July 2001 (revised) Aligning the Interests of Lawyers and Clients A. Mitchell Polinsky and Daniel L. Rubinfeld* Abstract: The potential conflict of interest between lawyers and clients is well known. If a lawyer is paid for his time regardless of the outcome of the case, the lawyer may wish to bring the case even when it is not in the best interest of the client, may spend more hours working on the case than the client would want, and may reject a settlement when the client would be better off if it were accepted. Alternatively, if the lawyer is compensated according to the conventional contingent fee arrangement — under which he is paid a fraction of any trial award or settlement but bears all of the cost of litigation — the lawyer may have an insufficient incentive to bring the case, may spend too little time working on it if it is brought, and may encourage a settlement when the client would be better off going to trial. In this article we propose a method of compensating lawyers that overcomes the conflict of interest between the lawyer and the client. Our system is a variation of the conventional contingent fee system, but, in contrast to that system, we would have the lawyer bear only a fraction of the cost of litigation — the same fraction that the lawyer obtains of the award or settlement. We demonstrate that when the fraction of the cost that the lawyer bears equals the fraction of the award or settlement that he obtains, he will have an incentive to do exactly what a knowledgeable client would want him to do with respect to accepting the case, spending time on the case, and settling the case. Under our modified contingent fee system, a third party would compensate the lawyer for a certain fraction of his costs, in return for which the lawyer would pay that party an up-front fee. In this way, the client would not bear any costs, even if the case is lost, just as under the conventional contingent fee system. * Stanford University and National Bureau of Economic Research; and University of California, Berkeley, respectively. Polinsky's research was supported by the John M. Olin Program in Law and Economics at Stanford Law School. Rubinfeld's research was undertaken in part while he was a visitor at New York University Law School. We received helpful comments from Joseph Bankman, Kevin Clermont, Winand Emons, Frank Easterbrook, Nuno Garoupa, Robert Hall, Steven Shavell, and Kathryn Spier. -1- I. Introduction If a client were as well informed about the law and the value of litigation effort as her lawyer, she could get the lawyer to do what she wants by hiring the lawyer on an hourly basis and directing his efforts.1 However, the fact that clients are generally less well informed about such matters, and consequently often defer to their lawyers, gives rise to a potential conflict of interest. Specifically, if the lawyer is paid for his time regardless of the outcome of the case, he may, in order to create more work for himself, try to convince the client to prosecute a case vigorously even though the expected winnings are less than the cost to the client of the lawyer’s time. Similarly, because a settlement would involve fewer hours of work than a trial, the lawyer may argue against settling the case even when a settlement is in the best interest of the client.2 Switching to the contingent fee method of compensation, under which the lawyer receives a certain percentage of any trial award or settlement but bears all of the cost of his time, changes the nature of, but does not resolve, the conflict of interest between the lawyer and the client. Then a lawyer may not be willing to take a case even though it would be in the interest of the client for him to do so, because the lawyer bears all of the cost and obtains only a fraction of the benefit. Moreover, if the case is accepted by the lawyer, he has an incentive to spend less time at trial than the client would want, for the same reason. And the lawyer generally has an excessive motive to settle the case, since by doing so he obtains a fraction of the settlement without having to invest the additional time that would be required if the case were to go to trial. In this article we propose a new method of compensating lawyers that resolves the conflict of interest between the lawyer and the client. Our system is a variant of the traditional contingent fee system, but differs from it in one important respect. Under the conventional contingent fee arrangement, the percentage of the reward obtained by the lawyer — typically 25 to 40 percent — differs significantly from the percentage of the cost borne by the lawyer — usually 100 percent. It is this divergence between the reward percentage and the cost- 1 We use the pronoun “he” to refer to the lawyer and “she” to refer to the client. 