Adopting Shapley values to address embedding biases in contingent valuation studies

Abstract

A variation of the contingent valuation model is used to determine the value of a special education school in Singapore. Shapley values have long been used in game theory in determining value in n-tuple games. An extension of the Shapley value is used in this exercise to show how it may be effective in removing the embedding effect in survey responses with respondents well-acquainted with the service under evaluation in order to determine option and use values for a specialist audience. A case study using a special school in Singapore is used for illustrative purpose in the following sections, but should not detract from the main thrust of the article.

Notes

¹ It is one of 17 Special Needs Schools in Singapore but it is one of only two award-winning specialized schools dealing with students with autism or multiple handicaps.

² For the purposes of this study, we group option and use values together because of the degenerative nature of the disabilities for children with multiple handicaps and autism. Just because a child is not using a particular service at the moment is no indicator that he will not be in the near future.

³ Government social workers usually are assigned to families to make a needs-based assessment before the school fee is determined.

⁴ Interviewers were briefed to look at the demographic statistics prior to assessing starting bids in the referendum approach. Household income and current school fees was the determining factor in deciding the starting bid. As with double-bounded approaches, if the first starting bid was accepted, the next bound would be selected. Based on the level of hesitancy, values between bounds were also used.

⁵ This estimate is reliable because it brings the question down to the level of affordability.

⁶ Parents were presented with the scenario that even with the addition to the present school fees, the school had no choice but to close down and had instead contracted out that therapy services to private organizations. A menu of prices was presented to respondents for individual services and a referendum approach was again employed to elicit willingness to pay for individual services.

⁷ The last two similar scenarios started with the story that the Board of Directors instead of closing down the school had opted to remove one or two therapy services instead and were offering to compensate parents for the loss of that service by reducing school fees. Parents again were asked via a referendum approach, for their willingness to accept values.