Open Crowd perception Ariely, 2001

Catch the average.

Twelve circles of different sizes, or twelve tilted lines, appear for half a second; then you set the average size or the average tilt. Twice there is a surprise question: which circle was in the set? What does your visual system keep from a crowd, and what does it let go?

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EXP. 045

After seeing twelve circles for half a second, can you set their average size? And can you recognise one of them?

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Science box

When the visual system glances at a set of similar things, it can keep a summary of the set, such as its average size or average orientation, with surprising accuracy, rather than the individual members. This is called ensemble perception.

What we measure

We measure how accurately you capture the average of a set in a half-second glance, and how well you remember its individual members at the same time. In three of the five rounds, twelve white circles appear on a navy background for 500 milliseconds. The circles come in four sizes (three of each), with diameters 0.66, 0.84, 1.16 and 1.34 times the mean diameter; the largest circle is about twice the size of the smallest. The mean diameter is chosen at random between 7.5 and 10.5 per cent of the width of the playing field. After a blank screen of 300 milliseconds a single circle appears in the middle, starting 26 to 42 per cent smaller or 35 to 73 per cent larger than the mean. Dragging your finger or mouse outward on the screen makes it grow, dragging inward makes it shrink, and the arrow keys fine-tune it. In the other two rounds twelve short lines appear, their orientations spread evenly over a 24-degree range on both sides of an average tilt; in these rounds you turn the long line in the middle, as if drawing a circle, to the average tilt. In rounds 3 and 5, after you set the average size, a surprise question follows: which of two circles was in the set? One is a real member (16 per cent smaller or larger than the mean); the other is exactly the mean size and was never in the set. Chance level is 50 per cent. The size error is the logarithm of the ratio of your diameter to the mean diameter; an error of about 8 per cent earns 5 points. The tilt error is measured in degrees; 6 degrees earns 5 points. Each round scores 10 / (1 + (error / k)^1.6), and the five rounds add up to at most 50 points.

What the research says

In 2001 Dan Ariely used two new methods to ask what the visual system knows about sets. His observers could discriminate a set's average size very finely: the threshold was about 4–6 per cent of the spot size for similar spots, and 6–12 per cent for spots of clearly different sizes. Yet the same observers could tell whether a spot had been in the set only at near-chance level, even though members and non-members differed in size by at least 18 per cent. In 2003 Chong and Treisman found that thresholds for judging the mean of sets of twelve circles of different sizes were close to those for sets of identical circles and for single circles, and were little affected by exposure durations between 50 and 1000 milliseconds or by delays of up to 2 seconds. In 2001 Parkes and colleagues showed that people can reliably report the average orientation of patterns in peripheral vision that are packed so closely that their individual orientations cannot be read. Similar summaries appear for faces: Haberman and Whitney (2007) found that people rapidly extract the average emotion and gender of a set of faces, and de Fockert and Wolfenstein (2009) found the same for average identity.

Why it happens

We cannot store everything we see at a glance one by one; short-term visual memory holds only a few objects. Storing a set's average and spread, on the other hand, is cheap and often enough: the average colour of a tree's leaves, the general direction of a crowd or the average size of the books on a shelf help us understand a scene more than the individual details. Whitney and Yamanashi Leib (2018) reviewed evidence that ensemble perception works at many levels, from simple features like colour and size to facial expressions. How the summary is computed is debated, though: Myczek and Simons (2008) showed with experiments and simulations that focusing on a few items and averaging only those could explain most findings on average size. The surprise question in this experiment does not directly separate the two views, but it tests one thing: does a circle of exactly the average size, which was never in the set, feel more familiar than a real member?

Limitations

We defined the average size as the arithmetic mean of the diameters; if the circles' areas were averaged instead, the corresponding diameter would be about 3.5 per cent larger. Which measure the visual system averages is debated in the literature; the scoring curve tolerates such a small difference. Display time depends on the screen's refresh rate, and screen size changes the visual angle of the circles. The surprise question is asked only twice; with chance at 50 per cent, one person's two answers say almost nothing, and the meaningful result comes from the crowd's data. Also, the second surprise question is no longer a surprise: after the first one you may start paying attention to the members; that is why we also show the crowd's answers to the first question separately.

~4–6% of spot sizeThreshold for discriminating a set's average size (similar spots)Ariely, 2001

near chanceTelling whether a spot was in the setAriely, 2001

50 msShortest display at which judging the mean of twelve circles held upChong and Treisman, 2003

reported reliablyAverage orientation of patterns too crowded to read one by oneParkes et al., 2001

more often than to real membersSaying 'it was in the set' to an average face that was notde Fockert and Wolfenstein, 2009

Ariely, D. (2001). Seeing sets: Representation by statistical properties. Psychological Science, 12(2), 157–162. View source ↗
Chong, S. C., & Treisman, A. (2003). Representation of statistical properties. Vision Research, 43(4), 393–404. View source ↗
Parkes, L., Lund, J., Angelucci, A., Solomon, J. A., & Morgan, M. (2001). Compulsory averaging of crowded orientation signals in human vision. Nature Neuroscience, 4(7), 739–744. View source ↗
Myczek, K., & Simons, D. J. (2008). Better than average: Alternatives to statistical summary representations for rapid judgments of average size. Perception & Psychophysics, 70(5), 772–788. View source ↗
de Fockert, J., & Wolfenstein, C. (2009). Rapid extraction of mean identity from sets of faces. Quarterly Journal of Experimental Psychology, 62(9), 1716–1722. View source ↗
Haberman, J., & Whitney, D. (2007). Rapid extraction of mean emotion and gender from sets of faces. Current Biology, 17(17), R751–R753. View source ↗
Whitney, D., & Yamanashi Leib, A. (2018). Ensemble perception. Annual Review of Psychology, 69, 105–129. View source ↗

A crowd at a glance

If you glance at the marbles in a jar and close your eyes, you can't say where each marble was. But you can usually say roughly how big the marbles were on average, and whether they were all about the same size or mixed. The visual system summarises crowds with a kind of statistics.

