Hello! Welcome to our lesson on evaluating voting systems.
In our previous session, we explored David Estlund's theory of epistemic proceduralism. We saw that democratic legitimacy can be grounded in a procedure's tendency to make correct decisions, even when it's fallible, as long as the procedure itself is acceptable to all reasonable citizens. This elegantly combines the instrumental value of getting things right with the intrinsic value of procedural fairness.
Today, we will apply this thinking to the very mechanisms that translate citizen judgments into collective decisions: voting systems. The design of a voting system is a fundamental choice in any societal architecture. It determines how individual preferences are aggregated and can profoundly impact political outcomes, stability, and the very legitimacy of the government.
Our learning outcome is to apply principles of procedural justice to evaluate different voting systems, such as majority rule, supermajority, and others. We will assess them based on criteria like fairness, accuracy in representing voter intent, and their susceptibility to strategic manipulation—issues that directly impact a procedure's epistemic and moral authority. Your background in statistics and game theory will be particularly useful here, as social choice theory is a rich intersection of these fields with political philosophy.
1. The Trouble with "Winner-Takes-All"
Let's start with the system used in many major elections, including in the US and UK: first-past-the-post (FPTP), also known as plurality voting. In this system, voters choose one candidate, and the candidate with the most votes wins, even if they don't have a majority. While simple, it has well-known and significant flaws.
Why Democracy Is Mathematically Impossible
The Veritasium video, 'Why Democracy Is Mathematically Impossible,' provides an excellent overview of the problems with first-past-the-post and introduces several alternatives.
Please watch from the beginning to 04:08. Pay close attention to the description of the 'spoiler effect' and Duverger's Law.
As the video explains, the "spoiler effect" is a major issue. A third candidate, even with no chance of winning, can "spoil" the election for a more popular, ideologically similar candidate by splitting their vote base. This often leads to an outcome that most voters, including those who voted for the spoiler candidate, consider worse. Over time, this incentivizes strategic voting and entrenches a two-party system (a phenomenon known as Duverger's Law).
This brings us to a core philosophical problem that undermines the epistemic value of voting.
The Dual-Role Dilemma
The spoiler effect forces voters into a difficult position. Should you vote for the candidate you truly believe is best (acting as a "True Believer"), even if they have little chance to win and your vote might help your least-preferred candidate? Or should you vote for the "lesser of two evils" among the viable candidates (acting as an "Instrumentalist")?
The philosopher Alexander Guerrero argues this "dual-role dilemma" compromises the very purpose of voting.
In his paper, 'The Epistemic and Metaphysical Roles of Voting,' Guerrero argues that plurality voting creates a dilemma that undermines both the epistemic (truth-tracking) and metaphysical (authorizing) functions of an election. Let's read the section where he introduces this core problem.
Please read Part II of the paper, titled 'The Dual-Role Dilemma' (starting on page 14). Focus on the distinction between the 'True Believer' and the 'Instrumentalist' and how the presence of Instrumentalists 'muddies the waters' for interpreting election results.
As Guerrero explains, when a significant portion of the electorate votes instrumentally, the final vote tallies become epistemically opaque. A vote for a candidate no longer signifies genuine support or a judgment that the candidate is good for the role. It might just be a strategic move to block a worse alternative.
This directly challenges the foundation of epistemic proceduralism we discussed last time. If votes don't reflect voters' true judgments about what is best, the procedure's ability to "track the truth" is severely degraded. The vote loses its moral force as an act of collective authorization and becomes a raw, strategic power game.
2. Exploring Alternatives and Their Paradoxes
Given the flaws of plurality voting, theorists and reformers have proposed numerous alternatives. Let's examine a few key ones and see if they solve the problem.
Ranked Systems
Instead of picking one candidate, ranked systems allow voters to rank candidates in order of preference.
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Instant Runoff Voting (IRV): Also known as Ranked-Choice Voting, this is a popular alternative. If no candidate has a majority of first-place votes, the candidate with the fewest is eliminated, and their votes are redistributed to their voters' next choice. This continues until one candidate has a majority.