2 While lawyers have a professional obligation to do what is best for their clients, and this obligation may dampen the self-interested behavior that we describe in this paragraph, it seems obvious that a lawyer’s financial incentives will affect his decisionmaking to some, and possibly to a significant, extent. -2- bearing percentage that causes the lawyer’s interest to differ from the client’s. Our system resolves the conflict between the lawyer and the client by making these two percentages the same. For example, in our system, if a lawyer receives 25 percent of any trial award or settlement, he would bear just 25 percent of the cost of litigation. If the lawyer’s cost-bearing percentage equals the lawyer’s reward percentage, the lawyer’s incentives regarding the case will be identical to those of a knowledgeable client. For if these percentages are the same, the lawyer in effect “owns” this percentage of the case and would want to do what maximizes the value of the case in order to maximize the value of his share.3 The lawyer then would accept a case if and only if it has positive expected value. He would invest an additional hour in the case if and only if the resulting increase in the expected award exceeds the value of an hour of his time. And he would settle the case if and only if the settlement amount exceeds the expected award at trial net of trial costs.4 In order for the lawyer’s cost-bearing percentage to equal the reward percentage, the lawyer would have to be compensated for a fraction of his time — specifically, for the complement of the reward percentage — regardless of the outcome of the case. To achieve this without requiring a payment from the client, we envision a third actor, referred to as the “third- party administrator,” who will contract with the lawyer and agree to pay him for the appropriate fraction of his time. (We explain in section IV.B how a version of our system could be implemented without the involvement of a third party, but then the client would have to pay for a fraction of the lawyer’s time even if the case is lost.) Thus, for example, if the reward and cost- bearing percentage is 25 percent, the third-party administrator would pay the lawyer for 75 3 Selling the case outright to the lawyer also would resolve the lawyer-client conflict of interest, but such a sale would be barred by the doctrine of champerty, under which it is considered unethical for a lawyer to pursue a claim in consideration for receiving all or a substantial portion of the financial rewards from the case. See generally Am. Jur. 2d, Champerty and Maintenance, Sections 1-15 (2000). (For reasons explained in note 29 below, our system is not equivalent to the sale of the case.) Even if a sale were permitted, it might not be desirable because the client would no longer have an interest in helping the lawyer pursue the claim. See note 18 below. 4 Because the subject of this article is the conflict of interest between lawyers and clients, our goal is to create incentives that are privately optimal, that is, that maximize the joint benefits of lawyers and their clients. It is well known that, due to significant externalities in the litigation process, what is privately optimal for the litigants is not generally socially optimal. See, for example, Shavell (1997). We will not be concerned with the differences between private and social optimality here. -3- percent of his time. In return for the administrator’s agreeing to compensate the lawyer for a certain fraction of his time, the lawyer would pay an up-front fee to the administrator. To see more concretely why the lawyer’s incentives would be aligned with the client’s under our system, consider the following example.5 Suppose the award if a lawsuit is won is $60,000 and that the lawyer can invest either 30 hours of time at trial — in which case the probability of prevailing is .4 — or 60 hours — in which case the probability is .7. The lawyer’s hourly rate of compensation is $200. A knowledgeable client — one who knows the productivity of the lawyer’s time — would hire the lawyer on an hourly basis and have him work 60 hours on the case: the expected payoff to the client net of the lawyer’s cost is $18,000 if the lawyer works 30 hours (= [.4 x $60,000] - [30 x $200]) and $30,000 if the lawyer works 60 hours (= [.7 x $60,000] - [60 x $200]). Now consider the conventional contingent fee system with a contingency percentage of 25 percent. If the lawyer works 30 hours on the case, his expected payoff net of his time cost is $0 (= [.25 x .4 x $60,000] - [30 x $200]); in other words, he is compensated at his hourly rate. If he works 60 hours on the case, however, his expected payoff net of his time cost is -$1,500 (= [.25 x .7 x $60,000] - [60 x $200]). Thus, under the conventional contingent fee system, the lawyer will be willing to take the case but will work fewer hours than a knowledgeable client would