Quantum Models of Voting Behavior

Introduction

Rational choice theory—the dominant framework in political science—assumes voters have stable, well-defined preferences and make choices that maximize expected utility. But decades of research reveal systematic violations:

• Voters support contradictory policies
• Preferences reverse with question order
• Small contextual changes produce large swings
• Information sometimes decreases rather than increases preference clarity

Quantum Decision Theory provides a coherent framework for these “paradoxes.”

The Classical Problem

Classical Expected Utility Theory says:

$EU(A) = \sum_i p_i \cdot u_i$

Where $p_i$ are probabilities and $u_i$ are utilities. This assumes:

1. Preferences exist before measurement
2. Probabilities follow classical laws
3. Information always reduces uncertainty

None of these hold in political cognition.

The Quantum Alternative

QDT replaces classical probabilities with probability amplitudes:

$|\psi\rangle = \sum_i \alpha_i|i\rangle$

Where $\alpha_i$ are complex numbers. The probability of outcome $i$ is:

$P(i) = |\alpha_i|^2 = \alpha_i^* \cdot \alpha_i$

This seemingly minor change has profound implications.

Key Phenomena Explained

1. Order Effects

When voters are asked about issues A then B, they respond differently than when asked about B then A. Classical theory calls this “bias.” QDT shows it’s non-commutative measurement:

$\langle A \rangle \langle B \rangle \neq \langle B \rangle \langle A \rangle$

2. Disjunction Effects

Voters sometimes prefer:

• Neither A nor B individually
• But support “either A or B”

This violates classical probability but follows naturally from quantum interference.

3. Preference Reversals

Introducing a third option can reverse preferences between two existing options—the famous “decoy effect.” QDT explains this through state space expansion.

Interactive Demonstration

Interactive Probability Calculator

State 1: |ψ₁⟩

Real part: 0.60

Imaginary part: 0.30i

Probability: 45.0%

State 2: |ψ₂⟩

Real part: 0.40

Imaginary part: -0.50i

Probability: 41.0%

Superposition Analysis

Classical Average

43.0%

Quantum Result

52.0%

Interference Effect

+9.0%

Formula: |ψ₁ + ψ₂|² / 2

Superposition state: (0.707 -0.141i)

Interpretation: The constructive interference of 9.0% shows quantum effects that cannot be explained by classical probability theory. This represents how voters' beliefs can amplify or cancel when combining multiple information sources.

💡 Try this: Adjust the imaginary parts to see how phase relationships create constructive or destructive interference. When states are "in phase," probabilities increase. When "out of phase," they decrease.

Empirical Evidence

Studies across multiple countries show:

Phenomenon	Classical Prediction	QDT Prediction	Observed
Order effects	~5%	20-40%	35%
Preference instability	Low	High	High
Context dependence	Minimal	Strong	Strong

Implications for Democracy

If voters don’t have pre-existing preferences, what does this mean for democratic theory?

1. Polling is interventionist: Surveys don’t measure—they create preferences
2. Deliberation matters differently: Discussion doesn’t reveal hidden preferences but generates new superpositions
3. Information campaigns have quantum effects: Messages create interference patterns

Conclusion

Quantum models don’t suggest voters are irrational. They suggest reality itself is quantum, and political cognition reflects this fundamental structure.

The question isn’t whether QDT is “right”—it’s whether we want democratic institutions that acknowledge the quantum nature of human decision-making.

Further Applications

• Campaign Strategy Under Quantum Uncertainty
• Polling Methodology and Quantum Measurement
• Debate Effects as Quantum Interference

References

1. Busemeyer, J. R., & Bruza, P. D. (2012). Quantum Models of Cognition and Decision. Cambridge University Press.
2. Pothos, E. M., & Busemeyer, J. R. (2013). Can quantum probability provide a new direction for cognitive modeling? Behavioral and Brain Sciences, 36(3), 255-274.
3. Wang, Z., & Busemeyer, J. R. (2013). A quantum question order model supported by empirical tests of an a priori and precise prediction. Topics in Cognitive Science, 5(4), 689-710.