We Add Near, Average Far

Quick, what is the best gift you ever got from a woman? From your parents? From a left-handed person? From a teacher? These aren’t easy questions to answer. But they seem easier than these questions: What is the total value of all the gifts you ever got from women? From your parents? From left-handed folks? From teachers?

For the first set of questions you can try to think of examples of particular people in those categories, and then think of particular gifts you got from those particular people. That can help you guess at the best gift from those categories. But to estimate the total value of gifts from people in categories, you’ll have to also estimate how many gifts you ever got from folks in each category.

Note that it also seems easy to estimate the average value of gifts from each category. To do this, you need only remember a few gifts that fit each category, and then average their values.

As another example, imagine you are looking at building entrance laid out in multi-colored tiles. Some tiles are blue, some red, some green, etc. You are looking at it from a distance, at an angle, in variable lighting. In this situation it will be much easier to estimate if there is more blue than red area in the tiles, than to estimate how many square inches of blue tile area is in that entrance. This later estimate requires you to additionally estimate distances to reference points, to estimate the total surface area.

These examples suggest that when we think in far mode, without a structured systematic representation of our topic, it is usually easier to average than to add values. So averaging is what we’ll tend to do. All of which I mention to introduce to a fascinating paper that I just noticed, even though it got a lot of publicity last December:

This analysis introduces the Presenter’s Paradox. Robust findings in impression formation demonstrate that perceivers’ judgments show a weighted averaging pattern, which results in less favorable evaluations when mildly favorable information is added to highly favorable information. Across seven studies, we show that presenters do not anticipate this averaging pattern on the part of evaluators and instead design presentations that include all of the favorable information available. This additive strategy (“more is better”) hurts presenters in their perceivers’ eyes because mildly favorable information dilutes the impact of highly favorable information. For example, presenters choose to spend more money to make a product bundle look more costly, even though doing so actually cheapened its value from the evaluators’ perspective. (more)

The authors attribute this to a near-far effect:

Presenters face many pieces of potentially relevant information and need to determine, in a bottom-up fashion, which ones to include in a presentation. This presumably draws attention to each individual piece of information as a discrete entity and a focus on piecemeal processing. If a given piece of information exceeds a neutrality threshold, the presenter will conclude that it is compatible with the message he or she seeks to convey and will include it. This results in presentations that would fare better under an adding rather than averaging rule. In contrast, evaluators’ primary task is to make a summary judgment of the overall presentation, which fosters a focus on holistic processing and the big picture and results in an averaging pattern as observed in many impression formation studies.

Additional experiments confirm this near-far interpretation. Those who prepare presentations and proposals tend to focus on them in detail, and so add part values in near mode style, while those who consume such presentations or proposals tend to pay much less attention, and so average their values in far mode style.

This result seems to me quite pregnant with interesting implications, none of which were mentioned in the dozen blog posts on the subject that have appeared since last December. So I guess it’s up to me.

First, this result predicts the usual academic advice to delete publications from low ranked journals from your vita. Yes those extra publications took extra work, and show more total intellectual contribution, but distracted readers evaluate you by averaging your publications, not adding them.

Second, this also predicts that academia will tend in general to neglect conclusions suggested by lots of weak clues, relative to conclusions based on a single strong theory or empirical comparison. People with a practical understanding of particular areas will correctly complain that academics tend too much to latch on to a few easy to explain and justify arguments, at the cost of lots of detail that practitioners appreciate.

Third, this predicts that in morality and politics, which are especially far sorts of topics, arguments tend to be won by those who push simple strong principles, even though people privately tend to choose actions that deviate from such principles. For example, while laws say no one can get medical advice from non-doctors, on the grounds that docs know best, but given a private choice most of us would often let other considerations convince us to listen to non-docs. While actions tend to be chosen in a near mode where lots of other weaker considerations get added, people know their best chance for winning an argument with a distracted audience is to focus on their one strongest point.

Fourth, this predicts Tetlock’s hedgehog vs. foxes result. Foreign policy is an especially far view sort of subject, and experts who focus on one strongest consideration get the most respect and attention, but experts who rely on many considerations, which are on average weaker, are more accurate.

Futurism is probably the most far view sort of topic, so I’d guess that all this holds there the most strongly. That is, while the most futurists who get the most attention from distracted audiences are those who harp endlessly on one clear plausible idea, the most accurate futurists are probably those who know and use hundreds of clues, many of them weak. Alas this is a problem for those of us who want to consider some aspect of the future in detail, since we quickly run out of strong principles, and then have to rely more on many weak clues.

Added Nov 25, 2012: This post gives data showing people donate money based more on the average than the total sympathy of the recipients. So you are better off asking for donations to help a particular especially sympathetic recipient, than to help many such folks.