Why Voting Doesn’t Tell Us What Voters Really Want

There are many reasons why one might choose to avoid the voting booth. This often stems from ethical dilemmas over the state’s monopoly on force. Some may emphasize their right not to vote, a right undervalued in undeveloped political systems with transparently corrupt regimes (making the “Vote or Die” tagline somewhat ironic). Others may view popular forms of democracy as opaquely crooked, and consider voting a signal of participation that perpetuates the system. Celebrity Russell Brand, for example, has publicly held this view (although he has distanced himself from this position more recently).

One may sympathize with this form of reasoning, but disagree regarding the importance assigned to such values. It follows that value-based decisions, while valid, are unlikely to be persuasive to anyone who doesn’t already hold the same values.

Thus, I hope to challenge the altruistic stigma associated with voting by presenting perspective grounded in more objective principles. My goal is not to attack democracy proper, but to illuminate how many obstacles there really are between the vote one casts and the abstract greater good they hope to reach.

Arrow’s Impossibility Theorem

First, let’s consider the domain of achievable outcomes for a voting system. How good can the best voting system get? Kenneth Arrow provided important insight in his seminal doctoral thesis of 1950 (updated in 1963). Arrow’s theorem illustrates a paradox of choice, revealing flaws in ordinal voting systems. Broadly speaking, if a group of two or more voters is faced with more than two options, a ranked voting system cannot aggregate the ranked preferences of voters into a single ordered list of preferences for the group without violating at least one of the following conditions:

1. Nondictatorship – the preferences of a single voter should not be decisive.

2. Pareto efficiency – if all individuals prefer A over B, the group should prefer A over B.

3. Independence of irrelevant alternatives – the removal of irrelevant choices should not change the preference ordering for the remaining ones. For example, if every voter prefers A to B and B to C, removing C should not change the fact that A is preferred to B.

4. Unrestricted domain – all possible preference orderings can be aggregated.

Although Arrow tediously proves this mathematically with a series of proofs by contradiction, the interpretation is straightforward. No voting system can establish social preferences by aggregating individual preferences. Condition 3 is most often violated by majoritarian electoral voting systems, leading to cycling group preferences (intransitivity of preferences after aggregation, loosely speaking). Enforcing transitivity after aggregation must imply a dictatorship.

Local voting for ballot measures (propositions) most obviously struggles to meet condition 4, but problems here may even transcend Arrow’s theorem. Voting only provides a binary signal of demand, not a magnitude of demand. Hence there is no economizing signal (i.e., people don’t express preferences for one thing relative to another in a comparable way). As a result, public real resource allocation is still difficult to prioritize following a local vote.

I don’t want to overstate the importance of Arrow’s theorem. This argument does not conclude that democracy is a lost cause. Rather, it demonstrates that there are limitations with all types of voting systems, and that getting more people to the polls won’t overcome them.

Political Scale Dependence

There is an additional issue complicating expected voting outcomes: scale. In 2019, Nassim Taleb drafted a paper arguing the importance of scale-free politics. He argues that democracy (or any political system) is not scale invariant.

As a societal unit grows larger, the coupling among agents becomes weaker and weaker, nearing independence. Local signals become subordinated by more dominant, concentrated signals at the federal level. As such, there is both less accountability behind political decision-making and a more uncertain impact.

This stands in contrast to strong reductionism, which suggests that we can understand intricate systems by summing up the effects of its constituents. In a world ruled by strong reductionism, the appropriateness of a political system for the entire planet could be induced by observing a single individual. Such a view leads people to confusingly treat politics as a top-down engineering project rather than a complex, adaptive, bottom-up system. In the face of complex interactions and nonlinear relations, properties can emerge under aggregation that are absent at the component level.

To better illustrate this concept, consider decision-making at the family level. One may agree that a pure democracy is of limited use for the family unit beyond settling dining or television disputes, lest a Lord of the Flies scenario transpire. Does this alone mean democracy is bunk? Of course not; it is simply being implemented on an inappropriate scale.

Consider further the unification of the United States and China into a single democratic nation. In such a scenario, majority voting may lead to policies that disproportionately favor the more populous culture. At the very least, outcomes are likely to deviate significantly from those that follow from two separate democracies.

The same concept applies at levels between these extremes. Political systems work differently at the various possible levels of population aggregation (i.e., town, city, state, etc.).

Accordingly, economic dynamics must be matched to the proper scale. This is naively existent in modern political systems, but is by no means ubiquitous. Consequently, people can rationally have different political stances at different levels of aggregation (e.g., Democrat at the local level, libertarian at the federal level, etc.).

When faced with a set of scale-ignorant options at a fixed level of aggregation (e.g., federal), intensions become moot, as voters are faced with insurmountably uncertain outcomes. Through this lens, one can’t blame the citizen who finds voting versus abstention a matter of indifference.

Independence

Let’s now assume that a severe lack of votes resulted in a deeply negative outcome. Under such an assumption, the decision not to vote would indeed be a fallacy of composition. Although the individual may get no marginal benefit from voting, the system as a whole would suffer.

This criticism is fair, but insufficient at the level of the individual. Following a discussion about scale, it’s fitting to point out that the decision of the individual is not the decision of the collective. This is because my decision to vote is independent from others’ decisions to vote. Even if I felt that political outcomes would improve if everyone who thought like me would change their tune and vote, I can’t personally vote for them, nor can I force another to abstain.

As a result, in a large enough democracy, the impact of an individual vote is statistically zero on the margin. No single person’s vote will ever impact an election in a democracy of even modest size (electoral college, popular, or any other), and since their decision is independent from other voters, the decision to vote is itself irrelevant. So the criticism can be both correct and immaterial.

Conclusion

A somewhat famous theorem of public choice theory states that in a voting system driven by majority rule, the median voter’s most preferred outcome will be selected. Such an idea casts voting in a comforting light. Each vote pulls the median closer to the voter’s preferences by a tiny margin.

Unfortunately, the median voter theorem has too many unrealistic assumptions to apply in practice. Not only does it fail in the face of Arrow’s theorem, it requires a separate vote for each issue, no more than two options, and an unbiased voter turnout, none of which are commonplace in a political election.

Voters are also assumed to be fully informed in the median voter theorem. In reality, although voters are often informed on particular topics, none are fully informed. This allows politicians to tailor their positions to what each group of donors or electorate is likely to be informed about. Election results end up molded by lobbyist and donor preferences rather than those of the median voter.

With the median voter theorem of little use outside the halls of academia, there is no marginal benefit for a single voter to hold on to. This leaves emotional stimulus, feelings of inclusion, and a vague sense of acting for the greater good as the chief motivators for being a proud and active voter.

I’ve attempted to elucidate the complexity and limitations accompanying the last motivation, purposely highlighting the prior two as the primary impetus behind castigation of nonvoters.