What Is the Monotonicity Criterion in Voting Systems?

In the beginning of our country’s history, the population was small enough that voting was a fairly easy process. People showed up at the appointed place and time, wrote a name on a slip of paper, and whoever got the most votes won. 

As the country grew and things became more complicated, various criteria were developed and put into place to test the equity and fairness of new and developing voting systems. The goal was to ensure that all voices were heard and that candidates were selected by the majority of voters. 

One such measurement is the Monotonicity Criterion. 

Join us as we attempt to demystify the Monotonicity Criterion by exploring its definition, significance, and implications in modern voting systems.

What Is the Monotonicity Criterion?

The Monotonicity Criterion was developed as a means of ensuring that a candidate's chance of winning does not decrease if their position improves in the preferences of voters. Simply put, if Candidate A is preferred over Candidate B in an election and, in a subsequent round or a different scenario, more voters rank A higher than they did previously, then A's chances of winning should not decrease. 

This criterion aims to prevent a situation where improving the standing of a candidate in the voters' preference could ironically lead to their loss. 

Sound like a paradox? Read on to learn how that could happen. 

Origin and Development

The Monotonicity Criterion, as a formal concept in the study of voting systems, emerged from the field of social choice theory. This field, which blends economics, political science, and mathematics, studies collective social decision-making processes.

While the specific term "Monotonicity Criterion" evolved as part of broader academic discussions and theories about voting systems, it’s more a product of collective study than it is the invention of a single person. However, the framework was set during the late 18th century by Nicolas de Condorcet (in collaboration with Jean-Charles de Borda, pioneer of the Borda Count voting method). 

Over the years, the work of notable scholars like Kenneth Arrow and Duncan Black has been influential in developing more formal, reliable criteria for voting systems. Arrow's Impossibility Theorem and Black's work on voting methods laid the groundwork for understanding criteria like monotonicity. 

Each asserts, to some degree, that there is no way of developing a voting system that meets all fairness criteria. 

The Monotonicity Criterion's Significance in Voting Systems

The importance of the Monotonicity Criterion lies in its ability to ensure a more fair and intuitive outcome in elections. It guarantees that efforts to increase a candidate's popularity are not counterproductive. This is particularly crucial in systems where strategic voting is common, and voters might be tempted to rank their second-choice candidates higher to avoid the risk of their least preferred candidate winning.

Application in U.S. Elections

The Monotonicity Criterion has been a theoretical concept for several decades, but its practical consideration in U.S. elections is more recent. The use and analysis of different voting systems in the United States, especially ranked-choice voting (RCV), have brought more attention to criteria like monotonicity.

In the U.S., with the increasing adoption of RCV in local elections (like in San Francisco, Minneapolis, and Maine), the relevance of the Monotonicity Criterion has grown. It's used to assess the integrity and fairness of these voting methods.

Overall Impact

The Monotonicity Criterion, while one aspect of assessing voting systems, plays a significant role in discussions about electoral reform and the adoption of alternative voting methods in the U.S. Its consideration is crucial for ensuring that elections are not only technically fair, but also perceived as fair by the electorate. 

The criterion's impact extends beyond the mathematical realm into the practical, influencing how voters and candidates approach elections.

As the U.S. continues to explore - and occasionally adopt - different voting systems, the relevance of assessment criteria like monotonicity is likely to increase. This is especially true for elections at the state and local levels. 

It’s essential for voters, policymakers, and election administrators to understand these concepts so they can make informed decisions about the future of electoral processes in the country. However, it is just as important for voters to understand how different voting systems impact their ballot once it is cast and trust that the systems used to select winners are as fair and impartial as possible.

Application and Examples

Not all voting systems can be considered purely monotonic. Often, the opinion on a voting’s system’s ability to meet the Monotonicity Criterion or not is arbitrary. There is no single, uniform standard criteria that can be applied, and advocates of one system over another will try to interpret the criteria to fit their preferred system. 

However, proponents of using monotonicity as a measure cite the following voting systems.

1. Single Transferable Vote (STV): In the STV system, which is a form of ranked-choice voting, monotonicity can sometimes be violated. This happens in scenarios where transferring votes from a less preferred candidate to a more preferred one might inadvertently eliminate the latter earlier in the counting process.

2. Borda Count: The Borda Count method, where voters rank candidates and points are assigned based on their positions, also fails the Monotonicity Criterion. Here, a candidate can lose points and their position in the ranking can worsen even if more voters rank them higher.

3. Approval Voting: In contrast, Approval Voting, where voters can vote for as many candidates as they approve of, satisfies the Monotonicity Criterion. A candidate's chances of winning increase as more voters approve of them.

Implications in Electoral Politics

Fair and representational elections depend on two things: a high turnout of engaged, informed voters and a fair method of calculating the outcome in a complex, diverse electoral system with lots of moving parts. As such, the adherence to - or violation of - the Monotonicity Criterion can significantly impact electoral politics in three ways:

1. Voter Strategy: In systems that do not meet this criterion, voters might need to strategize their votes to avoid counterintuitive outcomes. This can lead to less honest voting, where voters do not always rank their true preferences.

2. Election Outcomes: Elections using systems that fail the Monotonicity Criterion can sometimes result in unexpected and seemingly illogical outcomes. This, in turn, can undermine the voters' trust in the electoral process.

3. Election Reforms: Understanding and publicizing metrics like the Monotonicity Criterion can fuel election reforms. Advocates for voting system reforms often cite the failure to meet such criteria as reasons to consider alternative methods.

However, no system is failsafe. There are advantages and drawbacks to using monotonicity to evaluate the effectiveness and fairness of election systems. 

Pros and Cons of Using the Monotonicity Criterion

Pros

• Enhances Voter Confidence: By ensuring that a candidate's chance of winning increases with their popularity, the Monotonicity Criterion helps maintain voter confidence in the electoral process.

• Reduces Strategic Voting: It discourages voters from voting strategically (like voting for a less-preferred candidate to prevent an undesirable outcome), as it ensures that honest preferences are more likely to lead to expected results.

• Fairness: The Monotonicity Criterion promotes fairness, ensuring that a candidate benefiting from increased support is not inadvertently disadvantaged.

Cons

• Complexity in Implementation: Ensuring monotonicity in certain voting systems (like STV or Borda Count) can be complex and challenging.

• Limitation in Choice of Voting Systems: Some popular voting methods inherently fail the Monotonicity Criterion, which might limit the options for choosing voting systems.

• Potential for Unintended Consequences: In systems that meet the criterion, candidates might campaign in a way that focuses on marginal gains in preference at the expense of broader appeal, potentially leading to more divisive or targeted campaigning strategies.

• Misunderstanding and Misinterpretation: The concept of monotonicity can be difficult for the general public to understand, leading to misconceptions about how their vote is counted and the overall fairness of the election.

As you can see, the Monotonicity Criterion plays a vital role in the evaluation of voting systems. While it’s just one of many criteria used to assess these systems in the United States and elsewhere, its importance lies in ensuring that improvements in a candidate’s preference among voters lead to a corresponding increase in their chances of winning.

Support True Representation and Transparency in Elections

The presence or absence of this criterion in a voting system can greatly influence voter behavior, election outcomes, and the overall fairness of the electoral process. As the world continues to evolve in its understanding and implementation of democratic principles, the scrutiny of such criteria remains a cornerstone in the pursuit of fair and effective electoral systems.

At GoodParty.org, our mission is to transform our current, broken political system into one that is more fair and representative. You can do your part by joining the GoodParty.org community as a volunteer or by running for office as an independent.