EconTech

EDIT2: (Will only make sense if you have read the original post). It has been pointed out that my list of incomes fell short, leaving off the top two layers! This was an enormous oversight, and explains why everyone (myself included) was choosing E over D as the superior option. With the fixed data, the Gini for D and E are equal under the linear assumption (to two significant digits), with E having higher per capita income. Under non-linearity, E is both more wealthy and more equal. Amusingly, the same problem comes out. The survey doesn’t tell us which is more important in people’s minds, wealth or inequality, because it doesn’t present the trade-offs. It seems to me that a survey with varying levels of inequality/wealth tradeoffs presented to large groups and seeing where the breaking line(s) was(were) for opinions to spill over from one direction to the other would be much more informative. You can fix the code by changing the line “for I in [(10,20,...),(...)]:” to:

  for I in [(10,20,30,40,50,60,70), (1,10,10**2,10**3,10**4,10**5,10**6)]:

Thoma points us to Kenworthy’s post:

“Do People Care about Inequality?”

Lane Kenworthy says there is evidence suggesting “that inequality matters to people”:

Do People Care About Inequality?, by Lane Kenworthy: A question in the International Social Survey Programme’s 1999 survey offered respondents pictorial illustrations of various income distributions and asked “What do you think the distribution in your country ought to be like — which do you prefer?” The choices were depicted as follows:

A relatively small share, fewer than 20% in most countries, said they preferred type A, B, or C. This isn’t surprising; each of those three has a large share of the population at the bottom. The bulk of respondents selected either type D or type E.D and E are identical in their population shares at the bottom. The difference between them is that D has a larger share in the middle, whereas E has a larger share at the top. Average income is higher in E. Inequality is lower in D.Interestingly, more respondents in the ISSP survey preferred D than preferred E. The results are strikingly similar across countries, even among nations that seemingly have very different orientations toward affluence and equality.I wouldn’t go so far as to conclude from this that people tend to value low inequality over high incomes. Other ways of posing the question might yield different results. But it does suggest that inequality matters to people.

I chose E.

I asked for axis labels. Since my computer doesn’t talk back to me, I chose E too, but quite reluctantly. First of all, the framing of the question is all wrong for most respondents. While “ought” clearly implies to people who are familiar with the word some kind of moral, ethical, or preferential question, the “in your country” part makes it seem like a question of fact. If I prefer distribution X for country A, why would it be any different in another country? The attempt at context, in my mind, leads to a suggestion of a question of fact.

Now, I have no idea what is supposed to be the axes because Kenworthy does not link us to the actual survey questions, just the survey site’s front page, which is so unhelpful he might’ve well just said “Google it.” I am going with the presumption that we were given all the information that the survey respondents were given. I am now going to try to deduce the ‘proper’ response. My first intuition is to say that the vertical axis is supposed to be real income levels, constant across each graph with the horizontal axes (the X count) is the number of people at that income level (times some multiplier). As an economist, I want to know the total income level in the country before I get to distribution.[1]

For Income levels: 10,20,30,40,50 (i.e. linear scale):[2]

For Income levels: 1,10,100,1000,10000 (i.e. a logarithmic scale):[3]

I’m using Gini[4] instead of a more desirable poverty measure due to the lack of variance in the data making the others rather uninformative (said without explicit testing). Note that in these tables, Gini are comparable between the tables, but the other values are only comparable within each table. The surprise here is the behavior of the Gini coefficient. Under the linear assumption, inequality is lower in D, and indeed, GDP/capita is higher! Under the logarithmic assumption, E has lower inequality, but D still has higher GDP/capita.

A second possibility is that each level is % of GDP, with each total GDP constant. For pure preferences on inequality (as opposed to the inequality/income tradeoff), such a graph would be ideal. However, closer inspection of such an interpretation makes this rather unlikely (and if so, a terrible representation of such data) due to the incoherent interpretation of the X count in such a situation (I think).

So, do people care more about inequality or income? Well, if the linearity assumption holds, then there is no way to tell unless we are given a full ordering between the distributions! Under the logarithmic assumption, it appears income is more important.

Am I missing any other interpretations? Probably, though they weren’t obvious to me. Let me know if I am, and I’ll edit the above to include such interpretations (if they aren’t too time consuming to do).

Now, kids, remember to label your axes. Readers are not (usually) mind-readers. [Wouldn't Gelman hang you by your toes for this data representation? Probably, but I doubt he'll read this.]

Also, WordPress, your table handling sucks, terribly.

EDIT: Almost forgot, source code to the graphs can be found here.

Footnotes:

1. The size of the multiplier for population size is unimportant, as long as each step is equal. Well, obviously GDP and population will change under those assumptions, but I assume we don’t care too much about those levels. [↩]
2. The size of the step for income will not effect the relative results at all; so 100,200,300,400,500 will produce the same relative GDP/C, Median for the income inputs, and Gini will not change at all. [↩]
3. I did not test for sensitivity as to what log scale was used [↩]
4. remember, Gini==0 implies perfect equality, ==1 complete inequality [↩]