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Condorcet Method: A candidate is the winner if they would beat every other candidate in a one-on-one matchup.
These systems seem more expressive, but they introduce their own strange, counter-intuitive problems.
Why Democracy Is Mathematically Impossible
Let's return to the Veritasium video, which explains the mechanics and paradoxes of these ranked systems.
Please watch from 04:08 to 12:27. As you watch, identify the key paradox or flaw associated with each system: The problem with Instant Runoff (the Bohr/Einstein/Curie example). The problem with the Condorcet Method (the dinner example).
As you saw, even these more sophisticated systems have issues:
- IRV suffers from non-monotonicity: A candidate can lose because they gained more support. In the video's example, Bohr wins after a bad speech causes him to lose some first-round votes to Einstein. This violates a basic principle of fairness. Another issue, explored in the Primer video, is the "center squeeze," where a moderate candidate popular as a second choice can be eliminated early, leading to a more polarizing winner.
- Condorcet's method can result in a cycle: You can have a situation where A is preferred to B, B is preferred to C, and C is preferred to A. There is no clear "Condorcet winner," leaving the election indeterminate.
The Impossibility of a Perfect System
These paradoxes are not just isolated quirks. In 1951, the economist Kenneth Arrow, whose work you may have encountered, proved a profound and startling result.
The Veritasium video (from 08:05 to 18:49) provides a great explanation of Arrow's five conditions and a simplified proof of his Impossibility Theorem. The key takeaway is that when aggregating ranked preferences, we are forced to make trade-offs. There is no single voting system that is perfect on all dimensions of procedural fairness.
Rated Systems
Another class of systems, rated voting, escapes the confines of Arrow's Theorem because it's not based on ranking.
- Approval Voting: Voters can vote for, or "approve of," as many candidates as they like. The candidate with the most approvals wins.
- Range (or Score) Voting: Voters give each candidate a score on a scale (e.g., 0-9). The candidate with the highest total or median score wins.
These systems often perform well in simulations, but they also create unique strategic dilemmas.
Simulating alternate voting systems
The YouTube channel Primer has an excellent simulation-based analysis in the video 'Simulating alternate voting systems'. It visually demonstrates the strategic dynamics of Approval Voting.
Please watch from 07:54 to 11:58. Focus on the 'chicken dilemma' and how it creates a new form of strategic voting.
Approval voting effectively resolves the "spoiler effect" but introduces the "chicken dilemma." When two similar, popular candidates are competing, their supporters face a choice: do they approve of both candidates to form a strong bloc against a disliked third option, or do they "betray" their second choice to try to give their favorite an edge? If both sides betray too much, they might accidentally allow the disliked third candidate to win. This is a classic game-theoretic problem.
Guerrero, in the paper you read earlier, proposes a "Normative Approval Voting" system to resolve the dual-role dilemma. He suggests linking the powers of the elected official to their level of support, creating an incentive for voters to express their true judgments honestly. This is an intriguing piece of institutional design that connects procedural justice directly to the structure of power.
Test your understanding!
Imagine you are designing a voting system for a professional society of statisticians to elect its president. There are typically 5-6 candidates representing different sub-fields. Your primary goal is to elect a candidate who is broadly respected and competent, avoiding a niche candidate winning due to a split vote.
Based on what you've learned, would you choose First-Past-the-Post, Instant Runoff, or Approval Voting? Justify your choice by explaining the main weakness of the systems you reject and the main strength of the one you select for this specific context.
Show answer
- Reject FPTP: This is the worst choice. With 5-6 candidates, the vote would likely be heavily split. A niche candidate with a passionate but small base (e.g., 20% of the vote) could easily win, while more broadly acceptable candidates split the majority of the vote. This would fail the goal of electing a broadly respected leader.
- Reject IRV (or be wary): IRV is better than FPTP, but it's vulnerable to the "center squeeze." A consensus-building candidate who is everyone's second or third choice might be eliminated early if they don't have enough first-place votes. This could lead to a more polarizing but less broadly respected candidate winning in the final round.