want. Under our modified contingent fee system, suppose that the lawyer also receives 25 percent of the award, and thus would be compensated by the third-party administrator for 75 percent of his time. If the lawyer works 30 hours on the case, his expected payoff net of his unreimbursed time cost is $4,500 (= [.25 x .4 x $60,000] - [30 x $200] + [.75 x 30 x $200]). If he works 60 hours, his net expected payoff is $7,500 (= [.25 x .7 x $60,000] - [60 x $200] + [.75 x 60 x $200]). Thus, the lawyer will work 60 hours on the case, as a knowledgeable client would want. The reason, of course, is that now the lawyer bears the same percentage of costs as he obtains of the award, so his interests are aligned with the client’s. (Although the lawyer is 5 Although this example concerns just the lawyer’s decision regarding how much time to spend working on the case if it goes to trial, the general point of the example applies as well to the decisions involving whether to settle the case and whether to accept it in the first place. -4- partially reimbursed for his time cost under our fee system, he will not be better off than under the conventional contingent fee system because of his payment of the up-front fee to obtain the case.) We demonstrate below that our fee system duplicates the outcome that would occur if a client were as knowledgeable as her lawyer and hired the lawyer on an hourly basis. Not only will the lawyer’s decisions about taking the case, prosecuting the case, and settling the case be identical, as argued above, but also the value of the case will be split between the lawyer and the client in the same way. Specifically, if a knowledgeable client hired a lawyer on an hourly basis, the lawyer would be fully compensated for his costs and the client would obtain the entire expected value of the case in excess of these costs. The same is true under our system. We also show that the third-party administrator breaks even, and so would be willing to operate in the way envisioned in our system. The article proceeds as follows. In section II we develop a formal model of the lawyer’s behavior under both the conventional contingent fee system and our proposed system when it is assumed for simplicity that all suits that are filed result in a trial. Section III extends this model to account for the possibility that cases settle. In section IV we discuss some issues involved in implementing our system. Section V contains brief concluding remarks.6 II. All Cases Go to Trial We assume in this section that all cases that are brought result in a trial. Thus, our focus here is on whether a case is filed and, if it is, how much time the lawyer devotes to it at trial. We first examine the filing and lawyer-effort decisions that a knowledgeable plaintiff (one who knows the relationship between the lawyer’s effort and the expected award at trial) would make if she hired a lawyer on an hourly basis. These decisions will be referred to as the benchmark. 6 There is a large literature that discusses the conflict of interest between lawyers and clients under contingent and hourly fee arrangements. See, for example, Schwartz and Mitchell (1970), Danzon (1983), Miller (1987), Thomason (1991), Dana and Spier (1993), Gravelle and Waterson (1993), Rubinfeld and Scotchmer (1993), Hay (1996), and Emons (2000). No one has previously proposed a fee arrangement corresponding to the no-conflict fee system that we present here. Clermont and Currivan (1978), however, suggest a modification of the conventional contingent fee system that is in the same spirit as our proposal, though it differs from ours and does not fully resolve the conflict of interest between the lawyer and the client; see note 27 below. -5- We then examine the same decisions when they are made by a lawyer for an uninformed client and the lawyer is compensated according to the conventional contingent fee system. Lastly, we evaluate the lawyer’s decisions under our proposed compensation arrangement, which we call the no-conflict fee system.7 We assume throughout this discussion (and in section III) that all parties are risk neutral.8 A. The Benchmark Consider a plaintiff who is knowledgeable about the costs and benefits of litigation and who hires a lawyer on an hourly basis to pursue a claim against the defendant. The plaintiff will bring the case if the expected payoff at trial exceeds her litigation costs, and she will instruct the lawyer to continue working on the case as long as the marginal increase in the expected award exceeds the marginal cost of the lawyer. Let: k = fixed costs incurred by the plaintiff’s lawyer in bringing a case;9 h = number of hours worked by the plaintiff’s lawyer; p(h) = probability that the plaintiff will prevail at trial given h; pN(.) > 0; pO(.) < 0; w = hourly wage of the plaintiff’s lawyer; and a = award at trial if the plaintiff prevails. An asterisk will be used to indicate the optimal values of the plaintiff’s choices in the benchmark. First consider the plaintiff’s decision regarding how many hours the lawyer should work, conditional on a case being filed. The plaintiff will choose h to maximize her expected payoff at 7 We do not formally treat the case in which a lawyer who is paid an hourly fee makes litigation decisions for an uninformed client. We focus instead on the lawyer-client conflict of interest in the conventional contingent fee system because our proposed compensation scheme is a variant of that system. 