A study of deceit when reporting information in a known context

Derek Jones from The Shape of Code

A variety of conflicting factors intrude when attempting to form an impartial estimate of the resources needed to perform a task. The customer/manager, asking for the estimate wants to hear a low value, creating business/social pressure to underestimate; overestimating increases the likelihood of completing the task within budget.

A study by Oey, Schachner and Vul investigated the strategic reasoning for deception/lying in a two-person game.

A game involved a Sender and Receiver, with the two players alternating between the roles. The game started with both subjects seeing a picture of a box containing red and blue marbles (the percentage of red marbles was either 20%, 50%, or 80%). Ten marbles were randomly selected from this ‘box’, and shown to the Sender. The Sender was asked to report to the Receiver the number of red marbles appearing in the random selection, K_{report} (there was an incentive to report higher/lower, and punishment for being caught being inaccurate). The Receiver could accept or reject the number of red balls reported by the Sender. In the actual experiment, unknown to the human subjects, one of every game’s subject pair was always played by a computer. Every subject played 100 games.

In the inflate condition: If the Receiver accepted the report, the Sender gained K_{report} points, and the Receiver gained 10-K_{report} points.

If the Receiver rejected the report, then:

  • if the Sender’s report was accurate (i.e.,K_{report} == K_{actual}), the Sender gained K_{report} points, and the Receiver gained 10-K_{report}-5 points (i.e., a -5 point penalty),
  • if the Sender’s report was not accurate, the Receiver gained 5 points, and the Sender lost 5 points.

In the deflate condition: The points awarded to the Sender was based on the number of blue balls in the sample, and the points awarded to the Received was based on the number of red balls in the sample (i.e., the Sender had in incentive to report fewer red balls).

The plot below shows the mean rate of deceit (i.e., the fraction of a subject’s reports where K_{actual} < K_{report}, averaged over all 116 subject’s mean) for a given number of red marbles actually seen by the Sender; vertical lines show one standard deviation, calculated over the mean of all subjects (code+data):

Mean rate of deceit for each number of red marbles seen, with bars showing standard deviation.

Subjects have some idea of the percentage of red/blue balls, and are aware that their opponent has a similar idea.

The wide variation in the fraction of reports where a subject reported a value greater than the number of marbles seen, is likely caused by variation in subject level of risk aversion. Some subjects may have decided to reduce effort by always accurately reporting, while others may have tried to see how much they could get away with.

The wide variation is particularly noticeable in the case of a box containing 80% red. If a Sender’s random selection contains few reds, then the Sender can feel confident reporting to have seen more.

The general pattern shows subjects being more willing to increase the reported number when they are supplied with few.

There is a distinct change of behavior when half of the sample contains more than five red marbles. In this situation, subjects may be happy to have been dealt a good hand, and are less inclined to risk losing 5-points for less gain.

Estimating involves considering more factors than the actual resources likely to be needed to implement the task; the use of round numbers is one example. This study is one of few experimental investigations of numeric related deception. The use of students having unknown motivation is far from ideal, but they are better than nothing.

When estimating in a team context, there is an opportunity to learn about the expectations of others and the consequences of over/under estimating. An issue for another study 🙂