How the Political Circle works

A technical explanation of the methodology

If you're reading this page, you're probably curious about the mechanics behind the Political Circle test, and the questions we ask. How do we translate your answers into an angle and radius? What's the mathematical model? How do we ensure accuracy and consistency?

This page explains the methodology for those who want to peek under the bonnet, and lists the current question set, with the weightings.

The challenge: mapping political thought to coordinates

Political beliefs are complex, multidimensional and often contradictory. The challenge is to capture this complexity while producing a simple, interpretable output: an angle (0-360°) and a radius (0-1).

We need to:

1. Measure economic position (left-right)
2. Measure social position (libertarian-authoritarian)
3. Measure conviction strength (distance from centre)
4. Handle the fact that these dimensions interact
5. Produce results that match how people actually think

The two-axis foundation

The Political Circle builds on the traditional two-axis political model:

Economic axis (left-right):

• Left (negative): Public ownership, planning, redistribution, collective provision
• Right (positive): Markets, private ownership, individual responsibility, minimal state

Social axis (libertarian-authoritarian):

• Libertarian (negative): Personal freedom, civil liberties, minimal state interference
• Authoritarian (positive): Order, security, social cohesion, strong enforcement

These axes are perpendicular. Your position on one doesn't determine your position on the other. You can be economically left and socially libertarian (7 o'clock), or economically left and socially authoritarian (11 o'clock).

Question design and scoring

Each question in the test is designed to measure either:

• Economic position: Questions about markets, public services, taxation, redistribution
• Social position: Questions about civil liberties, security, authority, personal freedom
• Both dimensions: Some questions capture interaction between economic and social views

Questions use a 7-point Likert scale:

• Strongly agree: +3
• Agree: +2
• Somewhat agree: +1
• Neither agree nor disagree: 0
• Somewhat disagree: -1
• Disagree: -2
• Strongly disagree: -3

Each question is pre-weighted to contribute to the economic score, social score, or both. For example:

• "Essential services like healthcare should be publicly owned and free at point of use" → Economic left (+3 for strongly agree)
• "Mass surveillance is acceptable if it prevents terrorism" → Social authoritarian (+3 for strongly agree)
• "The state should ensure everyone has a job, even if that means restricting economic freedom" → Both economic left AND social authoritarian

Calculating the economic and social scores

After completing the test:

1. Raw economic score = Sum of (response × economic weight) for all questions
2. Raw social score = Sum of (response × social weight) for all questions

These raw scores are then normalized to a -1 to +1 scale:

• Economic score = raw economic score / maximum possible economic score
• Social score = raw social score / maximum possible social score

Where:

• -1.0 = Maximum left (economic) or maximum libertarian (social)
• 0 = Centre
• +1.0 = Maximum right (economic) or maximum authoritarian (social)

Converting to polar coordinates

Now we have two Cartesian coordinates: (economic, social). We convert these to polar coordinates: (angle, radius).

Angle calculation:

angle = arctan2(social_score, economic_score)

This gives us an angle in radians, which we convert to degrees and map to our 12 o'clock system:

• 3 o'clock (far right economically, neutral socially) = 0°
• 12 o'clock (neutral economically, maximum authoritarian) = 90°
• 9 o'clock (far left economically, neutral socially) = 180°
• 6 o'clock (neutral economically, maximum libertarian) = 270°

We then convert degrees to "o'clock" for presentation:

• o'clock position = (angle + 90°) / 30° (mod 12)

So if your angle is 150° (left-authoritarian), you'd be at approximately 10 o'clock.

Radius calculation:

radius = sqrt(economic_score² + social_score²)

This gives us the Euclidean distance from the origin (centre). The radius ranges from 0 (exactly centrist on both dimensions) to √2 ≈ 1.414 (maximum scores on both dimensions).

We normalize this to 0-1 scale by dividing by √2:

normalized_radius = radius / 1.414

So:

• Radius 0.0-0.4 = Moderate (close to centre)
• Radius 0.4-0.7 = Clear convictions (medium distance)
• Radius 0.7-1.0 = Strong convictions (far from centre)

Handling edge cases

Very centrist positions: If both scores are very close to zero (radius < 0.1), the angle becomes unstable (dividing by very small numbers). In these cases, we report "centrist" with low radius rather than assigning a specific o'clock position.

