Friday, February 2, 2018

Asymmetrical Category Relevance

There is something very interesting in this framing which I am wrestling to articulate. If I can nail it down, I think it is a class of error which is common in polling.



The basic frame is "Should we give more beneficial things to:" and then offers five categories.
Older Poeple
Poor People
Middle Class People
Younger People
Rich People
Their empirical conclusion is that the surveyed do not want to give more beneficial things to Rich People.

Fair enough. Not a surprising result. The rich are already disproportionate beneficiaries, and are usually well positioned to look after themselves. I am not disputing that these empirical numbers represent how most randomly selected people would respond.

The measurement issue in the framing is that four of the categories are different in nature from the fifth. Specifically, everyone, if not now, will be at some point Old. Everyone, if not now, could have a measurable chance of becoming Poor. Everyone, if not now, could have a significant chance of being Middle Class. Everyone, if not now, either was or has Young people in their lives. Of 1,000 people being surveyed, 100% of them are likely in one of these categories, have prospects of being in one of these categories, or have in their immediate networks of friends and family, members of these categories.

Only 29% people think they will ever be a millionaire. Currently, 5% of Americans are millionaires.

Looked at it from this way, the Pew question actually reads differently. In fact it is two different questions.
"Should we give more beneficial things to groups to which you currently belong, have belonged or will belong?" for four questions.

"Should we give more beneficial things to a group to which you do not belong and do not think you will belong?" for one question.
Again, this isn't about whether Pew randomized their target polling group or whether Pew was misleading in their questions or even whether this is an apples-and-oranges question. The issue is that the frame forces a hidden skew on the responses.

The structure is asking people to respond to two different categories: 1) categories which they see as relevant to themselves and 2) categories which they do not see as relevant.

I think it is a reasonable assumption that people will be inclined towards generosity for categories in which they repose and have/can anticipate being relevant to them. And correspondingly people are likely ill-disposed towards generosity for categories that they see as irrelevant to them.

Let's test this with other candidates in the irrelevant categories (groups of people who are small compared to the respondent population and/or whose distinctive attribute does not have material presence in the world of the respondent populations.)

"Should we give more beneficial things to any of the following groups to which you do not belong and do not think you will belong?"
African-Americans

Asian immigrants

Left-handed people

Muslims

Transgender people

Seventh Day Adventists from Germany

Eastern Orthodox Christians

Atheists

Maronites from Lebanon

Red haired people

Small family-owned farms
With this list I have tried to include groups that are not numerically large within the larger population. I have tried to include a range of groups for whom there are likely sympathies (small family-owned farms), indifference (Seventh Day Adventists from Germany) and antagonisms (Atheists).

Regardless of whether the population has a favorable, unfavorable, or indifferent attitude, I suspect that the responses for all these groups would look like the responses for Rich People. Because these are irrelevant attributes to the surveyed population, they would almost certainly be disinclined to extend more beneficial things to them. Not because of attitude towards the group but because of the irrelevance of the group to the surveyed population.

What do we call this phenomenon? I don't know. The Pew survey is framed in such a way that it appears that people favor Middle Class, Old, Young, and Poor and disfavor the Rich. But that is likely not what it is saying. It is saying that the respondents do not wish to extend favor to those in circumstances deemed irrelevant to the respondents.

The results are not due to relative favoring of groups but due to asymmetrical category relevance.

When pollsters do randomized surveys of a population, say on a political issue, they routinely have to normalize the results. Say the populace is equally divided among Democrats, Republicans and Independents. Once they collect the responses, they discover that the surveyed population deviates from the expected distribution of 33/33/33 and is actually 40/30/30. They have to normalize the results so that it reflects the known distribution of 33/33/33.

What the above line of thought implies is that they should also be doing some sort of normalization to address asymmetrical category relevance. Normalization of relevance equality as it were.

Having now seen the issue, it will be interesting to see how many surveys have symmetrical or asymmetrical category relevance. I suspect it is a more common issue than I might have recognized.

Taking asymmetrical category relevance into account might up-end how we understand various issues. Take some distinctly urban concerns such as densification, gentrification, and rent control. Each of those are more or less pertinent to perhaps some 10-30% of the population (people who live in urban centers). When you do a survey that includes people from the entire population, you have an asymmetric category relevance issue that needs to be addressed.

The best example of asymmetric category relevance is in Gallup's tracking of most important problems. The two big, and fairly constant problems are the Economy and the Government. Everybody is affected by the economy and everybody is affected by government. They are both universally relevant.

But after those two universal categories, it plunges markedly. Just about everything else is in the 0-10% category. Virtually all these other categories are strategic/material/important issues but most of them are only relevant to some subsections of the population.