8 We discuss risk-allocation issues in note 28 below. 9 We include such a cost so that the equilibrium contingency percentage in the conventional contingent fee system is positive. See note 15 below. None of the results concerning our proposed fee system depend on the existence of a fixed cost of bringing a case. -6- trial,10 p(h)a - wh. (1) Thus, h* is determined by the first-order condition11 pN(h)a = w. (2) The plaintiff will file a suit if the case has non-negative expected value, that is, if12 p(h*)a - wh* - k  0. (3) We assume that (3) holds strictly. B. The Conventional Contingent Fee System Now suppose that the lawyer makes litigation decisions for a client who is uninformed about the costs and benefits of litigation, and let the lawyer be compensated according to the usual contingent fee arrangement under which he receives a percentage of the award and bears all of his costs. Let θ = fraction of award given to the plaintiff’s lawyer under the conventional contingent fee system; 0 < θ < 1; and hC = number of hours worked by the plaintiff’s lawyer under the conventional contingent fee system. The lawyer will choose the number of hours to work to maximize his expected payoff at trial, p(h)θa - wh, (4) so hC will be determined by the first-order condition13 10 For expositional simplicity, we use the term “expected payoff at trial” (and similar terms) to refer to the benefit of going to trial net of the cost of going to trial. This language will be used both with respect to the client in the benchmark, as here, and with respect to the lawyer in the conventional contingent fee and no-conflict fee systems. 11 We assume that this solution is an interior optimum and is unique, and we make similar assumptions below without further comment. 12 We assume for simplicity that the plaintiff will file a suit (as will the lawyer if the lawyer makes the decision) if the expected value of the suit is zero; none of our results depend on this assumption. 13 We are implicitly assuming that the lawyer’s opportunity cost is his wage rate w; that is, if he were not working on this case he would be working on other cases at his hourly rate. We make the same assumption in the no-conflict fee system. (Note that, given this assumption, a lawyer who is paid on an hourly basis would be -7- pN(h)θa = w. (5) Given the declining marginal productivity of the lawyer’s time, it follows from a comparison of (5) and (2) that the lawyer will devote fewer hours to the case under the conventional contingent fee system than in the benchmark:14 hC < h*. (6) The lawyer will recommend filing a suit if the case has non-negative expected value to him, that is, if p(hC)θa - whC - k  0. (7) It is clear that the lawyer may not be willing to take the case under the conventional contingent fee system even when the case would be brought in the benchmark. This follows for two reasons. First, he will not be investing the number of hours that maximizes the expected value of the case (including his and the client’s interests). Second, he will only receive a fraction of the award. Formally, p(hC)θa - whC - k < p(hC)a - whC - k < p(h*)a - wh* - k. (8) We assume that lawyers compete for clients by offering to work for a lower contingency percentage. The equilibrium contingency percentage θ is such that the expected compensation of lawyers under the conventional contingency fee system equals their comparable hourly wages. In other words, θ is determined by p(hC)θa - k = whC. (9) There exists a unique θ between zero and one satisfying (9).15 Observe that the plaintiff is worse off under the conventional contingent fee system than indifferent between doing what is in the client’s interest or not. Realistically, however, the problems with the hourly fee method of compensation discussed in the opening paragraph of this article are likely to occur in practice.) 14 From (2), pN(h*) = w/a, while from (5), pN(hC) = w/θa > w/a. The result in (6) follows from the assumption that pO(h) < 0. 