Acta Psychologica Sinica

Abstract

No studies on the relational reasoning illusion or the Chinese reasoning illusion problem have been conducted before. Therefore, in an attempt to conduct research on this topic the present research studied whether the ancient Chinese relational reasoning problem — named ten Wen (a basic unit of currency in ancient China) problem — is a reasoning illusion problem and if so, whether the problem can be explained by a domain specific theory in accounting. The ten Wen Problem is as follows. In ancient China, three Chinese Certified Students were on their way to Peking for their final imperial examination. One day they had to rent a room in a hotel as it had gotten very late. The cost of a room at the hotel was 300 Wen, and the three students rented only one as they were very poor. After they paid the money, the owner, who was aware of their condition, asked his assistant to return 50 Wen back to the three students. But the assistant was puzzled because he didn’t know how to divide 50 Wen into three equal parts. So he kept 20 Wen for himself and returned 30 Wen back to the three students. But something obviously went wrong! Each student was returned 10 Wen, so each of them actually paid 90 Wen. Thus, they paid 270 Wen in all. Now, if the 270 Wen is added to the 20 Wen, which was pocketed by the assistant, we get only 290 Wen! So where did the 10 Wen go?

We conducted four studies wherein subjects solved this problem, and chi-square was used for most of the data analysis. In the first study, 166 undergraduate students including 78 students who had solved the problem before were asked to solve the problem and provide the reasons for their solutions on a booklet. In the second study, the problem was presented by means of a verbal protocol procedure to 14 postgraduate students, to study whether the problem could be represented in the single-entry bookkeeping way. In the third study, 100 undergraduates student were randomly selected to solve the ten Wen problem under one of three conditions: no cue condition, single-entry bookkeeping cue condition, and double-entry bookkeeping cue condition. In the fourth study, 100 undergraduate students were randomly selected to solve one of two problems — either the original problem or a modified problem that did not have the loop structure in terms of its representation.

The results indicated the following: (1) only 30% of the subjects succeeded in solving the problem; (2) the two typical mistakes while solving the problem were — wrongly deeming that the three Chinese Certified Students had actually paid only 280 Wen, and knowing the relationship of money among the students but not knowing the matter of relational reasoning in the problem; (3) the verbal protocol procedure showed the manner in which the subjects’ thoughts matched the single-entry bookkeeping representation; (4) under the terms of the double-entry bookkeeping cue condition, the students showed a significant improvement in being able to solve the problem; and (5) there were significant differences between the number of students who could solve the original problem and those who could solve the modified problem.

The results supported the hypotheses that the ten Wen problem is a reasoning illusion problem and the difficulty in solving this problem is partly due to the single-entry bookkeeping representation that people adopted and the problem having a loop structure with regard to relational reasoning.

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