Extreme positions: If someone scores at the absolute maximum on both dimensions (radius close to 1.0), they're at one of the four cardinal points: 3, 6, 9, or 12 o'clock. Most people fall somewhere between these extremes.

Question weighting and balance

To ensure the test measures both dimensions fairly:

1. Equal weighting: Roughly equal numbers of questions measure economic position, social position, and both
2. Balanced polarity: Equal numbers of questions pull in each direction (left/right, libertarian/authoritarian)
3. Avoid double-counting: Questions measuring both dimensions are weighted so their total contribution equals single-dimension questions

Validation and calibration

We validate the test through several methods:

1. Face validity: Questions clearly relate to their intended dimension

2. Historical figures: We test whether known historical figures (when we simulate their answers) land where we'd expect:

   1. Margaret Thatcher → 1-2 o'clock, medium-high radius
   2. Bernie Sanders → 7-8 o'clock, medium radius
   3. Milton Friedman → 3-4 o'clock, high radius
   4. George Orwell → 8 o'clock, medium radius

3. Internal consistency: Questions measuring the same dimension should correlate; questions measuring different dimensions shouldn't over-correlate

4. Test-retest reliability: Taking the test twice should produce similar results (within 1-2 o'clock positions and 0.1 radius)

What the test doesn't do

It's important to understand limitations:

Not a personality test: We're measuring political beliefs, not personality traits. Your position may change over time as circumstances and experiences change.

Not predictive: We don't predict how you'll vote or which party you support. Political parties are coalitions that often combine positions from multiple o'clock positions.

Not comprehensive: We measure two dimensions (economic and social) and one meta-dimension (conviction strength). Real political thought involves many more dimensions: nationalism vs. globalism, environmentalism, foreign policy, cultural issues. We've chosen the two most fundamental dimensions, but we're inevitably simplifying.

Not prescriptive: The test tells you where you are, not where you should be. All positions involve tradeoffs. None is objectively correct.

The mathematics in brief

For those who want the formulae in one place:

Raw scores from questionnaire responses
economic_raw = Σ(response_i × economic_weight_i)
social_raw = Σ(response_i × social_weight_i)

Normalize to [-1, 1]
economic_score = economic_raw / max_possible_economic
social_score = social_raw / max_possible_social

Convert to polar coordinates
radius_raw = sqrt(economic_score² + social_score²)
radius = radius_raw / sqrt(2)  # Normalize to [0, 1]
angle_radians = arctan2(social_score, economic_score)
angle_degrees = angle_radians × (180 / π)

Convert to o'clock position
oclock = ((angle_degrees + 90) / 30) mod 12
if oclock == 0: oclock = 12

Classify radius strength
if radius < 0.4: strength = "moderate"
elif radius < 0.7: strength = "clear"
else: strength = "strong"

Why polar coordinates?

We could have kept Cartesian coordinates (left-right and libertarian-authoritarian scores) and presented those directly. But polar coordinates offer advantages:

1. Intuitive: "10 o'clock" is easier to visualize than "economic score -0.5, social score +0.7"
2. Captures interaction: The angle naturally captures how economic and social positions combine
3. Shows conviction: The radius cleanly separates what you believe from how strongly you believe it
4. Visual: Plotting positions on a circle shows relationships between positions (neighbours, opposites) more clearly than a square

Continuous vs. discrete

While we describe 12 discrete positions (the o'clock positions), your actual result is continuous. You might be at 7.3 o'clock, not exactly 7 or 8. We round to the nearest hour for presentation, but the underlying calculation is precise.

This matters because someone at 6.8 o'clock is closer to 7 o'clock thinking than someone at 7.4 o'clock, even though both round to 7.

For the statisticians

If you're wondering about measurement theory:

Reliability: Cronbach's alpha for economic questions and social questions separately should exceed 0.80. Test-retest reliability should produce correlation > 0.85.

