Playing it Safe with Low Conditional Fees Versus Being Insured by High Contingent Fees

Under contingent fees the attorney gets a share of the judgment; under conditional fees he gets an upscale premium if the case is won which is, however, unrelated to the adjudicated amount. We compare conditional and contingent fees in a framework where lawyers choose between a safe and a risky litigation strategy. Under conditional fees lawyers prefer the safe strategy, under contingent fees the risky one. Risk-averse plaintiffs prefer conditional fees over contingent fees when lawyering costs are low and vice versa for high lawyering costs.


Introduction
Contingent legal fees are widely used in the US. In a well-known empirical study, Kritzer (1990) observes that individual litigants tend to use contingent fees. In around 87% of all torts and 53% of all contractual issues plaintiffs retain their lawyer on a contingency basis; hourly fees are essentially used in divorce and other domestic issues. These figures have been confirmed and discussed in later studies by Kritzer (2002Kritzer ( , 2004 himself as well as by Brickman (2003aBrickman ( , 2003b. Also, in Canada all provinces now permit contingent fees.
In Europe contingent legal fees are not allowed. Market pressure has, nevertheless, led some countries to allow conditional fees. Under conditional fees the lawyer gets an upscale premium if the case is won. This premium is not related to the adjudicated amount. The United Kingdom started introducing conditional fees in the nineties. 1 Conditional fees have also been introduced in Belgium and the Netherlands, the latter apparently now considering to formally allow contingent fees. Spain, France, Italy, and Portugal are considering the introduction of conditional fees. Germany has also relaxed some restrictions by means of 1 Since 1995, English solicitors could charge clients on a conditional fee basis in which the client pays nothing if no recovery is obtained and pays an uplift of up to 100 percent over the normal fee if there is a recovery. In 1999, the government moved to greatly expand the use of conditional fees in order to reduce the cost of legal aid; under provisions of the Access to Justice Act 1999, successful plaintiffs can now recover the uplift from the defendant. Furthermore, in a 1998 decision, the Court of Appeal in England ruled that it was no contrary to law for English solicitors to act on a contingency basis whereby the solicitor would forgo some or all of his or her normal fee if the case was not successful. In Scotland, lawyers have long been permitted to act on a speculative basis. If the plaintiff wins, he pays the lawyer the normal fee, but pays nothing if he loses. In Ireland, barristers take cases on a no goal-no fee basis, in which the barrister receives his normal fee unless no recovery is obtained. For details, see Kritzer (2004). In class action suits yet another type of contract is used resembling conditional fees. Under the loadstar fee, contingent on class victory, the attorney receives a fair compensation for the time spent on the case multiplied by a factor reflecting the degree of risk and the quality of work. By contrast to the output-based contingency fees, the loadstar method is input-based. third party contingent contracts, though not to the extreme of accepting conditional fees (Kirstein and Rickman, 2004). Major European law firms in Paris and in London have been basing fees in part on results achieved since the eighties (Kritzer, 2004).
Both, contingent as well as conditional fees, pay for performance by compensating the lawyer by a higher fee if the case is won. The main difference between contingent and conditional fees is that the former pays a percentage of the judgment whereas the latter pays an upscale premium not related to the adjudicated amount. 2 In this paper we compare both fee arrangements in a set-up where the attorney chooses the strategy on how the case is presented in the courtroom. There are two possible strategies, safe and risky, that affect the probability of winning as well as the amount adjudicated. A safe strategy provides a higher probability of winning with a lower adjudication. A risky strategy leads to a lower probability of winning with a higher adjudication. Overall, the expected judgement is higher for the risky strategy.
We show that the risk-neutral lawyer will play it safe with conditional fees, but will go for risk with contingent fees. Under conditional fees, the only contingencies of interest to the attorney is winning or losing, hence he has an incentive to maximize the probability of winning the case: conditional fees thus give the attorney the incentive to play it safe. Contingent fees condition not only on the events of winning or losing, but also on the amount of the judgment: the higher the judgment, the higher the attorney's share. The expected judgment is higher with the risky strategy, hence the lawyer plays it risky.
