Ellinor Fackle-Fornius. Foto: Statistiska institutionen

To find out what people are willing to pay for things that are beneficial to society that cannot be bought on any larger market, you need to do a special type of experiment. This could be about access to cleaner air, national parks or, as in this case, organically produced clothes.

The experiment is known as the “will-to-pay” experiment. Here, respondents are asked if they are prepared to pay more for an environmentally friendly t-shirt than a “regular” one and if they answer yes, they are asked if they are prepared to spend a certain amount of extra money.

### Extra difficult to get right

Establishing a reasonable level for the question asking how much a person is prepared to pay – to decide the right bidding level – is a question for the researcher. In a project financed by the Swedish Research Council, Ellinor Fackle-Fornius and Hans Nyquist at Stockholm University and Linda Wärnström at Linköping University have studied a certain type of experimental design that works for this question: the minimax design.

“For certain statistical models, it is extra difficult to find the best design. And when I say design of an experiment, I mean how many bidding levels will be included, what the bidding levels will be and how distribute the respondents to the various bids,” says Ellinor Fackle-Fornius.

Creating the experiment is complicated by the fact that to be able to decide the right bidding levels, you need to know the real model parameters.

“And by definition, you don't know these before you do the experiment – that is why you do the experiment”.

### An interval of guesses

One option is to guess some model parameters and using them as a guide, create some suitable bidding levels.

“This gives you a design. But if you have guessed wrong, it's it might not turn out very good,” says Ellinor Fackle-Fornius.

One solution is to use what is known as the Minimax design. With this you can play it somewhat safe.

“You don't just make a guess, you make an entire interval. You ask: what is the worst that can happen if you find yourself in this interval – and then you design the best possible experiment for this,” says Ellinor Fackle-Fornius.

Here, the solution was to choose a single bidding level and give the same one to all respondents: to ask the respondents if they accept or reject the extra cost of SEK 79 for an environmentally friendly top.

### An algorithm is like a recipe

One of the aims of the project is to apply a new algorithm, the H algorithm, to a few practical situations. Ellinor Fackle-Fornius describes an algorithm as a recipe that you follow to do a certain type of task.

In this case, the task – or the “meal” – is creating a minimax design with the right bidding levels. Designing an experiment to answer the question of what we are willing to pay for environmentally friendly clothes is, therefore, one application for the H algorithm.

“We contacted Elsa Levinson who wrote her Master's thesis in the Sthlm Resillience Center, and decided to try this application.

The H algorithm makes it easier to create the Minimax design,” explains Ellinor Fackle-Fornius. In this study, they have shown both that the algorithm works and how it works when applied in practice.

“There aren't a lot of people who have used the minimax design since they are so difficult to derive. But with this algorithm, it is much easier”.