Misuse of ‘Majority’: The Unfair Game of Democracy

We often hear politicians claim that they represent an “absolute majority” and that their decisions reflect the will of most people. But, mathematically speaking, this claim is not as solid as it sounds. Democracy has a built-in flaw that makes it impossible to perfectly reflect the wishes of every voter. So, when politicians boast about their majority, they’re often misrepresenting how complex collective decision-making really is.

What if I told you that a Nobel Prize-winning theorem proves democracy can never fully capture the true will of the people? (https://plato.stanford.edu/entries/arrows-theorem/)

The Group Dilemma: 10 People, 3 Choices, No Easy Solution

Imagine you are part of a group of 10 people trying to make an important decision—what to invest in for a neighborhood community project. There are three options on the table:

A new playground for kids
An outdoor gym for fitness enthusiasts
A community garden for growing fresh vegetables

Each person has different priorities, and everyone ranks their preferences as follows:

Person 1: Playground > Garden > Gym
Person 2: Gym > Playground > Garden
Person 3: Garden > Gym->Playground
Person 4: Playground > Gym > Garden
Person 5: Garden > Gym > Playground
Person 6: Gym > Garden > Playground
Person 7: Playground > Garden > Gym
Person 8: Garden > Gym-> Playground
Person 9: Gym > Playground > Garden
Person 10: Playground > Gym->Garden

Now, let’s try to figure out which project wins based on these preferences. It might seem simple—just pick the option that gets the most support. But here’s where things get complicated.

Playground is the top choice for 4 people.
Garden is the top choice for 3 people.
Gym is the top choice for 3 people.

It looks like the Playground has the most first-place votes. But does that mean it truly reflects the will of the group? Not really.

When we look at the second preferences, the results shift:

Gym is ranked second by 5 people.
Playground is ranked second by 2 people.
Garden is ranked second by 3 people.

Now the Gym seems like a strong compromise since it’s a lot of people’s second favorite. However, choosing it over the Playground will leave 4 people who wanted the Playground feeling disappointed, as it was their top choice.

The Impossibility Theorem: Why No Solution is Perfect

This example shows how, even with clear preferences, there’s no perfect way to make everyone happy. Kenneth Arrow’s Impossibility Theorem explains this problem in mathematical terms. Arrow, who won the Nobel Memorial Prize in Economic Sciences in 1972 for this and other groundbreaking work, proved that when there are three or more choices, no voting system can fully satisfy everyone’s preferences. Specifically, any voting system that tries to do so will always break one of these key rules:

Respect everyone’s preferences—everyone’s vote should count.
Be fair—no single person’s vote should always determine the outcome.
Avoid contradictions—the choice between two options shouldn’t change just because a third option is added or removed.

In our example, even though Playground gets the most first-place votes, it doesn’t reflect the overall sentiment of the group. The Gym, which is a strong second choice for many, might seem like a better compromise, but it doesn’t satisfy the top preferences of a significant portion of the group either. The Garden has dedicated supporters too, but not enough to win outright.

Why Politicians Misuse “Majority”

When politicians claim they have an “absolute majority,” they often ignore these complexities. Winning the most votes doesn’t necessarily mean they have widespread support across all segments of the population. They may be representing the largest group, but not the entire community’s will. In fact, much like in our example, the so-called “majority” might only reflect a small portion of the population’s preferences.

For example, in a three-party election, a politician might win with just 40% of the vote, while the other 60% of voters preferred someone else. But since the votes were split, the 40% winner claims a “mandate” from the people. This isn’t truly a majority—it’s a flaw in how we aggregate choices.

So, What Does This Mean for Democracy?

Does this mean democracy is doomed? No, but it does mean we need to be more careful about how we interpret voting results. No voting system is perfect, and we must acknowledge that the outcome of any vote will not always reflect the true will of everyone involved.

The lesson is simple: take claims of “absolute majority” with caution. Voting is still one of the best ways to make decisions in a group, but it’s not mathematically perfect. Understanding its limitations helps us make more informed decisions and demand more transparent representation.

Conclusion: The Limits of Democracy

In conclusion, democracy isn’t as straightforward as it appears. Kenneth Arrow’s Nobel-winning work shows us that no voting system can fully represent the will of the people without contradictions. So, when politicians claim to represent the “majority,” remember: the game of democracy is always unfair.