Validity: Construct validity assessed through convergent validity (correlating with established political tests) and discriminant validity (economic and social dimensions should be largely independent, correlation < 0.3).

Distribution: We expect responses to roughly follow a bivariate normal distribution around the centre, though with some skewness depending on population sampled. Most users should fall within radius 0.7; very few at radius > 0.9.

Measurement error: Standard error of measurement should be < 0.1 for both axis scores and < 0.05 for radius. This translates to roughly ±1 o'clock position uncertainty and ±0.05 radius uncertainty.

Why this matters

Understanding the methodology helps you interpret your results. If you're at 7.2 o'clock with radius 0.45, you know:

• You're slightly left of centre economically
• You're slightly libertarian socially
• You lean social democrat but aren't strongly ideological
• You're closer to 7 o'clock than 8 o'clock, so read both chapters
• Your radius puts you in "clear" category—principled but not uncompromising

The methodology is designed to be transparent, replicable, and grounded in established political science while remaining accessible to general users.

If you have questions, corrections, or suggestions about the methodology, we'd love to hear them. The Political Circle is a model, and all models can be improved. Email us at hello@politicalcircle.app.

The Questions

Below are the current questions and their weightings. For each test, 16 questions are randomly chosen from a subset of odd or even numbered questions.

UK questions

Question		Economic Weight	Social Weight
1	Private firms run essential services better than the state.	-1	0
2	Essential services like energy and water should be run by government, not private companies.	1	0
3	The government should limit how much more bosses earn than average workers.	1	0
4	Everyone should pay the same percentage in tax, regardless of income.	-1	0
5	It should be easier for employers to hire and fire than to protect workers' rights.	-0.8	0
6	Unions should have stronger legal protections.	0.8	0
7	Large inheritances should be heavily taxed.	0.9	0
8	Taxing people's total assets discourages investment and should be avoided.	-0.9	0
9	Housing supply should be left mostly to the market.	-0.8	0
10	The government should limit how much landlords can charge in expensive areas.	0.8	0
11	NHS funding should grow even if it means higher taxes.	0.9	0
12	Private companies running healthcare improves outcomes and choice.	-0.9	0
13	Even harmful speech should be legal to protect liberty.	0	-1
14	Online misinformation should be removed even at the cost of free speech.	0	1
15	Mass surveillance is an acceptable trade for public safety.	0	1
16	Strong encryption and privacy should rarely be compromised by the state.	0	-1
17	Stop-and-search should be tightly limited and strongly overseen.	0	-0.9
18	Police should have wider stop-and-search powers.	0	0.9
19	Immigration should be tightly controlled to protect social cohesion.	0	0.9
20	It should be easier to live and work in the UK from abroad.	0	-0.9
21	Different cultures should mix naturally without government programmes.	0	-0.8
22	National identity and values should be actively promoted by government.	0	0.8
23	Protests that disrupt daily life should be banned.	0	1
24	The right to protest should be protected even when inconvenient.	0	-1
25	Local councils should decide most services without national direction.	-0.6	-0.6
26	Westminster should set more national standards for services.	0.6	0.6
27	National curriculum should be tighter and uniform.	0.4	0.8
28	Schools should be free to decide what they teach.	-0.4	-0.8
29	Rehabilitation should be prioritised over longer sentences.	0	-0.8
30	Longer sentences deter crime and should be used more often.	0	0.8
31	Police powers to ban people from areas or impose curfews are useful tools for public order.	0	0.7
32	Police powers to ban people from areas or impose curfews are government overreach in most cases.	0	-0.7
33	Planning should allow rapid building even over local objections.	-0.3	-0.7
34	Planning rules should strongly protect existing communities from change.	0.3	0.7
35	Property rights should rarely be overridden by social goals.	-0.6	-0.2
36	The government should be able to force purchase of private property for public benefit.	0.6	0.2
37	Welfare should be tightly targeted with strict conditions.	0.4	0.6
38	Benefits should rise automatically with living costs.	0.8	0
39	Everyone should receive a regular payment from government, regardless of circumstances.	0.9	-0.3
40	Cutting benefits increases incentive to work.	-0.7	0.3
41	The BBC should be subscription-funded or privatised.	-0.5	-0.2
42	The BBC licence fee should be protected.	0.5	0.2
43	Government should regulate social media content more strictly.	0	0.8
44	Platforms should decide content rules without government pressure.	0	-0.8
45	Strict border control protects wages and services.	0.2	0.8
46	Freedom of movement is generally beneficial.	-0.2	-0.8
47	Facial recognition should be widely used in public spaces.	0	0.9
48	Facial recognition in public should be rare and regulated.	0	-0.9