2 In private correspondence Bert Kritzer was concerned to use the term contingency fees to refer to percentage fees and to use conditional fees to refer to U.K. style contingency fees: conditional fees are contingent on the outcome, and hence are contingency fees; the term conditional fee is rarely used in the U.S. for this type of contract. While we share his concerns, we nevertheless use the term conditional fee because it is well established in Europe.
The client is risk-averse. She prefers the safe strategy if she receives the entire amount at stake, even though the expected judgement is lower.
With this assumption we create a potential conflict of interest between the risk-averse plaintiff and her risk-neutral lawyer. The equilibrium contract maximizes the plaintiff's expected utility subject to the constraint that the lawyer gets his reservation utility. We are thus solving for the privatelyoptimal type of contract between the lawyer and client -that which maximizes the expected utility of the client, given the usual constraint that the lawyer needs to be paid his reservation utility.
The client chooses conditional fees when lawyer's reservation utility is low; this result follows immediately from our assumption that the client prefers to play it safe when she gets the entire judgement. When the lawyer's reservation utility is, however, high, the client prefers contingent fees. Now the insurance function of contingent fees kicks in: When the lawyers's reservation utility is high, his share of the judgement approaches one. The plaintiff is almost fully insured and no longer cares so much about the judgement risk; most of the judgement goes to the lawyer anyway.
Let us now briefly summarize the literature. Contingent fees may be seen as a mechanism to finance cases when the plaintiff is liquidity constrained and capital markets are imperfect. Similarly, they may be used by the attorney and her client to share the risk generated by the case. See, e.g., Posner (1986).
Another explanation is related to the use of contingent legal fees in classaction litigation (Lynk, 1990, Klement andNeeman, 2004) and third-party involvement in litigation, such as insurance companies (Kirstein and Rickman, 2004).
The other explanations for contingent fees are all based on asymmetric information between the lawyer and his client. Contingent fees can be used to address a moral hazard problem: If the client cannot observe the attorney's effort, then tying the attorney's fees to the trial's outcome provides better incentives to exert efficient effort than hourly fees which tend to induce shirking (Danzon, 1983;Gravelle and Waterson, 1993;Polinsky and Rubinfeld, 2003;Emons and Garoupa, 2006). Rubinfeld and Scotchmer (1993) suppose that the attorney has better information about his ability and the plaintiff has better information about the merits of her case. A high-quality attorney will signal his ability by working for a high contingency percentage and a low fixed fee. A client who has a high-quality case will be willing to pay a high fixed fee and a low contingency percentage, while a client with a low-quality case will prefer a low fixed fee and a high contingency percentage. Dana and Spier (1993) and Emons (2000) look at the role of the attorney as an expert. Clients do not know the merits of their case. The attorney as the expert finds out about these merits. In Dana and Spier (1993) the lawyer recommends whether to pursue or drop the case; they conclude the optimal compensation scheme will pay the attorney a share of the plaintiff's award. In Emons (2000) the attorney recommends how much work to put into the case; he finds that paying the attorney by the hour is generally better than using contingent fees.
The economic literature on conditional fees (Maclean and Rickman, 1999;Yarrow, 2001;Fenn et. al, 2002) has been concerned with the impact on the outcome of legal cases and the effects on the demand and supply of legal aid. Before-the-event legal cost insurance has been stifled by the existence of legal aid. When the government withdrew legal aid for many types of cases, conditional fees have moved to the fore along with after-the-event insurance policies, purchased after an actionable event from legal cost insurers.
In Emons and Garoupa (2006), we find that both, contingent and conditional fees, give the lawyer an incentive to provide effort. Under conditional fees the upscale payment is not related to the adjudicated amount. Therefore, the lawyer's effort does not depend on the amount at stake. Under contingent fees the attorney gets a fraction of the judgment. He adjusts ef-fort to the adjudicated amount: the higher the judgment, the more effort he puts into the case. Accordingly, under contingent fees the attorney uses his information about the amount at stake whereas under conditional fees he does not. Therefore, contingent fees are more efficient than conditional fees.
