The science of making good choices

By Juliana Chan

SMU Office of Research & Tech Transfer – In times of humanitarian crisis, organisations such as the Red Cross swoop in to provide food, shelter and medical help to those in distress. Here, life and death hinges on good decisions being made, as rescue units and medical supplies must be distributed to assistance centres prior to an emergency situation by anticipating where disaster will strike next.

These are challenging decisions to make, shares Xue Jingyi, Assistant Professor of Economics at Singapore Management University (SMU), as humanitarian organisations do not know beforehand where or when an emergency situation will occur, nor how large the damage will be.

Using mathematical models, Professor Xue studies how best to make decisions using the information at hand. She analyses human behaviour in a rigorous manner, advising individuals and policy makers on how best to allocate resources in the face of risk and ambiguity. “My work covers two types of decision theory: the first focuses on individual decision making while the other involves social decision making,” Professor Xue said.

When nothing is black or white

Choice is an essential part of daily life, and investors have to pick from hundreds or thousands of stocks listed on the stock market index. Although they may not know exactly the return on their investments, experienced investors know the probability of what their returns would be, based on historical data. This type of uncertainty, called risk, measures the exact degree of uncertainty that an investor has to take to realise an investment gain.

“But the other type of uncertainty, which is very relevant in real life, is called ambiguity. That is, you don’t even know what the probability of a certain outcome will be. When most of us invest, can we say exactly that we will get an expected earning with 38% confidence?” Professor Xue said.

In such a scenario, decision makers do not even have a probability to describe the risk involved. Here, Professor Xue studies how an individual makes choices under ambiguity, and how a society evaluates fairness and efficiency in situations of ambiguity.  

Avoiding wastage of public resources

Policy makers everywhere are tasked with dividing up public funds to finance the development of public facilities such as roads, hospitals and libraries. They commit to a deterministic allocation of resources, based on estimates of historical public demand and statistical analysis.

“But there are many public districts, and the money has to be allocated before we know exactly the local public demand of each district. We don’t know precisely how heavy the traffic flow will be on a particular road, or how many people will show up at the library or hospital,” Professor Xue said.

In a research paper titled “Fair division with uncertain needs” and published in Social Choice and Welfare, Professor Xue studied how best to avoid wastage when allocating resources, especially under situations of uncertainty.

Take a hypothetical situation with two agents: one agent needs 50 units of a resource, while a second agent needs 0 or 100 units of a resource, with both options equally likely. If one were to take the average for both agents they appear to have the same average need, Professor Xue explained. Yet the degree of the riskiness of their needs are different, as the second agent involves a large degree of risk.

“If the resource is money, giving the second agent any amount of money – even just one dollar – may be wasteful as there is a 50% chance the second agent needs nothing. If the planner is extremely averse to waste, then the planner should allocate the whole 50 units to the first agent,” she said.

However, this may not seem fair, Professor Xue pointed out, as the second agent has at least a 50% probability of needing 100 units of a resource. Professor Xue therefore proposed a family of rules that strikes a balance between the two extremes, one being too sensitive to uncertainty, and the other being unresponsive to uncertainty.

“A waste-minimising rule will always impose a severe punishment on the agent that has a riskier need. My rules still punish the agent with the riskier need, but not to such an extreme extent,” Professor Xue said.

Introducing real-life uncertainty

The problem of optimal resource allocation has been extensively discussed in the operations research literature, Professor Xue said. However, unlike operations research which is practical and assumes a clear objective, her research does not assume any particular objective to begin with and only starts with normatively desirable requirements on allocation rules.

“My work gives policy makers guidance on how to allocate resources, such as government funds, in cases of uncertainty. Policy makers only need to check whether they agree with the normative requirements considered in my research. If they agree, they can then adopt this rule.”

While the existing literature on fair division mainly focused on how to divide resources among agents with deterministic needs, Professor Xue’s research tackles real-life considerations, such as uncertainty.

“Uncertainty is new in the literature of fair division, and waste becomes a very important issue when we introduce uncertainty. Through our work, we have come up with rules that address waste in a proper way, to better reflect real life.”

Back to Research@SMU Aug 2019 Issue