EDIT
 Compressing Reality

# Political Beliefs PCA

## Disclaimer

Nearly a year ago, I stumbled across a dataset of thousands of people’s answers to 63 political questions. I was pretty sure it was from Political Compass, but this seems contradicted by two facts:

1. I can’t find the dataset again
2. Political Compass states:, It is important to us — and most of our respondents — that the test remains anonymous, and purely for personal information. If we were to log anyone's results, those results would have to be given voluntarily. This would mean that our sample would be self-selected, and therefore not statistically valid. which certainly seems to imply that they don’t collect (let alone disseminate) such data…
3. Whatever the source, the data is probably not from a random sample, so take everything here with a heavy helping of salt. If anyone finds out where the data came from (it’s at the end), please shoot me an email or leave a comment.

## What is PCA?

PCA stands for principle component analysis. In this case, it solves this problem: “How can we compress someone’s someone’s political beliefs to a few numbers, so that if I only gave you their numbers you could guess their beliefs?”

For example, if I wanted to compress someone’s political beliefs down to a single number, it would probably be something like “How liberal (Conservative) are they on a scale from 1 to 100?” If I had 63 answers to questions, I can define your “liberalness” as a weighted sum of your answers.

For instance, your stances on abortion and welfare are a better predictor of your “liberalness” than your stance on, say, space exploration and whether judges should be elected. So, if those were our four questions, we might weigh the first two higher than the second two.

Extending this to 63 questions, gives us the single dimension that corresponds to the most significant way that people’s beliefs differ.

Of course, we can use more than one dimension. In PCA analysis, the dimensions are given in order of importance. This means that the first dimension tells us the most significant that political beliefs vary. We can also ask for a 2nd dimension that accounts for the 2nd most significant way political beliefs vary. Likewise, for the 3rd dimension, etc.

The issue with PCA is that instead of giving you dimension with convenient names like “Liberalness”, it gives you the weights given two each question and you have to guess what each dimension “means.”

## Dimension 1: Liberal v. Conservative

Unsurprisingly, first dimension appears to correspond to liberal v. conservative. To see why, let’s look at the top 4 questions at both extremes:

 Negative (“Liberal”) Positive (“Conservative”) Nobody should go hungry, even if they refuse to work. Anybody who wants top-quality health care should expect to have to pay for it. It's more important to rehabilitate criminals than to punish them. Everyone should stand up for the National Anthem. Services like health care, education and social security should be provided by the government, not by private enterprise. Aggressive foreign policies can put a stop to international terrorism. The wealthy should pay a larger proportion of their income in tax than the poor. Some crimes are so serious that the only proper punishment is the death penalty.

It turns out this continuum explains 24% of the variance in people’s responses to the 63 questions. To put this in perspective, if people’s responses to questions were independent, then we’d expect one continuum to explain only 1.6%. On the other hand, this still leaves a whopping 76% that isn’t explained by the left-right continuum, confirming the wisdom of not clumping all conservatives or liberals together.

## Dimension 2: Libertarianism

Here are the 4 questions at both extremes:
 Negative (“Libertarian”) Positive (???) Scientists bear no moral responsibility for how their discoveries are used. Shared religious beliefs should be an important part of our society. It's more important to make the poor richer than to decrease the gap between rich and poor. There are some sexual acts which are immoral, even between consenting adults. Anybody who wants top-quality health care should expect to have to pay for it. Some technologies should never be used, whatever their benefits. New roads and railways should be built by private companies, not the government. The government should subsidise farmers so that they stay in business, even if it would be cheaper to buy food from abroad.

This dimension explains 6.7% of the variance in people’s responses (bringing us to a total of 31%). The interesting thing is that this corresponds with Political Compass

## Dimension 3: Economic and Social Isolationism

Now we get into less-obvious territory. As far as I can tell these positions don’t really correspond well with any political commentary.

 Negative (Isolationist) Positive (???) Officials like public prosecutors should be directly elected rather than chosen by the government. Our nation has a glorious history. Aid projects abroad should always be funded by charities, not the taxpayer. Overall, economic migrants bring benefits to our country. Economic globalisation will increase inequality. Dealing with nuisance crimes like petty vandalism makes serious crime less likely. There are some ethnic groups who can never be fully integrated into our society. Our armed forces should intervene to stop genocide in other countries.

As we go on with our analysis, our dimensions become less and less explanative. This dimension explains 4.2% of the variance (for a total of 35%).

## Dimension 4: Religious

Still in less-obvious territory, it should be clear that one side of this dimension is basically how religious fundamentalist someone is, but the opposite end of the spectrum has no obvious connections.

 Negative (???) Positive (Religious) Members of our society should be familiar with the history and traditions of our culture. Religious faith should be based on the literal word of God. Correct grammar is important. No woman should be allowed to have an abortion, whatever the circumstances. Smokers should be required to kick the habit before receiving medical care for smoking-related illnesses. Our sense of right and wrong comes from religious faith. Services like health care, education and social security should be provided by the government, not by private enterprise. Schools should not teach children anything which contradicts their parents'' religious faith.

This dimension explains 3.3% of the variance (for a total of 39%). After this, the remaining 58 dimensions each explain less than 3% of the total variance and become very difficult to categorize according to intuitive political divides.

## Conclusion

Ultimately, then, it seems like even an “optimistic” analysis finds that trying to clump people together into groups of similar political beliefs accounts for a mere 39% of the variance, indicating that even together, the political dichotomies presented by the media fail to capture even half of the political variety within the country.

On the other hand, we see that the left-right divide is very real, accounting for more than 3 times as much of the variance as the second-greatest dimension.

Here is the raw data.

Here are the PCA- dimensions and the questions’ weights for each dimension.