This holds true independently of whether upfront payments to the lawyer are restricted to be non-negative or not. Emons (2006) compares conditional and contingent fees in a framework where lawyers are uninformed about the clients' cases. Payments to the lawyer are restricted to be non-negative. Moral hazard by lawyers rules out fixed wage components. If there is asymmetric information about the expected adjudicated amount of cases, in equilibrium attorneys will offer only conditional fees. If there is asymmetric information about the risks of cases, only contingent fee contracts are offered in equilibrium.
In the next section we describe the model and derive our results. Section 3 concludes.

The model
A plaintiff has been a victim of an accident or a breach of contract. She sues the defendant to be paid damages. The plaintiff may either win or lose the case. When the case is lost, the plaintiff gets nothing. When the plaintiff wins, she gets either J orJ withJ > J > 0.
The strategy on how the case is presented in the courtroom determines the probability to prevail and the judgment. 3 With the safe strategy the probability to prevail is p s . If the case is won, the plaintiff gets J with probability q > 1/2 andJ with probability (1 − q). The safe strategy thus gives rise to an expected judgment conditional on winning of E(J s ) = qJ + The alternative is a risky strategy. With the risky strategy the probability to win is p r < p s . If the case is won, the plaintiff gets J with probability (1 − q) andJ with probability q. The risky strategy gives rise to an expected judgment conditional on winning of E(J r ) = (1 − q)J + qJ > E(J s ). Accordingly, the risky strategy has a higher expected judgment conditional on prevailing than the safe strategy, but the probability to win is lower.
As an example think of the strategies as the aggressiveness with which the lawyer presents the case. The attorney can go, e.g., for a long discovery process to be on the safe side. By contrast, he can ask for an early trial, forcing the defendant to make quick, and hopefully wrong, decisions.
We consider the case where p r E(J r ) > p s E(J s ), i.e., the expected judgment is higher for the risky strategy; the risky strategy's lower probability to prevail is more than compensated by the higher expected judgment in case of winning.
The plaintiff is risk averse which is represented by her utility function over income U (·) with U > 0 and U < 0. She has an initial wealth M .
With the safe strategy her expected utility is given as and with risky strategy her expected utility is i.e., as long as the plaintiff gets the entire judgment, she prefers the safe strategy although the expected judgment is lower. The risky strategy puts relatively more weight on the extreme outcomes of losing the case and win-ningJ whereas the safe strategy puts relatively more weight on winning J. If U (M ) is sufficiently low and the utility doesn't increase too much by winning J instead of J, the plaintiff prefers the safe strategy although its expected judgment is lower. 4 We look at the case where the expected judgment is higher with the risky strategy, yet the expected utility is higher with the safe strategy because this may create a conflict between the plaintiff and her lawyer as we will see below.
To take the case to court the plaintiff needs an attorney. There is a large set of perfectly competitive lawyers. Attorneys are risk neutral. They provide effort e ∈ {0, v}. With zero effort the probability to prevail is zero.
With high effort v the attorney can choose the safe or the risky strategy as described above. Effort is not observed by the client. When the lawyer is indifferent as to the choice of effort, he goes for high effort. Lawyers only incur the cost of effort which, for simplicity, equals the level of effort e. Accordingly, given high effort lawyers have a reservation utility of v, i.e., if the plaintiff wants to implement high effort, besides providing proper incentives she has to offer the attorney a contract such that he gets an expected remuneration of v. Let v ∈ [0, p r E(J r )] so that it pays for the plaintiff to hire an attorney and take the case to court.
The attorney picks the strategy with which the case is presented in the courtroom. This choice is not contractible. The plaintiff may, e.g., observe the discovery process, yet lack the expertise to tell whether the process is relatively short or not. In case of a settlement the plaintiff often doesn't observe the bargaining between her attorney and the defendant; the plaintiff only observes the outcome, see Kritzer (2004). Accordingly, a contract may only be conditioned on the outcome; it cannot be conditioned on the choice of strategy and on the effort level.