15 Rewrite (9) as p(hC)θa - whC - k = 0, where p(hC)θa - whC - k is the expected value of the case to the lawyer. If θ = 0, the lawyer will choose hC = 0, so the expected value of the case is -k. If θ = 1, the lawyer will choose hC = h*, so the expected value of the case is p(h*)a - wh* - k > 0. Since p(hC)θa - whC - k clearly is continuous and strictly increasing in θ, there must exist a unique θ between zero and one such that p(hC)θa - whC - k = 0. (Note that if there were no fixed cost of litigation k, the expected value of the case would be 0 when θ = 0 and positive for all θ > 0, implying that the equilibrium θ would be 0.) -8- in the benchmark. This is because the joint value of the case will be lower under the conventional contingent fee system (the lawyer works fewer hours than is optimal); and since the lawyer must still be compensated for the value of his time, there will be less left for the client.16 C. The No-Conflict Fee System Next consider the lawyer’s decisions if he is compensated according to our proposed fee arrangement, under which he bears the same percentage of his costs that he receives of the award. Let γ = fraction of award given to the plaintiff’s lawyer under the no-conflict fee system; 0 < γ < 1. For the lawyer to bear this fraction of his costs, he must be compensated for the fraction (1 - γ) of his costs whether the case is won or lost. In addition, the lawyer pays an up-front fee to the third- party administrator. Let t = payment by the plaintiff’s lawyer to the third-party administrator to obtain the case. First consider the lawyer’s decision regarding how many hours to work on the case. Let hN = number of hours worked by the plaintiff’s lawyer under the no-conflict fee system. The lawyer seeks to maximize his expected payoff at trial. If he prevails, he obtains γa, his share of the award. Whether he wins or loses, he bears γwh, his share of the cost of his time. Hence, he will choose h to maximize p(h)γa - γwh = γ[p(h)a - wh], (10) so hN will be determined by the first-order condition pN(h)a = w. (11) Comparing (11) and (2), it is obvious that the lawyer will spend the same number of hours as in the benchmark: hN = h*. (12) Aside from the up-front fee t, the lawyer will recommend filing a suit if the case has non- negative expected value to him, that is, if 16 The value of the case to the client in the benchmark is p(h*)a - wh* - k. The value of the case to the client under the conventional contingent fee is (1 - θ)p(hC)a. The conclusion in the text follows from observing that p(h*)a - wh* - k > p(hC)a - whC - k = p(hC)a - p(hC)θa = (1 - θ)p(hC)a, where the first equality follows from (9). -9- γ[p(hN)a - whN - k]  0. (13) Since γ > 0, if the term in brackets is negative, the lawyer will not file suit. However, if the term in brackets is non-negative, the lawyer would be willing to take the case to trial. Since hN = h*, this means that any case that would be brought in the benchmark (see (3)) will be brought by the lawyer under the no-conflict fee system; and conversely, any case that would not be brought in the benchmark would not be brought by the lawyer under our system. Next consider the up-front payment t for cases that a lawyer would want to bring (that satisfy (13)). We assume that the magnitude of this payment will be determined by a bidding process among lawyers competing to obtain the case, and that the winning bid will leave the winner indifferent between taking and not taking the case. If the case has positive expected value, then the lawyer’s share of this value is given by (13) and the winning bid will be t = γ[p(hN)a - whN - k]. (14) Lawyers will be willing to bid up to this amount because any lower t would result in their obtaining compensation in excess of their hourly wage. If the case has zero expected value, lawyers obviously will not be willing to pay anything to take the case. We now describe the distribution of payments among the parties under the no-conflict fee system. If the case is won, the defendant pays the third-party administrator the award a. The administrator then pays the plaintiff the amount (1 -γ)a and the plaintiff’s lawyer the amount γa + (1 - γ)(whN + k). (15) If the case is lost, the defendant pays nothing, the plaintiff receives nothing, and the third-party administrator pays the plaintiff’s lawyer the amount (1 - γ)(whN + k). (16) In essence, our system works just like a contingent fee system — in which the lawyer receives the fraction γ of the award and the client receives the fraction (1 - γ) of the award — with the important exception that the administrator also pays the lawyer for the fraction (1 - γ) of his legal costs (and the lawyer makes an up-front payment to the administrator). Aside from the up-front payment t, therefore, the administrator’s net payout is (1 - γ)(whN + k). Including receipt of the up-front payment, the administrator’s net revenue is t - (1 - γ)(whN + k), which, using (14), can be expressed as γp(hN)a - whN - k. Thus, the administrator’s net - 10 - revenue is increasing in γ. We assume that potential administrators compete for clients by offering to pay a higher