Free and fair elections vs. Muslim share
Holds up after adjusting for income
A country is not a person. Countries where more people are counted as belonging to this group also tend to differ on the other measure, and that is all. It does not follow that the people in the group are the people with the different score. Making that leap is called the ecological fallacy: reading a pattern across places as a fact about individual people. It is the most common misuse of this kind of data. Religion also varies strongly with region, history and national income, so much of what looks religious here is really those. That is what the adjusted figures are for. The religion shares are estimates for two years only, and the survey questions are asked in rounds that can be ten years apart.
Across 168 countries, Free and fair elections and Muslim share rise and fall together at r = -0.51 (on a scale from −1 to +1, where 0 means no link). It holds up almost unchanged when only countries with similar income (GDP per person) are compared (r = -0.47, q = 0.043, allowing for the many pairs tested).
Comparing countries across the middle half of muslim share, 0.338% to 64.9% of population, free and fair elections is worse by 0.288 points at the top of that range than the bottom. Comparing only countries with similar national income, the gap is 0.223 points.
Link before adjusting (r)-0.509p = 1.8e-12 · 168 countries
After adjusting for national income-0.467p = 2.0e-10 · likely range [-0.58, -0.34]
p, allowing for regions0.017standard error 0.142 · 7 regions
Check for luck (q)0.043across 12,497 pairs
How to read these.r runs from −1 (one goes up as the other goes down) to +1 (they rise together), and 0 means no link. Adjusting for national income means comparing countries with the same GDP per person, so differences in wealth can’t explain the link. Income is used in percentage terms, since an extra $1,000 means more to a poor country than to a rich one. p is how likely a link this strong would be if there were really none. Below 0.05 means it is unlikely to be chance. Very small values are written in short form: 1.1e-32 means a decimal point followed by 31 zeros and then 11, so very close to zero. The likely range is where the true figure probably lies, and a range that crosses zero means the link could easily be chance. Countries in the same region tend to resemble each other, so the third figure allows for that, which gives a fairer p. The standard error is the typical size of the error in r. Finally, testing this many pairs means some will look strong by luck alone. A q below 0.05 means this link is unlikely to be one of those.
Free and fair elections · index (0-1)link with income +0.61 · high
Muslim share · % of populationlink with income -0.14 · independent
“Link with income” is how closely each measure tracks GDP per person across countries, from −1 to +1.
Every country as a dot
best-fit line line after adjusting
Four ways to measure the link
| Method | r | p | Countries |
|---|---|---|---|
| Standard (Pearson), not adjusted | -0.509 | 1.8e-12 | 168 |
| By rank (Spearman), not adjusted | -0.417 | 1.9e-8 | 168 |
| Standard (Pearson), adjusted for national income | -0.467 | 2.0e-10 | 168 |
| By rank (Spearman), adjusted for national income | -0.402 | 7.0e-8 | 168 |
The rank version uses only each country’s place in line, from lowest to highest, so a few extreme countries count for less. The adjusted and unadjusted versions use the same 168 countries: those that report both measures and GDP per person. So the gap between them comes from the adjustment, not from a change in which countries are counted. Drop in the size of r after adjusting: +0.042 (a minus sign means it grew).
How solid is it?
Leaving out one country at a time, r ranges from -0.492 (without GMB) to -0.449 (without SAU). The bar above shows that range on a scale from −1 to +1, with the solid line at the full result. The single country that moves r most: GMB (-0.025).
Within each region
Countries are not separate, unrelated cases, and neighbors share a lot. A link that holds inside each region is far more believable than one that shows up only when comparing regions.
| n | r | ||
|---|---|---|---|
| East Asia & Pacific | 21 | -0.03 | |
| Europe & Central Asia | 49 | -0.35 | |
| Latin America & Caribbean | 23 | -0.10 | |
| Middle East, North Africa, Afghanistan & Pakistan | 21 | -0.61 | |
| Sub-Saharan Africa | 46 | -0.23 |
By income third
If the link shows up only in the richest third of countries, it is a feature of rich countries, not a general pattern.
| n | r | ||
|---|---|---|---|
| Poorest third | 56 | -0.30 | |
| Middle third | 56 | -0.44 | |
| Richest third | 56 | -0.74 |
By largest religious group
Countries grouped by a label they share, such as main religion, rather than by a number. Groups of fewer than twelve countries are not shown. These groups differ in income, region and history all at once. So a gap between them is a place to start asking questions, not an answer.
| n | r | ||
|---|---|---|---|
| Christians | 99 | -0.09 | |
| Muslims | 48 | -0.02 |
By last european coloniser
Countries grouped by a label they share, such as main religion, rather than by a number. Groups of fewer than twelve countries are not shown. These groups differ in income, region and history all at once. So a gap between them is a place to start asking questions, not an answer.
| n | r | ||
|---|---|---|---|
| France | 25 | -0.00 | |
| Never a European colony | 21 | -0.60 | |
| Spain | 19 | +0.04 | |
| United Kingdom | 49 | -0.58 |
Without outliers (countries far outside the middle half of countries on either measure, by more than one and a half times the width of that middle half): r = -0.467 after dropping 0 countries.