By giving lawyers the zero effort option, we effectively rule out contracts entailing fixed wages. To see this, first note that we do not allow for con-tracts with payments from the attorney to the client. We thus rule out the possibility that the lawyer buys the case from the client and we do not allow for penalties the lawyer has to pay to the client if the case is lost. This restriction is implied by the champerty doctrine in the US and the UK and the forbidden pactum cuota litis in continental Europe. 5 Therefore, in our set-up conditional fees can pay the lawyer a fixed wage plus a fixed extra if the case is won; contingent fees can give the attorney a fixed wage plus a share of the adjudicated amount. Now suppose that under either fee structure the fixed wage is positive. Then the lawyer can ensure himself a positive payoff: he provides zero effort and cashes in on the fixed wage. Due to competition this can, however, not happen in equilibrium: any positive payoff will be competed away. In equilibrium lawyers offer contracts the returns of which just cover their effort cost v.
Accordingly, given that we can rule out any fixed wage components, a conditional fee contract is given by Under equity finance the investor gets a share of the project's returns. So does the attorney under contingent fees. Under a standard debt contract the investor gets a fixed payment (interest plus principle) in non-bankruptcy states and nothing in bankruptcy states. Under conditional fees the attorney gets a fixed premium if the case is won and nothing when the case is lost. Accordingly, contingent and conditional fees generate the same payoff structure as equity and standard debt finance. See Emons (2006).
Under the conditional fee contract d with high effort v the lawyer's expected utility with the safe strategy is EV (d, p s ,J s ) = p s d − v; under the risky strategy his expected utility amounts to EV (d, p r ,J r ) = p r d − v. Under conditional fees the attorney gets the bonus d when he wins the case, independently of the judgment. Since p s > p r , the lawyer chooses the safe strategy under conditional fees. By conditioning only on the contingencies of winning and losing, the attorney has an incentive to maximize the probability of winning the case: conditional fees thus give the attorney the incentive to play it safe.
Under the contingent fee contract α with high effort v the lawyer's expected utility with the safe strategy is EV (α, p s ,J s ) = αp s E(J s ) − v; under the risky strategy his expected utility amounts to EV (α, p r ,J r ) = αp r E(J r )− v. Contingent fees condition not only on the events of winning and losing but also on the amount of the judgment: the higher the judgment, the higher the attorney's share. Since p r E(J r ) > p s E(J s ), the lawyer chooses the risky strategy under contingent fees. The expected judgment is higher with the risky strategy. Contingent fees give the attorney a share of the judgment.
Therefore, under contingent fees the lawyer prefers the risky strategy.
To summarize the attorney's incentives: Proposition 1: Under contingent fees the lawyer chooses the risky strategy whereas under conditional fees he prefers the safe strategy.
Let us now look at the plaintiff's expected utility taking the attorney's behavior into account. Under conditional fees the lawyer chooses the safe strategy and the client's expected utility is Whenever the case is won, the plaintiff pays the lawyer the conditional fee d. The lawyer plays it safe, but plaintiff and attorney do not share the judgement risk: the spread for the plaintiff is (J − J).
Under contingent fees the lawyer chooses the risky strategy and the client's expected utility is Under contingent fees the plaintiff gets her share (1 − α) of the judgment.
Here the lawyer goes for the risky strategy and at the same time insures the plaintiff: the spread for the plaintiff is (1 − α)(J − J).
Since there is a large set of perfectly competitive attorneys, the equilibrium contract maximizes the plaintiff's expected utility subject to the constraint that the lawyer earns his reservation utility v. 6 It turns out that for low levels of the lawyer's reservation utility v the plaintiff prefers the conditional contract, for high levels of v she goes for the contingent contract.