share (1 - γ) of the trial award to the client or, equivalently, a lower share γ to the lawyer. The equilibrium fraction γ is such that the administrator’s net revenue under the no-conflict fee system equals zero: γp(hN)a - whN - k = 0. (17) There exists a unique γ between zero and one satisfying (17).17 Observe that the outcomes for all of the parties under our system duplicate those in the benchmark (either actually or in expectation). We have already shown that the same cases are brought and that the plaintiff’s lawyer spends the same amount of time on the case. Thus, the expected cost to the defendant also is the same as in the benchmark. Clients receive (1 - γ)a if the case is won, which occurs with probability p(hN), and they receive and pay nothing if the case is lost. Hence, the expected value of the case to a client is p(hN)(1 - γ)a. Using the zero-net revenue condition for the administrator (17), this can be expressed as p(hN)(1 - γ)a = p(hN)a - whN - k = p(h*)a - wh* - k, (18) the same as in the benchmark. Similarly, the expected value of the compensation received by the plaintiff’s lawyer equals that in the benchmark. On one hand, he receives (15) if the case is won and (16) if the case is lost, so the expected value of the case to him in excess of his hourly wage, but excluding his up-front payment t, is {p(hN)[γa + (1 - γ)(whN + k)] + (1 - p(hN))(1 - γ)(whN + k)} - whN = γ[p(hN)a - whN - k]. (19) But this equals his up-front payment t (see (14)), so the lawyer earns his hourly wage.18 17 First observe that for any positive γ, the lawyer will choose to work hN = h* hours. As γ goes to zero, γp(hN)a - whN - k goes to -wh* - k < 0. If γ = 1, γp(hN)a - whN - k = p(h*)a - wh* - k > 0. Since γp(hN)a - whN - k is continuous and strictly increasing in γ for all positive γ, there must exist a unique γ between zero and one such that γp(hN)a - whN - k = 0. 18 We have not considered within our formal analysis the incentive of the client to help prosecute the case against the defendant. Frequently, a client will be a significant source of information for the lawyer, and will be expected to prepare for and attend depositions and to testify at trial. Under the no-conflict fee system, the client has some incentive to engage in such effort because her receipt of a payment depends on a successful outcome at trial (or, as we discuss in the next section, on a settlement). However, the no-conflict fee system does not provide as much of an incentive of this sort as in the benchmark (for there the difference between a trial victory and a trial loss - 11 - III. Settlements are Possible In this section we extend the analysis of section II to allow for the possibility of a settlement. We employ an asymmetric information model of settlement in which the defendant knows his defense cost at trial, while the plaintiff or her lawyer knows only the distribution of possible defense costs. The plaintiff or her lawyer is assumed to make a take-it-or-leave-it settlement demand, which is accepted or rejected by the defendant.19 Let c = defendant’s litigation costs; c = lowest level of defendant’s litigation costs; c  0; _ _ c = highest level of defendant’s litigation costs; c > c ; and ¯ ¯ _ f(c) = probability density of defendant’s litigation costs; f(.) > 0 on [c , c ]. _ ¯ Let F(.) represent the cumulative distribution of f(.). Although the plaintiff’s litigation costs vary with the number of hours that her lawyer works, we assume for simplicity that the defendant’s litigation costs are fixed. Additionally, let s = settlement demand of plaintiff or her lawyer. We also assume for simplicity that if there is a settlement, it occurs after the plaintiff’s lawyer has incurred the fixed cost of bringing a case, k, but before any other litigation costs have been borne. In the benchmark, in order for the plaintiff to be able to extract a settlement from the defendant, the plaintiff must have a credible threat to go to trial; otherwise, the defendant would refuse to pay anything, knowing that the plaintiff will drop the case. In other words, for a settlement to be paid, the plaintiff’s lawsuit must have non-negative expected value at trial. Thus, we assume in the discussion of the benchmark below that (3) holds. Similarly, under the conventional contingent fee and no-conflict fee systems, we assume that the plaintiff’s lawyer has a credible threat to go to trial — that is, that (7) and (13) hold, respectively. is a, whereas in the no-conflict fee system it is (1 - γ)a). 