- Choose Approval Voting: This is likely the best choice for this context. It allows members to express their support for all candidates they deem competent and respectable. A candidate from a small sub-field can be supported alongside a candidate from a larger one. This system is designed to find the most broadly acceptable candidate and would be most effective at preventing a niche candidate from winning due to vote splitting. While the "chicken dilemma" exists, in a professional society setting with a shared goal of good governance, voters may be less likely to engage in extreme strategic betrayal.
3. Context is Key: Majority vs. Supermajority Rules
So far, we've focused on choosing one winner from many. But another crucial aspect of procedural justice is the threshold for a decision. When should a simple majority suffice, and when should a supermajority (like 60% or two-thirds) be required?
The U.S. Senate provides a fascinating real-world case study. For decades, it has maintained a supermajority requirement (the filibuster) for passing legislation but has moved to a simple majority rule for confirming judicial and executive appointments. Why would the same body use different rules for different tasks? The traditional arguments for supermajority rules—protecting minority rights, promoting stability—seem to apply equally, if not more so, to lifetime judicial appointments.
A recent paper uses a game-theoretic model to provide a powerful explanation rooted in procedural logic.
The Waning and Stability of the Filibuster
The paper 'The Waning and Stability of the Filibuster' by Judd and Rothenberg presents a formal model to explain this divergence. Their core insight is highly relevant to applying procedural justice principles.
Please read the Abstract, the introduction (first two pages), the 'Model' section (page 8), and the 'Main Results' section (pages 13-14). Focus on the fundamental distinction the authors draw between the policy impact of lawmaking versus judicial appointments. This is the key to their entire argument.
The authors' central insight is that the choice of procedure depends on the inherent constraints of the domain.
- Lawmaking: A new law can, in principle, create radical policy change from the status quo. The only constraint is the legislative process itself.
- Judicial Appointments: A new judge joins an existing court. Their influence is inherently constrained by the need to form a majority with other sitting judges. A single appointment rarely causes a radical, immediate shift in legal precedent.
Therefore, from the perspective of a median legislator who wants to avoid wild policy swings, a supermajority rule (which adds a constraint) is valuable for lawmaking. For judicial appointments, however, that same supermajority rule can be excessive, as the institutional structure of the court already provides a natural check on radical change.
This is a brilliant application of procedural analysis. It shows that the "fairest" or "best" procedure isn't a universal constant; it is contingent on the institutional architecture in which the decision is being made. The choice of a voting rule is a strategic one, balancing the desire for decisive action against the need for stability and constraint.
Conclusion
Today we've seen that the seemingly simple act of voting is fraught with complexity and paradox. The design of voting systems is not a neutral technical choice; it is a profound decision about how a society balances competing values and navigates the challenges of collective decision-making.
Key Takeaways:
- First-Past-The-Post voting creates a "dual-role dilemma," forcing strategic behavior that undermines the epistemic and legitimating functions of elections.
- Alternative systems like Instant Runoff and Approval Voting resolve the spoiler effect but introduce their own strategic paradoxes (non-monotonicity, center-squeeze, chicken dilemma).
- Arrow's Impossibility Theorem provides a formal proof that no ranked-voting system can be perfect, forcing us to make normative trade-offs.
- The choice between majority and supermajority rules can be a rational one based on the institutional context. A supermajority may be justified in unconstrained domains (like lawmaking) but excessive in inherently constrained ones (like judicial appointments).
Preview of the Next Lesson:
This lesson has served as a deep dive into one specific, but crucial, component of societal architecture. In our final lesson, we will zoom out to the widest possible lens. We will begin the task of synthesis, pulling together concepts from the entire course—natural law, pluralism, republicanism, and proceduralism—to analyze how different macro-level societal architectures systematically prioritize or sacrifice fundamental values. We will start to build a framework for thinking about that "least bad" arrangement you are interested in exploring.