The Quest for the Fairest Voting System

Imagine a scenario: a new spaceport is to be built on Mars, and the 100 colonists must decide which of the four bases will host it. Each base has a different population: West Base (42 colonists), North Base (26), South Base (15), and East Base (17). Assuming everyone wants the spaceport closest to their home, what's the fairest way to decide?

This question delves into the complexities of voting systems, revealing that fairness is not as straightforward as it seems. Let's explore a few methods and their potential pitfalls.

Plurality Voting: Simple but Flawed

The most basic approach is plurality voting, where each person casts a single vote, and the location with the most votes wins. In our Martian example, West Base would win with 42 votes. However, this outcome might be considered the worst by the majority, as it's the furthest from everyone else. Is this truly fair?

Instant Runoff Voting: Accounting for Preferences

Instant runoff voting aims to capture the full spectrum of voter preferences. Here's how it works:

• Voters rank each option from 1 to 4.
• The option with the fewest first-place votes is eliminated.
• The eliminated option's votes are then allocated to the voters' second choice.
• This process repeats until one option has a majority.

In our scenario, South Base is eliminated first, and its votes go to East Base. Then North Base is eliminated, with its votes ultimately going to East Base as well. East Base wins with 58 votes. But is this fair? East Base started near the bottom and was a low preference for most.

Tactical Voting: Gaming the System

Another approach involves multiple rounds of voting, with a runoff between the top two winners. In this case, West and North would likely win the first round, with North winning the second. However, residents of East Base might employ tactical voting. They could vote for South Base in the first round to prevent North from advancing, ultimately leading to South Base winning the final round, despite being the least populated. This raises the question: is a system fair if it encourages misrepresentation of preferences?

The Condorcet Method: Head-to-Head Matchups

The Condorcet method involves voters expressing a preference in every possible head-to-head matchup. For example, in a West vs. North matchup, all 100 colonists vote for their preferred option. The victor is the base that wins the most matchups.

In our Martian example:

• North wins three matchups.
• South wins two matchups.

North emerges as the winner, as it's a more central location and not anyone's least preferred choice. But is the Condorcet method ideal?

Consider an election with three candidates where voters prefer A over B, B over C, but C over A. In this scenario, the Condorcet method fails to produce a clear winner.

The Illusion of a Perfect System

Over time, researchers have developed numerous voting systems, some of which have been implemented in real-world elections. However, every system has the potential to yield an unfair outcome.

Our intuitive understanding of fairness is complex and often contradictory. We want every voter to have equal influence, but we also want to consider minority preferences and discourage manipulation of the system.

Mathematical proofs have demonstrated that in any election with more than two options, it's impossible to create a voting system that satisfies all theoretically desirable criteria.

While democracy often focuses on counting votes, it's crucial to consider who benefits from the various methods of counting them. There is no perfect system, and each has its own set of trade-offs.