19 This is a standard model of the litigation process. See, for example, Bebchuk (1984). In a model with perfect information or in which the parties have differential beliefs about the plaintiff’s probability of prevailing, the general conclusions in this section will still apply. If, however, the defendant makes a take-it-or-leave-it settlement offer, the analysis will be more complex and the results may differ because the defendant will be “signaling” information about his defense costs through his offer. - 12 - A. The Benchmark As previously, we consider here a plaintiff who is knowledgeable about the costs and benefits of litigation and who hires a lawyer on an hourly basis. We first examine the defendant’s decision whether to accept a settlement demand s made by the plaintiff. If he rejects the settlement, the plaintiff will go to trial and the defendant will bear expected costs of p(h*)a + c, where h* is determined by (2). Assuming that the defendant knows that the plaintiff’s threat to go to trial is credible, he will accept the settlement if and only if s  p(h*)a + c, (20) or, equivalently, if and only if c  s - p(h*)a.20 We will refer to this critical value of defense costs as c*(s), below which a defendant will reject the settlement demand s and at or above which he will accept it. In other words, c*(s) = s - p(h*)a.21 (21) The plaintiff will choose the settlement demand s to maximize her expected receipts, which are F(c*(s))[p(h*)a - wh*] + [1 - F(c*(s))]s. (22) The first term reflects the chance that the defendant will have a relatively low defense cost and therefore will reject the settlement, in which case the plaintiff will go to trial, while the second term reflects the chance that the defendant will have a relatively high defense cost and will accept the settlement. If s is less than or equal to p(h*)a + c , the defendant will accept the settlement _ regardless of his defense cost, so it will never be optimal for the plaintiff to set s below p(h*)a + c . Conversely, if s exceeds p(h*)a + c , the defendant will reject the settlement regardless of his _ ¯ defense cost, so we can assume without loss of generality that s is less than or equal to p(h*)a + c. ¯ The derivative of (22) with respect to s can be written as f(c*(s))[p(h*)a - wh* - s] + [1 - F(c*(s))], (23) 20 None of our results depend on the assumption that we are making here that the defendant will accept the settlement demand when he is indifferent. 21 We demonstrate below that the optimal s equals or exceeds p(h*)a, so c*(s) cannot be negative. - 13 - and interpreted as follows. If the plaintiff raises s by a dollar, she will obtain an additional dollar from the defendant if the defendant continues to accept the settlement; this occurs with probability [1 - F(c*(s))]. But, by raising the settlement demand, the plaintiff reduces the probability that the defendant will accept the settlement; this probability declines by f(c*(s)). If the defendant switches to rejecting the settlement demand, the plaintiff receives the expected payoff from trial, p(h*)a - wh*, but foregoes the settlement, s. Because, as explained above, s must equal or exceed p(h*)a + c , p(h*)a - wh* - s must be negative, so it is costly to the plaintiff _ for the defendant’s probability of acceptance of the settlement to decline. What can be said about the optimal settlement demand in the benchmark? First note that s* is such that there is a positive probability that the case will settle. To see this, consider the derivative of the plaintiff’s welfare when the settlement demand is at its upper bound, p(h*)a + c . ¯ Then c*(s) = c and F(c ) = 1, so (23) becomes -f(c )[wh* + c ], which clearly is negative. Thus, s* ¯ ¯ ¯ ¯ must be strictly less than its upper bound, p(h*)a + c , which implies that the probability of ¯ settlement is positive. Second, observe that s* could be at its lower bound, p(h*)a + c , in which _ case a settlement occurs regardless of the defendant’s litigation cost. At s = p(h*)a + c , c*(s) = c _ _ and F(c ) = 0, so (23) becomes 1 - f(c )[wh* + c ]. If the second term is sufficiently large, this _ _ _ expression will be negative, implying that s* = p(h*)a + c , in which case a settlement occurs for _ all values of defense cost. To summarize, p(h*)a + c  s* < p(h*)a + c . _ ¯ (24) We will assume that s* is strictly greater than p(h*)a + c so that there will be a positive _ probability of both trial and settlement in the benchmark. Then s* will be determined by the following first-order condition: f(c*(s))[p(h*)a - wh* - s] + [1 - F(c*(s))] = 0. (25) B. The Conventional Contingent Fee System Next consider the settlement demand when it is made by the plaintiff’s lawyer and the lawyer is compensated according to the conventional contingent fee arrangement with contingency percentage θ.22 The lawyer will choose s to maximize his expected receipts, which 22 Both here and in the no-conflict fee system, we assume that the plaintiff lawyer’s share of a settlement is the same as his share of a trial award. There would be no advantage in the no-conflict fee system to allowing the - 14 - are F(cC(s))[p(hC)θa - whC] + [1 - F(cC(s))]θs, (26) where hC is determined according to (5) and the critical