Before we get started, let’s take a moment to think about some of the voting experiences we’ve had. I remember when I was in primary school, our teachers would have us vote for a class or courses representative, right? That was my first memory on voting. As we grew up. Every time there’s a national election, we get to choose our country’s leaders. And even now, as a student, we still cast votes at the end of each semester to evaluate the courses we’ve taken.
In general, voting is a big part of our lives, playing an important role in decision-making. But here’s the thing—do we really understand how the voting rules affect the outcomes? To be honest, I had no idea before taking this course. Things like the domination paradox, different kinds of consistency, and strategic manipulation, these kind of terminologies were absolutely new to me.
So Today, I’m going to talk about the voting rules, which are Majority Judgment versus Majority Rule.
I’ll divide my presentation into four parts:
- Majority Rule
- Majority Judgment
- Handling Polarisation in Voting
- Resisting Strategic Manipulation
Let’s start with Majority Rule. The idea is pretty simple: whoever gets the most votes wins. It’s straightforward, especially when there are only two options. Whether we’re choosing between two leaders, two policies, or even two ice cream flavours, the Majority Rule feels like the natural choice. But sometimes, it doesn’t seem fair. One issue is called Condorcet consistency. The idea is that if a candidate beats every other candidate in a head-to-head comparison, they should be the overall winner. The Majority Rule aims to do this, but it often fails, especially when there are more than two candidates.
For example, as you can see here, we have three candidates: X, Y, and Z. After the pairwise comparison, we can see that X beats Y, Y beats Z, and Z beats X, forming a Condorcet cycle. So, there’s no clear winner because each candidate is preferred over another. Even though X got 35, has the most first-choice numbers, the majority prefers Z over X in the direct comparisons. This is the Condorcet Consistency Problem. It highlights some weaknesses in Majority Rule.
Another problem tied to Majority Rule is the domination paradox. Let me give you an example to explain this. Look at this table: Candidate A clearly outperforms Candidate B, with more 5-star ratings, more 3 stars or higher, and fewer 1-stars. But suppose we only count the stars above 3, using a simple majority rule to calculate. In that case, Candidate B got 51, and the Candidate A only got 50. This is the Domination Paradox. Which means the voting rules can lead to an unreasonable result that doesn’t match the overall preference. So we need a better voting rules.
Now, let’s introduce Majority Judgement. There is an example of restaurant voting in our campus. We have three restaurants: The Foundry, Ancestral, and Café 1894, the clients voting based on the three criteria: food quality, service, and atmosphere. The voting is on a scale from 1 to 5 stars, where 1-2 stars are considered as “Poor,” 3-4 stars are “Average,” and 4-5 stars are “Excellent.” Compare to the traditional voting rules, the Majority Judgment, instead of just picking a favourite restaurant, each restaurant is evaluated by this kind of criteria or metrics. So that is the way how Majority Judgement collect the votes.
In majority judgement, we need to focus on 3 key components: Merit Profile, Majority Grade, and Majority Gauge:
In this diagram, we can see 3 types of assessments—Poor (red), Average (yellow), and Excellent (blue). The height of each bar represents the number of votes the restaurant received in each category, which is the merit profile. This gives us an overview of how the restaurant performed.
You can also see a dashed line across here, which represents the middle point or median value, where half of the voters rated it higher and half rated it lower. Essentially, this grade indicates the central tendency of the evaluations about the restaurant.
The Majority Gauge provides more detail and displays distribution around the majority grade. It’s telling us something like, 30% of the assessments are above Excellent, and 20% are below Poor. By apply this metrics we can see how strongly people feel like about the restaurant.
Now, let’s move onto polarisation in voting systems. So, what is polarisation? In voting systems, polarisation happens when voters are split into two groups with strong and opposing opinions or stances. We see this often in political elections. For example, in the 2012 French presidential election, voters were divided between two candidates—Hollande and Sarkozy. Each candidate had strong supporters, and these groups clearly disagreed with each other. This kind of division brings challenges for any voting system.
So, how do Majority Judgment and Majority Rule handle these situations?
Well, with Majority Rule, it’s simple—it just displays which side has more supporters. But with Majority Judgment, Instead of just choosing yes or no, they voting by the multi dimension. This displays a more specific view of what people think, even if they completely agree or disagree. So, in polarised elections, Majority Judgment gives a better metrics to express how people thinking, which is great!
Finally, let’s talk about one of the biggest problems in any voting system: strategic voting.
So, what is strategic voting? Well, first of all, strategic voting is dishonesty. They don’t picking their favourite option directly. They try to game the voting system to get benefits for themselves. For example, as we can see here we got 3 candidates A, B, and C, under the honest voting, candidate A got 40% of the votes, candidate B got 30% and candidate C got 30%, and the candidate A is an apparent winner. Right? But suppose 20% of the voters of candidate C shift to candidate B, the winner will shift from A to B.
There’s even a famous rule called the Gibbard-Satterthwaite Impossibility Theorem. It says that in any voting system with three or more options, it’s impossible to create a system that is both fair and free from strategic voting. In other words, no matter how you set up the rules, people will always find a way to vote strategically, instead of honestly.
So, why does Majority Judgment do better?
Majority Judgment gives each candidate a score, which encourages honest voting. It makes manipulation less effective because dishonest scoring often backfires.
This system is particularly strong in polarised situations as I mentioned earlier.
In addition, Majority Judgment provides a fairer and more accurate reflection of what people really want, compared to traditional methods.
Majority Judgment is being used in various real-world scenarios, such as political elections, academic evaluations, and companies feedback system.
Okay, in summary, we’ve talked about …
Thank you for listening. Don’t hesitate to ask if you have any questions.