consistent ranking, although here my “irrelevant alternative” actually got the victory (T.T)

Resistance to Strategic Voting

In the above situation, the Pizza lovers could anticipate the results and decide to all vote for the pizza option that is the more likely to win. Likewise, the hot-dog lovers may decide to unite under the hamburgers — even while this is not their favorite meal — to avoid the unbearable, meat-poor pizzas.

Voting for a candidate that is not your real favorite in order avoid a candidate that you’d like to reject is generally referred to as strategic voting. While this strategy is well known & widely used, it is a bigger issue than one might think…

The point of voting, besides generating a clear-cut decision, is to summon something that we could call the “collective will”. But how could we possibly achieve that with a system that pushes people to vote differently than what they actually think? The whole process is doomed to fail!

Thus, Resistance to strategic voting is a fundamental property for a voting system to have. In practice, this is impossible to achieve fully — but there are degrees of resistance.

On that matter, Majority Judgment has been shown to perform better than its alternatives. There are several reasons for that. Some are quite technical and would require an entire article, so to let’s stay on the surface here:

  • Voters judge every candidate, so they can vote against the candidate they don’t like without having to alter their real preferences.
  • Extreme grades, as long as they are in minority, won’t change the median grade — in the words, overshooting won’t impact the results much.
  • Giving the best grades to your favorites & dismissal to candidates that don’t fit you is what is expected… There’s not much you can do beyond that.
  • Majority Judgement creators proved that, most often than not, giving grades that don’t reflect your real preferences will impact the results in the wrong direction. Thus, voters are incentivized toward integrity.

Explicit Consent

As I mentioned earlier, the function of voting is sometimes more about making a clear-cut than a good cut. What’s magical with Plurality Voting is that, no matter how bad the candidates are, you’ll always get a winner!

That’s another point where Majority Judgement makes a massive difference: it allows for rejection of all the candidates, which is a desirable property as it implements the notion of explicit consent.

Back to our example, you cannot tell, by looking at Plurality Voting results, whether the voters were pleased by the options they had or on the contrary selected the candidate they hate the less.

On the other hand, here’s what would happen with Majority Judgement in case our buddies were not in tune with the food proposal:

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A no-winner case in Majority Judgement

This property is similar to jury outputs − for example when judging wines or ice skating. With Majority Judgement, candidates are not only ranked: they also receive an explicit (and generally useful) appreciation by the community.

Conclusion

When it comes to governance, having a well-designed, robust voting system is an absolute requirement. Luckily, people such as Michel Balinksi & Rida Liraki, as well as many other scientists, have covered this problem in great extents.

Leveraging their work, Cosmic.vote goes to the point by implementing, before anyone else in the industry, the best available solution on that matter. As to know if this will turn into a successful adventure & definitive advantage for Stellar… Well, I guess that’s a community decision ;)


Pedagogic Content

Mr President, did you won this election? [fr/en subtitles] − Shows that an election’ result may depend as much on the voting rules than on the votes.

Scientific Content (Publications of M. Balinski & R. Liraki)

− [2011, Book] Majority Judgment: Measuring, Ranking and Electing

− [2007] A theory of measuring, electing and ranking
− [2010] Election by Majority Judgment: Experimental Evidence
− [2013] How Best to Rank Wines: Majority Judgment
− [2014] What Should “Majority Decision” Mean?
− [2020] Majority Judgment vs Approval Voting

About Majority Judgment Inventors:

Michel Louis Balinski was emeritus director of research of the CNRS at the Ecole Polytechnique (Paris). He was the Founding Editor of Mathematical Programming and a former President of the Mathematical Optimization Society. In 2013 he was awarded the John von Neumann Theory Prize by INFORMS for “fundamental, sustained contributions to theory in operations research and the management sciences.” [More…]

Rida Liraki is director of research CNRS in computer science at LAMSADE (University of Paris Dauphine) since 2013 (and researcher at the CNRS since 2001). From 2006 to 2017, he was professor at the École Polytechnique and since September 2017, he is professor at the University of Liverpool (computer science department, part-time). [More…]

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Applications & developer resources for Stellar

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