In this experiment you look at twelve circles or twelve short lines for only half a second. Then you set the average size or the average tilt. Twice there is a surprise question: which of two circles was in the set? One really was in the set; the other never was, but its size was exactly the set's average.

Ariely's spots

In a study published in Psychological Science in 2001, Dan Ariely showed two observers sets of 4, 8, 12 or 16 spots for half a second. In one task he asked whether a single spot that followed was larger or smaller than the set's average; in another, whether a spot had been in the set at all.

The result was striking. The observers could discriminate the average very finely: the threshold was about 4–6 per cent of the spot size for similar spots and 6–12 per cent for spots of clearly different sizes. But they could tell whether a spot had been in the set only at near-chance level, even though members and non-members differed in size by at least 18 per cent. They knew the set's average, but not its members.

Short display, solid average

In 2003 Chong and Treisman tested this finding with sets of twelve circles of different sizes. The threshold for judging the set's average was close to the thresholds measured for sets of identical circles and for a single circle. Cutting the display time to 50 milliseconds, or delaying the answer by 2 seconds, changed the result very little.

The twelve circles and the half-second display in this experiment are inspired by these studies. The circle sizes come in four steps, spread symmetrically around the average, so the average is a size that is not in the set at all. The closer your circle is to that average, the higher your score.

Average orientation and crowding

Averages are not just about size. In 2001 Parkes, Lund, Angelucci, Solomon and Morgan showed oriented patterns packed closely together in peripheral vision in Nature Neuroscience. The patterns were so crowded that observers could not report the orientation of the central one; yet they could reliably report the average orientation of all of them. Information that could not be read individually was not lost; it went into the average.

In two rounds of this experiment we test the same idea with tilt: the orientations of twelve short lines are spread evenly on both sides of an average tilt, and you set that average. Ensemble perception also works for faces: in 2007 Haberman and Whitney found that people rapidly extract the average emotion and gender of a set of faces.

Recognising a circle you never saw

If the visual system keeps only the average, an interesting error is expected: a circle that was never in the set but is exactly the average size should feel more familiar than a real member. In 2009 de Fockert and Wolfenstein showed this with faces: participants who saw the faces of four different people said 'it was in the set' more often to an average face morphed from those four faces than to the real members.

The surprise question in this experiment follows the same logic. One of the two circles is a real member; the other was not in the set but is exactly the average size. If you guess, you will pick the real member half the time; a memory that drifts toward the average pulls you toward the average-sized circle. One person's two answers say little; we will look at which circle the crowd picks more often.

A summary, or a few samples?

How to interpret these findings is debated. One view is that the visual system processes all the items in a set in parallel and extracts a special summary. Myczek and Simons challenged this in 2008: with experiments and simulations they showed that focusing on a few items and averaging only those could explain most findings on average size. Ariely replied the same year and the debate continued; it is still not settled.

In their 2018 review, Whitney and Yamanashi Leib argued that ensemble perception works at many levels, from colour and size to facial expressions, and that it may be a way for a limited memory to summarise the world. Whichever route it takes, the practical result is the same: when you glance at a crowd, what stays with you is usually not the individual faces but the crowd itself.

FAQ

What is ensemble perception?

It is the visual system's ability to represent a set of similar things with summary information, such as their average size, average orientation or average colour. This summary can be extracted in a brief glance and is often more accurate than the memory of individual members.

How is my score calculated?

In the size rounds the error is the logarithm of the ratio of your diameter to the mean diameter; an error of about 8 per cent earns 5 points. In the tilt rounds the error is in degrees; 6 degrees earns 5 points. Each round scores 10 / (1 + (error / k)^1.6), rounded to two decimals. The total for five rounds is at most 50. The surprise question does not count toward the score.

What was the right answer to the surprise question?

One of the two circles really was in the set (16 per cent smaller or larger than the average); the other was never in the set but was exactly the set's average size. Picking the real member was correct; if you picked the average-sized circle, your memory may have leaned on the set's summary. With chance at 50 per cent, two answers prove nothing on their own.

Why is the average size never in the set?

The circles come in four sizes spread symmetrically around the average (0.66, 0.84, 1.16 and 1.34 times). So the average size is not in the set; the circle you set can be right not by copying a member but by summarising the set.

How do I make the circle bigger or smaller?

Drag your finger or mouse away from the centre anywhere on the screen and the circle grows; drag toward the centre and it shrinks; you don't need to press on the circle itself. On a keyboard the arrow keys fine-tune it, and with Shift it changes faster. In the tilt rounds you turn the line as if drawing a circle.

What are the daily series and the challenge?

In free play you get new sets every time. In the daily series everyone sees the same sets in the same order that day; the day changes according to Istanbul time. In a challenge you play exactly your friend's sets via their link; in a race room 2–6 people play the same sets at the same time. Only your first game is kept in the scientific data.

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