Returning to the original Pew results, you can see how the reported numbers, unadjusted for asymmetrical category relevance, might skew policy thinking. 95% of people are not millionaires and therefore, their indifference to Rich People makes sense. But because 64% think we are already doing too much can lead to an unhealthy position: Rich People are an outgroup to the majority of the population and therefore it is acceptable to shift more the burden of increased taxes and decreased benefits to them and away from the majority. Taken too far, you end up in the position of Connecticut, New Jersey and others where the outgroup of Rich People are so heavily taxed that the departure from the state of even one or two billionaires can throw the state budget into complete disarray. Despite it appearing from the Pew results that a commanding percentage of the population thought that was a good idea.

RELATED:


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Blue Room, 2010 by Linden Frederick

Blue Room, 2010 by Linden Frederick

Click to enlarge.

Normal distribution serendipity

When you scan large volumes of disparate information from varying sources, you get to enjoy a lot of serendipity.

Yesterday morning I was speculating about the surprising abundance of instances where there appears to be a normal distribution of an attribute. My thought process was something along the lines of:
There seem to be an awful lot of instances of normal distribution.

Well, probably a lot of those distributions are near-normal but not perfectly normal distributions, so perhaps it is not as common as I assume.

But the utility for quotidian decision-making of switching from an average number to the concept of a distribution is so high, that it exceeds any error arising from deviance from normal distribution.

Even if they are only near-normal distributions, why does it occur with such frequency?
Today I come across:

Lyon is getting to a much deeper aspect of the "why" than I have the maths chops to follow.

Purity

From the estimable XKCD.

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Thursday, February 1, 2018

Be kind. Read more books. Spend time with your family.

It is not data analysis (my preferred mode) but does speak to greater truths. Read the whole thread. With Kleenex nearby.


Summary:


UPDATE: Echoes of Aldous Huxley
It is a bit embarrassing to have been concerned with the human problem all one's life and find at the end that one has no more to offer by way of advice than 'Try to be a little kinder.'
Quoted by Huston Smith in "Aldous Huxley--A Tribute," The Psychedelic Review, (1964) Vol I, No.3, (Aldous Huxley Memorial Issue), p. 264-5.

And a wit that was both wry and rather perversical

I did enjoy these review in The Economist, April 9th, 2005. Reviewing Ogden Nash: The Life and Work of America's Laureate of Light Verse by Douglas M. Parker. The review is in the form of verses in the Ogden styles.
How odd of Og to have no dog—
Well, he did once have a terrier
To make the household merrier.
But mostly he was pugless,
We're told by Parker—not Dorothy but Douglas.
Actually, we're not:
This aperçu
May not be true.

He had a fairly quiet life,
Two lovely girls, a lovely wife,
And lived a while in Baltimore,
Which wasn't all his fault, for sure.

He didn't go in much for travel:
The thought of flight made him unravel.
So, no, he never saw Majorca,
But wrote a lot for the New Yorker.

He was a most delightful man, with many a charming idiosyncrasy—
And his great-great-great-uncle, a general, gave his name to Nashville in Tennasy.
But, more to the point, he had a gift for writing a versicle,
And a wit that was both wry and rather perversical.
Only with cocktails did he like to make a splash,
That Ogden Nash.

Dying candle, 1903 by Marcus Behmer

Dying candle, 1903 by Marcus Behmer

Click to enlarge.

Southern restaurants

From The New Yorker.

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"Appeal to authority", down for the count.

Well this seems a refutation of the "97% of experts agree", "the science is settled", "the consensus view among experts is . . ." crowd's appeal to authority argument style. From Associations of fats and carbohydrate intake with cardiovascular disease and mortality in 18 countries from five continents (PURE): a prospective cohort study by Mahshid Dehghan, et al.
High carbohydrate intake was associated with higher risk of total mortality, whereas total fat and individual types of fat were related to lower total mortality. Total fat and types of fat were not associated with cardiovascular disease, myocardial infarction, or cardiovascular disease mortality, whereas saturated fat had an inverse association with stroke. Global dietary guidelines should be reconsidered in light of these findings.

Pleonasm

New word with which I am unfamiliar.

Pleonasm. From Wikipedia:
(/ˈpliːənæzəm/; from Greek πλεονασμός (pleonasmós), from πλέον (pleon), meaning 'more, too much') is the use of more words or parts of words than are necessary or sufficient for clear expression: for example black darkness or burning fire. Such redundancy is, by traditional rhetorical criteria, a manifestation of tautology. However, pleonasm may also be used for emphasis, or because the phrase has already become established in a certain form.
The entry has an interesting discourse on the use and history of ploenasm.