Men, Women, & Balls
I caught an interesting episode of Freakonomics Radio today, and it got me thinking. It described an experiment by Uri Gneezy of U.C. San Diego. He wanted to explore attitudes to competition in men and women and determine if the differences he has observed are innate to the sexes, or if they are acquired from the culture. He conducted an experiment that gauged people’s attitude to competition and risk, in two different cultures. The first was the Masai in Tanzania. This is a very patriarchal society and women are not held in high esteem there. The second culture was the matriarchal Khasi society of India. In this society women have most of the power and make most of the decisions.
Participants in the experiments were tasked with throwing tennis balls into a bucket from a distance. The more balls they got in the bucket, the more money they could win. However each participant could chose from two payment options. A participant could chose the first option and be paid $1 per ball. However, each participant was partnered with an unseen participant around the corner. The second option paid out $3 per ball, provided that the participant got a higher score than the partner. But if the parter got a higher score, the participant got nothing.
Gneezy found that Masai men were more likely to take the risky option than Masai women. But among the Khasi, the women were more likely to take the risky option. That was interesting.
But it was the game design itself that caught my attention.
A U.S. Dollar is a lot of money in a very poor country. If I was playing this game my attitude might be very different if each ball payed €1 than it would be if it payed out €100. Risking €5, to win €15, is not the same as risking €500 to win €1500. I wonder if smaller or larger amounts of money were used would the results have been different? If the cost of living in India and Tanzania were different, it might distort the results. I suspect, however, that they are comparable.
What really struck me was the 1-to-3 payout. Why $3? Why not $2? Why not $1.2? I think it matters. If an average player does not know who his opponent is, then his chances of winning are roughly 50%. [Let’s for simplicity minimise the possibility of a draw by assuming that each player throws a large number balls]. If I understand the experiment correctly, any participant who selects the less risky option gets paid irrespective of what option his partner chose. Let’s say that on average each player gets 10 balls in the bucket. An average risk-adverse player gets $10. A competitive player gets paid $30 if he wins, and nothing if he loses. If such players win half the time, then the average competitive player wins $15. That this value is higher than that paid on average to the risk-adverse player is significant.
Suppose that Gneezy and his team wanted to run the experiment in Ireland. The Maths Society might rally its members on campus to participate in the experiment to earn some money for the end of year party. They might agree that all of the money earned will go into the kitty to buy some beer. How might the students from the Maths Society behave on the day? Every student that selects the risk-adverse option will generate $1 per ball. But every student that selects the risky option will get either $3 or nothing for each ball. On average that’s $1.50 per ball. Taking the riskier option is the best way for the group to extract the most money from these crazy Americans who are just givin’ it away.
What if Gneezy’s experiment turned out not to measure a group’s attitude to risk and competition, but its ability to do math?
Perhaps the experiment just measured trust. Even if everyone understood the benefits of choosing the risky option one might see differences between groups where the levels of trust are different. If everyone is going to be honest and put the money in the kitty to buy the beer, then the risky option is, in fact, risk-free. But it is only risk-free if you trust the other participants to share their prize money. Perhaps results would vary in societies where people have different degrees of trustworthiness or differing capacities for cooperation. In fact, Gneezy made a point of highlighting just how trustworthy the people of the Khasi Hills actually are. He felt safe leaving his suitcase with $60,000 in cash with the cook in the house he rented in the village, even though that was the equivalent of $60 million to him. Perhaps the cook had done his math, trusted the rest of the community, and knew that they would all share $60 million anyway.
A zero sum game could have made all the difference.