The Value of a Statistical Judgment: a New Approach to an Insurer's Duty to Settle

Abstract: When liability insurance carries a limit that is smaller than the potential claim of a third party plaintiff, the insurer and the insured can have a conflict of interest as to settlement. The majority of jurisdictions in the United States impose upon insurers a duty to ignore liability limits when considering a settlement offer, and do not place limits on an insurer's liability when the duty is violated. In this paper I take an incomplete contract approach and derive the optimal duty to settle. I propose limiting the insurer's liability for an excess judgment to the Value of a Statistical Judgment (VSJ), which is derived from the amount a policy holder is willing to pay to avoid a risk of a large excess judgment. Setting damages for bad faith refusal to settle to the Value of Statistical Judgment causes the insurer to efficiently internalize the harm to the insured from an excess judgment. Although calculating the exact VSJ and corresponding duty to settle requires knowledge of the utility function of the insured, I show that courts can use a revealed preference approach to closely approximate the VSJ as a linear function of the liability limit and the vulnerable assets of the insured. The rule I propose applies excess liability which is a small multiple of the sum of the liability limit and the policy holder's wealth. In addition to being nearly optimal rule from the ex-ante perspective for the insured, the proposed VSJ rule is attractive from a broader social welfare perspective; it discourages nuisance settlements, and directs more compensation towards victims with legitimate claims.