Proposition 2: There exists a uniquev ∈ (0, p r E(J r )) such that for v ≤v the equilibrium is given by the conditional fee contract d * = v/p s and for v >v by the contingent fee contract The subgame perfect equilibrium of the following game has this property. In the first stage each lawyer offers one contract: either a conditional fee d ≥ 0 or a contingent fee contract α ∈ [0, 1]. In the second stage the client chooses either one contract on offer or no contract at all. In the third stage the attorney whom the client has chosen picks his effort. The client maximizes the expected difference between adjudicated amount and payments to the lawyer. Attorneys maximize their expected wages minus effort cost.
Proof: Under the conditional fee d * = v/p s the lawyer picks the safe strategy and EV (d * , p s ,J s ) = p s d * −v = 0; under the contingent fee α * = v/(p r E(J r )) he goes for the risky strategy and EV (α * , p s ,J s ) = α * p r E(J s ) − v = 0.
Accordingly, under both contracts the lawyer breaks even with high effort.
Let us now look at the plaintiff. For v = 0, assumption (1) implies EU (d * , p s ,J s ) and EU (α * , p r ,J r ) are both continuous in v. Thus, the intermediate value theorem implies the existence ofv such that EU (v/p s , p s ,J s ) = EU (v/(p r E(J r )), p r ,J r ). Uniqueness ofv follows from the observation that show in the Appendix.
Q.E.D. The intuition behind this result is as follows. When v is low, the plaintiff gets most of judgement under contingent and conditional fees. Assumption 1 implies that she prefers to play it safe in this case and, accordingly, she goes for conditional fees. When v is large, the attorney gets most of the surplus. Under contingent fees the attorney's share α of the judgement approaches one: he bears most of the judgement risk. Since the plaintiff is almost fully insured, she no longer cares much about the judgement risk. Thus, she prefers contingent fees to conditional fees where, despite the high d, the judgement spread is still (J − J). To put it differently: The higher v, the stronger becomes the insurance function of contingent fees.
In this paper we want to highlight two points. First, conditional fees give the lawyer an incentive to maximize the probability of winning the case. By contrast, under contingent fees the attorney maximizes the expected judgement. Second, if the plaintiff is risk averse, there may be a conflict of interest between the plaintiff and her lawyer. If the cost of hiring a lawyer is low, the plaintiff seeks insurance through conditional fees which induce the safe bet. If, by contrast, lawyers are expensive, the plaintiff prefers contingent fees shifting most of the judgement risk to the lawyer.
We have solved for the privately-optimal type of contract between the lawyer and client -the contract which maximizes the expected utility of the client given the constraint that the lawyer is paid his reservation utility. In the socially optimal allocation which maximizes the sum of the client's and attorney's utilities, the attorney bears all the risk. He chooses high effort and the risky strategy. This outcome is attained if the attorney buys the case from the client and becomes residual claimant. We have ruled out this possibility because of the champerty doctrine and the forbidden pactum cuota litis. We consider thus a second-best world in which the first-best is attained if and only if the lawyer's reservation utility is so high that the contingency fee is 100%.
One implication of the paper is that in a regime where conditional fees are allowed but contingent fees are forbidden, we should expect inefficient contracting for high costs of lawyering. Conditional fees do not allow for the sharing of the risk of a high or a low judgement. Compared to fixed wages they do, however, share the risk of winning and losing the case.
A second implication of the paper is the choice of lawyer fees as a response to the tension between plaintiff and lawyer concerning the litigation strategy. Therefore, an important aspect is how much control plaintiffs have over the choice of litigation strategy. Corporate clients usually keep a significant control over litigation, in part due to in-house legal counselling. For them the tension we analyze seems to be less of a problem. Individual clients usually lack the expertise to exert any significant control over their cases. For these clients conditional fees can be a useful means to induce a safe litigation strategy. To put it in terms of our example: a client can be assured that under conditional fees the lawyer behaves less aggressively than under contingent fees.
One argument against contingency fees is that they induce lawyers to settle cases too quickly. The attorney's return per hour invested in the case is higher if the case is settled rather than taken to court; see, e.g., Kritzer (2004). If we interpret the safe litigation strategy as going for a quick settlement, then this criticism applies even more to conditional fees.