There's an interesting insight here. From Women’s Attitudes on the Gender Pay Gap May Surprise You by Emily Ekins which includes this results from Pew Research:
I wonder if we might be able to create some sort of Reality Distortion Index based on three perspectives of Truth.
The first perspective is the empirical and objectively measured Truth (Empirical Aggregate Truth) of the aggregate issue. Whatever the designated aggregate population, what are the associated empirical and objective measures of the issue? In this instance, perhaps we are interested in the question of how much land in the USA is owned by the Federal Government, a pressing issue for some, and an irrelevance for others. There are all sorts of measurement issues attached to such a question. Are we talking contiguous US (lower 48) or continental (including Alaska and Hawaii), are we including commonwealths (like Puerto Rico) or unincorporated territories such as Guam or American Samoa), are we including bodies of water, etc. The Empirical Aggregate Truth is that the Federal Government owns 28% of all land in the USA. In a world of epistemological perfection, 100% of people would know the objective truth.
The second perspective is the perceived abstract Truth (Perceived Aggregate Truth). What does the population believe to be true at an aggregate level? Framing and wording is of course critical. One might ask "Does the Federal Government own the majority of land in the US?" The Empirical Aggregate Truth is 28% and so one would anticipate that in an ideal world, 100% of people would answer "No, the Federal Government does not own the majority of land in the USA". Anything less than 100% is a measure of their miscomprehension of the Empirical Aggregate Truth. It doesn't tell you why they have that misapprehension - could be ignorance, poor education, ideological beliefs, religious beliefs, lack interest or engagement with the issue, confusion about the difference between local and aggregate, etc.
The third perspective is the Empirical Local Truth. What are the empirical measures of the local truth. Extending the land example, if I live in Georgia, the Empirical Local Truth is that the Federal Government owns only 4% of the land in the State of Georgia, compared to Alaska where the Federal Government owns 61% of the land. A challenge with this perspective is to set some parameters on what effectively constitutes "local". Georgia is a big state and citizens can easily know only there own corner, the Appalachians, the Piedmont, the Plains, the Coast. Local could be at the State level or it could be even more circumscribed.
The fourth perspective is the locally perceived Truth (Perceived Local Truth). What does the population believe to be true at the local level? If you ask "Does the Federal Government own the majority of land in Georgia?" you would anticipate that close to 100% would know that that is not true. Some portion of the residents near Federal Forests or near some of the Army bases might understandably answer in the affirmative, but you would expect the gap between 100% knowing that the statement is not true locally would be small.
From this structure, you can derive two indices - the Aggregate Misperception Index (the gap between aggregate empirical and aggregate perceived) and the Local Misperception Index (the gap between local empirical and local perception).
Turning to the Pew data, we know empirically, across the OECD and over several decades, it has been documented that men and women earn the same amount for the same work. The claim that women earn only 65,70,80% of what men earn has been repeatedly disproved. The claim rests on comparing apples and oranges. When you normalize populations by holding constant things like education attainment level, number of years continuously at work, nature of degree earned and field of practice, work schedule flexibility, number of hours worked, etc. men and women earn the same amount. In a world of epistemological perfection, 100% of people would know the objective truth.
What the Pew data shows us is that 55% ((47+62)/2) of the population believe men to earn more for the same work. The Aggregate Misperception Index is therefore 55% (the percentage who inaccurately know that men earn more for the same work).
We cannot objectively measure the local truth because we don't know where the participants are located but it is reasonably safe to assume, (given that it is illegal to discriminate compensation based on sex and given that such discrimination is not evidenced at the macro level), that the correct answer is that men and women are also paid the same for the same work.
Here, the Local Misperception Index is only 12% ((9+14)/2) with most people accurately believing that men and women are paid the same for the same work.
Lots of interesting speculation arises from this index approach. Throughout the discussion, it is important to keep in mind just how significant is the wording of the question.
Q1 - Why is the Local Misperception Index so low? Salaries are among the more tightly controlled pieces of information in companies. HR policies often explicitly forbid sharing of salary information on threat of dismissal. On the other hand there is the countervailing reality that people have a more attuned awareness through local networks and actual engagement. In general, I would expect local participation to improve the Local Misperception Index but have no idea what the normalized range of the Index would be, recognizing that it likely varies materially by topic.
Q2 - Why is the Aggregate Misperception Index so high? In this case, I think it is reasonably understandable. One political party is heavily invested in the issue as a tribal signaling function ("we are the same tribe if we both believe X") and the mainstream media routinely contributes by publicizing the issue despite the known empirical evidence contradicting the belief. This is a classic example of received wisdom and narrative that is simply wrong.
Q3 - What is the implication of such a large gap of 43% (12% versus 55%) between the Local Misperception Index and the Aggregate Misperception Index? +/- 5% margin of error would be perfectly understandable but 43%? That's a huge gulf. That seems to indicate that people's sources of information for conceptual (Aggregate) information is far inferior to their sources of information for the concrete (Local). Is it that people are not engaged with aggregate information collection or is it that aggregate information sources are misleading?
I'll kick this around a bit. Could be an interesting approach.