Two series, one country
Both measures over the years for one country you pick. The two charts are stacked so they share only the years along the bottom.
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Over time, within countries
Everything above compares countries with each other at one moment. This section compares each country only with itself over 0years. So a link here can’t come from anything about a country that stays the same, such as its history, geography, institutions or culture.
Not enough history inside each country to look at this over time. That needs countries measured for several years in a row, and at least one of these measures is measured too rarely.
The data
index (0-1) | % of population | Years | |
|---|---|---|---|
| Belgium BEL | 0.968 | 6.81% | 2025, 2020 |
| Norway NOR | 0.966 | 4.11% | 2025, 2020 |
| Australia AUS | 0.962 | 3.5% | 2025, 2020 |
| Finland FIN | 0.961 | 1.61% | 2025, 2020 |
| Denmark DNK | 0.961 | 4.22% | 2025, 2020 |
| Germany DEU | 0.957 | 6.55% | 2025, 2020 |
| Spain ESP | 0.956 | 3.58% | 2025, 2020 |
| Chile CHL | 0.956 | 0.067% | 2025, 2020 |
| New Zealand NZL | 0.954 | 1.36% | 2025, 2020 |
| Netherlands NLD | 0.954 | 5.5% | 2025, 2020 |
| Estonia EST | 0.952 | 0.598% | 2025, 2020 |
| Uruguay URY | 0.947 | 0.0893% | 2025, 2020 |
| Sweden SWE | 0.945 | 8.1% | 2025, 2020 |
| Italy ITA | 0.945 | 4.42% | 2025, 2020 |
| Ireland IRL | 0.945 | 1.69% | 2025, 2020 |
Coppedge, M. et al., V-Dem Dataset, Varieties of Democracy (V-Dem) Project
Pew Research Center, Religious Composition by Country, 2010-2020. Pew Research Center bears no responsibility for the analyses or interpretations of the data presented here.
One of these measures is published under a licence that forbids changes. Values are shown exactly as published and must not be republished in a changed or rescaled form.
Sources
Free and fair elections
Free and fair elections index
V-Dem Institute, University of Gothenburg · via Our World in Data · CC BY 4.0 · updated annual
Whether elections are run without voter-registration fraud, widespread irregularities, government threats against the opposition, vote buying or election violence. This asks a narrower question than whether a country is a democracy, and one that is easier to answer. A state can run clean elections while barring the opposition from standing. It can also run dirty elections and still change government. It is the clean-elections part of the electoral democracy index. So its pair with that index, and with liberal and participatory democracy, is built from the same numbers and flagged as such.
Muslim share
Share of the population identifying as Muslim
Pew Research Center · via Our World in Data · Pew Research Center terms of use, excerpts with attribution · updated decennial · comparable from 2010 only
The second largest religion. The three religion shares are parts of one total. So for any pair of them, more of one means less of the others. They are built from the same numbers, so they are bound to match, and the site flags this. Hindu, Buddhist, folk and other religions are not included, so that what is taken from Pew's dataset stays a small excerpt of it. No "better" direction is set.
How this was computed
Data used: most recent value in 2010-2025; values come from 2020–2025. To adjust for income, each measure is first predicted from GDP per person (in percentage terms, on a log scale) with a straight-line fit. Only what is left over is then compared. This is called a partial correlation. The line is drawn the standard way (ordinary least squares), which picks the line that comes closest to all the countries at once. The error margins allow for countries in the same region resembling each other, using 7 World Bank regions. The q-value corrects for testing all 12,497 pairs at once, using the Benjamini–Hochberg method. Underlying data last updated DYB 2024. How the country data works · explore Free and fair elections and Muslim share
This page shows that two measures go together. It does not show that Free and fair elections changes Muslim share, or the reverse. These figures also describe countries, not individual people. See the ecological fallacy.
More links with Free and fair elections or Muslim share
- Free and fair elections vs Women's political empowerment before +0.78 → after adjusting +0.72
- Free and fair elections vs Rule of law before +0.78 → after adjusting +0.65
- Free and fair elections vs Political corruption before -0.78 → after adjusting -0.65
- Alcohol consumption vs Muslim share before -0.57 → after adjusting -0.55
- Gender Development Index vs Muslim share before -0.56 → after adjusting -0.55
- Corruption Perceptions Index vs Free and fair elections before +0.72 → after adjusting +0.54
- Control of corruption vs Free and fair elections before +0.72 → after adjusting +0.54
- Free and fair elections vs Gender score before +0.59 → after adjusting +0.51