© Shutterstock

An ancient voting system -

One of the oldest and simplest voting methods in the world is known as the "first past the post" system, which asks voters to choose one candidate and the one with the highest vote count wins. Although it sounds straightforward, this system has inherent issues affecting democratic fairness.

© Getty Images

Historical roots -

Dating back to the 14th century, this system has been in use in the British House of Commons and remains prevalent in 44 countries, many of them former British colonies, including the United States, where it influences national elections.

© Getty Images

Misrepresented majorities -

The problem with the first past the post system is that, sometimes, a candidate gets elected into power that is not the one most people actually voted for. This happened during the 2016 US election when Donald Trump defeated Hillary Clinton for president despite receiving fewer votes.

© Getty Images

Spoiler effect -

The 2000 US presidential election highlighted the “spoiler effect,” where third-party candidate Ralph Nader 'stole' votes from Al Gore, and so indirectly helped George W. Bush win. The first past the post system restricts voters’ ability to express preferences, which often skews results.

© Getty Images

Two-party dominance -

The first past the post system pushes voters to vote strategically rather than for their true favorite party, which is a flawed system. This pressure ultimately leads to a concentration of power in larger parties and, in the end, you’re left with nothing more than a two-party system.

© Shutterstock

Duverger’s law -

Political scientist Maurice Duverger observed that winner-take-all voting systems, like the first past the post system, all naturally evolve toward two-party systems. There isn’t true democratic representation, since voter choice is minimized and smaller parties are made even smaller.

© Getty Images

Ranked-choice voting -

An alternative to this system would be ranked-choice voting. Instead of choosing only one party, voters would rank candidates by preference. If no candidate wins an outright majority, the candidate with the fewest votes is eliminated and their supporters’ second choices are distributed to the other parties.

© Shutterstock

Instant runoff -

This voting system is also known as “instant runoff,” and it eliminates candidates sequentially based on rankings until one achieves a majority. This system mimics repeated elections but saves time, allowing for fairer representation of voters’ preferences.

© Getty Images

Reduced hostility -

In a ranked-choice system, candidates tend to avoid antagonistic campaigning. For example, during the 2013 Minneapolis mayoral race, the candidates remained cordial and respectful since they were looking to secure secondary and tertiary preferences from voters.

© Getty Images

Imperfection -

While ranked-choice voting minimizes some issues, it’s still imperfect. There are cases where a candidate’s poor performance can paradoxically benefit them due to the dynamics of ranking redistribution.

© Shutterstock

A fair voting system -

French mathematician Nicolas de Condorcet pioneered social choice theory, which aimed to create a voting system that accurately reflected majority preferences. His work emerged during the French Revolution (a period keen on fair representation) and laid the foundation for voting science.

© Getty Images

The Borda count -

At the same time, another French mathematician named Jean-Charles de Borda suggested a ranked voting system that assigned points based on voter rankings. For example, a candidate ranked in first place on a voter’s ballot would get four points, the second would get three, and so on.

© Getty Images

Criticism -

Condorcet critiqued Borda’s approach and noted that irrelevant factors (like the number of candidates) could influence outcomes unfairly.

© Shutterstock

Head-to-head competition -

In 1785, Condorcet proposed a system where the winner would need to beat other candidates in individual head-to-head elections. But instead of having an inordinate number of elections, voters would simply use a ranked-choice voting system. The winner would be the one who receives the highest ranks, which is a fairer assessment.

© Shutterstock

Llull’s voting system -

Ramon Llull, a 13th-century monk, proposed a similar method for voting in church leadership elections. Although his work didn’t influence his time, it was rediscovered in 2001.

© Public Domain

Paradox -

Unfortunately, Condorcet discovered a paradox in his system, where ranking preferences could lead to circular outcomes. If enough people rank different candidates equally, then it would create a deadlock with no clear winner. Condorcet died before he could solve the issue.

© Shutterstock

Failed attempts -

Over the 150 years following Condorcet’s death, many mathematicians (including Lewis Carroll, pictured) attempted to devise a perfect voting method. Despite various adaptations and proposals, no system could fully resolve the issues that Condorcet and Borda had identified.

© Getty Images

The impossibility theorem -

In 1951, American economist Kenneth Arrow demonstrated that, if there are three or more candidates in an election, no ranked voting system could perfectly meet all the essential fairness criteria. This impossibility theorem, which earned him a Nobel Prize, formalized the limitations of ranked-choice voting.

© Getty Images

Five conditions -

Arrow proposed five conditions when it came to voting systems: unanimity, non-dictatorship, unrestricted domain, transitivity, and independence of irrelevant alternatives. These rules seemed essential for rational voting, yet he proved that no voting method could satisfy all of them simultaneously.

© Shutterstock

1. Unanimity -

In Arrow’s criteria, unanimity asserts that if all voters prefer one candidate over another, the system should reflect this collective preference.

© Shutterstock

2. Non-dictatorship -

Arrow’s second condition, non-dictatorship, ensures that no single voter’s preference can determine the entire outcome. This principle is essential for democracy, since one person’s vote should not be the deciding factor. Otherwise, it would be a dictatorship.

© Shutterstock

3. Unrestricted domain -

The third condition, unrestricted domain, is that everyone should be permitted to vote how they see fit, and their votes cannot be ignored. This condition ensures inclusivity and avoids arbitrary or biased decision-making.

© Shutterstock

4. Transitivity -

Transitivity requires that if voters prefer one option over a second, and the second option over a third, then the first option should (logically) be preferred over the third. It places candidates in an ordered hierarchy.

© Shutterstock

5. Independence of irrelevant alternatives -

This condition states that adding or removing candidates should not change existing preferences. For instance, if one candidate is preferred over a second, introducing a new candidate shouldn’t impact the voter’s choice. This condition prevents outside options from disrupting prior rankings.

© Shutterstock

Proof -

Arrow’s proof shows that any ranked voting system that meets his five conditions ultimately relies on a dictator to resolve preferences, which undermines the very principles of democracy. As such, a fair voting system is mathematically impossible to achieve with three or more candidates.

© Shutterstock

The pivotal voter -

Arrow’s theorem reveals that under his five conditions, any person whose singular vote determines the winning candidate (known as the pivotal voter) would essentially hold dictatorial power.

© Shutterstock

Approval voting -

There is an alternative voting system known as rated voting methods (like approval voting), which can be used to allow voters to select all candidates they approve of. Research shows it reduces negative campaigning and enhances fairness, as voters can support multiple candidates without fearing their vote will be “wasted.”

© Shutterstock

Historical examples -

Approval voting was historically used in Vatican elections between 1294 and 1621, and it is also used in the selection of the United Nations secretary-general. Despite its effectiveness in specific contexts, it hasn’t been widely adopted in large-scale elections.

© Getty Images

Endorsement -

Kenneth Arrow was initially skeptical of rated systems, but eventually acknowledged their advantages over ranked methods, especially in their ability to avoid dictatorships and paradoxes.

© Shutterstock

Churchill’s perspective -

Being politically engaged is incredibly important and is one of the few ways in which people could make a difference in the world. As Winston Churchill once said: “Democracy is the worst form of government, except for all the other forms that have been tried.”

© Getty Images

The only game in town -

Ultimately, democracy (with all its complexities and imperfections) remains the best option we have. It may be mathematically challenging, but the principles of fairness and representation it strives for make it a worthy pursuit.

Sources: (Veritasium) (Yale University Press) (Journal of Political Economy) (American Political Science Review) (Britannica)

See also: How NASA astronauts vote from space

© Getty Images