How Voting Rules Impact Legitimacy

Carina I. Hausladen, Regula Hänggli-Fricker, Dirk Helbing, Renato Kunz, Junling Wang, Evangelos Pournaras

Why US Politics is Broken—and How to Fix it.
1,481,549 views | Andrew Yang | April 2024

How are different voting methods perceived?

Are there differences with respect to legitimacy?

Behavioral Experiment

A voting method

consists of an

input mechansim and

an aggregation rule.

Four voting methods

choose one

approve,

stay neutral,

disapprove

assign points

0

1

3

5

choose & rank

1

2

3

majority

voting

combined approval

voting

range

voting

modified Borda

count

Measuring Legitimacy

Scharpf (1999), Schmidt (2013)

input-legitimacy
output-legitimacy
throughput legitimacy

acceptance

influence

trust

fairness

Weil and Hänggli (2021)

empirically measure those dimensions
four clusters of questions
found that all factors load on PC1 (74% of variance)
allows us to address them with a single question

acceptance

influence

trust

fairness

Measuring Legitimacy

"I would comply with the result and accept it as fair, reflecting my and others’ opinions."

strongly agree | somewhat disagree | neutral | somehwat agree | strongly agree

Please assess the following statement for each voting method applied.

Context

Polarizing

Context

Polarizing

Vaccine regulation
- How should the government regulate COVID-19 vaccines?
ICU access
- Among COVID-19 patients, which criteria should grant access to an intensive care unit?
Infection protection
- Which protection measure(s) against a COVID-19 infection is the most effective one?
Government strategy
- Which strategy should the government adopt to fight the COVID-19 pandemic?

Vaccine regulation
ICU access
Infection protection
Government strategy

Control question

What is your favorite color?

Control question

Legitimacy rating

Vaccine regulation
ICU access
Infection protection
Government strategy

Legitimacy rating

choose one

approve,

stay neutral,

disapprove

assign points

0

1

3

5

choose & rank

1

2

3

Results

$n = 120$
36% female
Mean age: $μ = 25.47$
37% with Bachelor's degree
22 countries

vaccination

Vaccine regulation

ICU access

Infection protection

Government strategy

Winning options vary by input method.

Why?

Vaccine regulation

ICU access

Infection protection

Government strategy

Standard deviation
(Schmitt, 2016)

Divisiveness
(Navarrete et al., 2022)

\[ s_{mv} \in \{0,1\} \]

\[s_{cav} \in\{-1, 0, 1\}\]

\[s_{sv} \in\{0,1,2,3,4\}\]

\[s_{mbc} \in\{0,1,2,3,4\}\]

Vaccine regulation

ICU access

Infection protection

Government strategy

Standard deviation
(Schmitt, 2016)

Divisiveness
(Navarrete et al., 2022)

Infection protection

Government strategy

Vaccine regulation

ICU access

The choice of voting method is especially crucial when preferences are highly polarized.

For each pair of options $o_m$ and $o_n$, let:

$s(o_m, o_n)$ be the rating when o_m is preferred over $o_n$
$s(o_n, o_m)$ be the rating when o_n is preferred over $o_m$

Then, divisiveness for each voting method $vm$ for each question $q$ is defined as:

$D_{v}^q = \frac{1}{n(n-1)} \sum_{m=1}^{n} \sum_{n=1}^{n} \|s(o_m,o_n) - s(o_n,o_m)\| $

Divisiveness

"I would comply with the result and accept it as fair, reflecting my and others’ opinions."

strongly agree | somewhat disagree | neutral | somehwat agree | strongly agree

How do participants evaluate the perceived legitimacy of various voting methods?

Color

COVID

Vaccine regulation

ICU access

Infection protection

Government strategy

4—

3—

2—

1—

0—

legitimacy rating

range
voting

modified
Borda
count

combined
approval
voting

majority
voting

declining nuance

COVID

4—

3—

2—

1—

0—

legitimacy rating

range
voting

modified
Borda
count

combined
approval
voting

majority
voting

Color

4—

3—

2—

1—

0—

legitimacy rating

range
voting

modified
Borda
count

combined
approval
voting

majority
voting

Color

COVID

7.02e^-06***

0.04*

Flexibility in voting methods is perceived as more legitimate in a political context.

Is range voting always the best choice in a political context?

It depends on the voter.

0

1

3

5

1

2

Measuring consistency

Among COVID-19 patients, which criteria should grant access to an intensive care unit?

no vaccine denial

no lockdown violation

no health self-damage

youngest

oldest

majority

voting

combined approval

voting

range

voting

modified Borda

voting

Consistent Voter

0

1

3

5

1

2

Measuring consistency

Among COVID-19 patients, which criteria should grant access to an intensive care unit?

no vaccine denial

no lockdown violation

no health self-damage

youngest

oldest

majority

voting

combined approval

voting

range

voting

modified Borda

voting

Inconsistent Voter

The Inconsistent Voter.

0

1

3

5

1

2

no vaccine denial

no lockdown violation

no health self-damage

youngest

oldest

Preference Reversal is well documented since the 1970s.

Lottery A: 90% chance to win $10

Lottery B: 10% chance to win $100

Which lottery would you prefer to play?

How much would you be willing to pay for each lottery?

Lichtenstein and Slovic (1971)

A > B

B > A

How much would you be willing to pay for each lottery?

A > B

B > A

Choice focuses on probability.

Pricing focuses on potential payout.

Cognitive & Behavioral Factors.
Comparability Bias.
Framing Effect.
Cognitive Limitations.

Which lottery would you prefer to play?

increasing nuance

Voters who consistently express their preferences
rate voting methods that allow for detailed preference expression
as more legitimate than those
who vote inconsistently.