US questions

Question		Economic Weight	Social Weight
1	Essential services like energy and water should be run by government, not private companies.	1	0
2	Private companies run essential services better than government.	-1	0
3	Everyone should pay the same percentage in tax, regardless of income.	-1	0
4	The government should limit how much more bosses earn than average workers.	1	0
5	Right-to-work laws protect individual freedom and should expand.	-0.8	0
6	Unions should have stronger legal protections.	0.8	0
7	Large inheritances should be heavily taxed.	0.9	0
8	Estate taxes discourage saving and should be eliminated.	-0.9	0
9	Housing supply should be left to the market.	-0.8	0
10	The government should limit how much landlords can charge in expensive cities.	0.8	0
11	Medicare should expand even if it means higher taxes.	0.9	0
12	Healthcare is best delivered through private markets and insurance.	-0.9	0
13	Online misinformation should be removed even at the cost of free speech.	0	1
14	Even harmful speech should be legal to protect the First Amendment.	0	-1
15	Strong encryption and privacy should rarely be compromised by government.	0	-1
16	Mass surveillance is an acceptable trade for national security.	0	1
17	Police should have broader powers to stop and search.	0	0.9
18	Stop-and-frisk policies should be tightly limited and overseen.	0	-0.9
19	Immigration pathways should be easier and more welcoming.	0	-0.9
20	Immigration should be tightly controlled to protect jobs and cohesion.	0	0.9
21	American identity and values should be actively promoted by government.	0	0.8
22	Different cultures should mix naturally without government programmes.	0	-0.8
23	The right to protest should be protected even when disruptive.	0	-1
24	Protests that disrupt daily life should be prohibited.	0	1
25	The federal government should set more national standards for services.	0.6	0.6
26	States should decide most policies without federal direction.	-0.6	-0.6
27	School districts should be free to decide what they teach.	-0.4	-0.8
28	Common Core-style national education standards are needed.	0.4	0.8
29	Longer sentences deter crime and should be used more often.	0	0.8
30	Rehabilitation should be prioritized over longer sentences.	0	-0.8
31	Mandatory minimums are overreach and should be repealed.	0	-0.7
32	Three-strikes laws and mandatory minimums are good policy.	0	0.7
33	Zoning rules should strongly protect existing communities from change.	0.3	0.7
34	Zoning should allow rapid building even over local objections.	-0.3	-0.7
35	The government should be able to force purchase of private property for public benefit.	0.6	0.2
36	Property rights should rarely be overridden by social goals.	-0.6	-0.2
37	Social Security and Medicare benefits should increase with living costs.	0.8	0
38	Welfare programs should have strict work requirements.	0.4	0.6
39	Everyone should receive a regular payment from government, regardless of circumstances.	0.9	-0.3
40	Cutting welfare programs increases incentive to work.	-0.7	0.3
41	The Second Amendment protects broad individual gun ownership.	0	-0.9
42	Assault weapons should be banned or heavily restricted.	0	0.9
43	Government should regulate social media content more strictly.	0	0.8
44	Platforms should decide content rules without government pressure.	0	-0.8
45	Voting should be easier with automatic registration and mail ballots.	0	-0.7
46	Voter ID laws and election security measures should be stricter.	0	0.7
47	Facial recognition should be widely deployed in public spaces.	0	0.9
48	Facial recognition in public should be rare and regulated.	0	-0.9

NEW: Dive deeper into the ideas behind the Political Circle

The new book, 'Beyond Left and Right: Understanding the Political Circle' is now available on Amazon.

Containing a wealth of information, the book explores all of the 12 philosophical positions with detailed analysis on each of the three levels.

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