Actually, this story has nothing to do with voting, at least not directly. But elections have been on our minds recently, and my first reaction was: these are the people who are electing our leaders.

A group of French researchers report the results of a survey. The premise is trivially simple:

In this paper, we analyze the answers of a sample of 1,540 individuals to the following question “Imagine that a coin will be ‡ipped 10 times. Each time, if heads, you win 10€. How many times do you think that you will win?”

The average answer? About 3.9, with 75% of the respondents saying less than 5.

The details are a little more subtle, but no more reassuring.

…the mean value for the number of times (out of ten) the individual announces he is going to win is equal to 3.925 or the mean subjective probability of gain is equal to 0.3925. Moreover, 75% of the individuals give an answer below 5. This result is quite striking and in favour of the existence of a behavioral bias towards pessimism in individual beliefs. The same results have been obtained on a sample of undergraduate and graduate students in management and mathematics (236 individuals). Besides, notice that when individuals are asked about the number of times (out of ten) they think “heads” will occur without associated gains, the average answer is 5 as expected and 90% of the answers are exactly 5. This would mean that our results are not related to numerical skills or to knowledge of elementary probability.

*via Kevin Drum*