value of defense costs (below which the defendant will reject the settlement demand and at or above which he will accept it) is cC(s) = s - p(hC)a. (27) By reasoning analogous to that used above, it must be that s is at least equal to p(hC)a + c and no _ greater than p(hC)a + c . ¯ The derivative of (26) with respect to s is f(cC(s))[p(hC)θa - whC - θs] + [1 - F(cC(s))]θ, (28) which has an interpretation analogous to that of (23) above. If the lawyer raises s by a dollar, he obtains the additional fraction θ of a dollar from the defendant if the defendant continues to accept the settlement, which occurs with probability [1 - F(cC(s))]. But by raising the settlement demand the lawyer reduces, by f(cC(s)), the probability that the defendant will accept the settlement. Then the lawyer would receive his expected payoff from trial, p(hC)θa - whC, but forego his share of the settlement, θs. Because s equals or exceeds p(hC)a + c , p(hC)θa - whC - θs _ must be negative. As in subsection II.B, assuming lawyers compete for clients by offering to work for a lower contingency percentage, the equilibrium contingency percentage θ equates their expected compensation under the conventional contingency fee system to their corresponding hourly wages. Thus, θ now is determined by F(cC(s))p(hC)θa + [1 - F(cC(s))]θs - k = F(cC(s))whC. (29) There exists a unique θ between zero and one satisfying (29).23 settlement share to differ from the trial award share, for even with the two constrained to be equal, the no-conflict fee system leads to the same outcome as in the benchmark (see subsection III.C below). While there generally would be an advantage in the conventional contingent fee system to allowing the two percentages to differ, the results still would be inferior to those in the benchmark and in the no-conflict fee system. Thus, for simplicity, we assume that the lawyer’s share of a settlement is the same as his share of a trial award. 23 Rewrite (29) as F(cC(sC))[p(hC)θa - whC] + [1 - F(cC(sC))]θsC - k = 0, (29') where the left-hand side of (29') is the expected value of the case to the lawyer. If θ = 0, the lawyer will choose hC = 0, so the expected value of the case is -k. If θ = 1, the lawyer will choose hC = h* and sC = s*, so the expected value of the case must be at least as high as p(h*)a - wh* - k > 0 (the lawyer can obtain this expected value by setting s - 15 - How does the settlement demand under the conventional contingent fee system compare to that in the benchmark? Because the answer to this question is somewhat complicated and not essential to the main point of the present article, we have analyzed this topic elsewhere.24 It can be shown that if the number of hours worked on the case by the lawyer under the conventional contingent fee system were the same as in the benchmark, the settlement demand chosen by the lawyer under the conventional contingent fee system, sC, would be lower than the settlement demand chosen by the plaintiff in the benchmark, s*. Consequently, settlement would be more likely under the conventional contingent fee system. But the fact that the lawyer actually devotes fewer hours to the case under the conventional contingent fee system (see (6)) implies that the settlement demand could be higher in the conventional contingent fee system and that the probability of settlement could be lower. Observe that the plaintiff is worse off under the conventional contingent fee system than in the benchmark. The reasoning is essentially that used to make the same point in subsection II.B. Specifically, the joint value of the case will be lower, leaving less for the client after taking account of the lawyer’s expected compensation.25 C. The No-Conflict Fee System Finally, consider the lawyer’s choice of the settlement demand if he is compensated according to our proposed fee system with award and cost-bearing percentage γ. The lawyer will choose s to maximize his expected receipts, F(cN(s))γ[p(hN)a - whN] + [1 - F(cN(s))]γs, (30) high enough to induce the defendant to reject the settlement demand regardless of his defense costs). Since the expected value of the case is continuous and strictly increasing in θ, there must exist a unique θ between zero and one such that (29') is satisfied. 24 See Polinsky and Rubinfeld (2001). 25 The value of the case to the client in the benchmark is F(c*(s*))[p(h*)a - wh*] + [1 - F(c*(s*))]s* - k. The corresponding value under the conventional contingent fee is (1 - θ){F(cC(sC))p(hC)a + [1 - F(cC(sC))]sC}. The conclusion in the text follows from observing that F(c*(s*))[p(h*)a - wh*] + [1 - F(c*(s*))]s* - k > F(c*(sC))[p(h*)a - wh*] + [1 - F(c*(sC))]sC - k > F(c*(sC))[p(hC)a - whC] + [1 - F(c*(sC))]sC - k > F(cC(sC))[p(hC)a - whC] + [1 - F(cC(sC))]sC - k = F(cC(sC))[p(hC)a - whC] + [1 - F(cC(sC))]sC - {F(cC(sC))[p(hC)θa - whC] + [1 - F(cC(sC))]θsC} = (1 - θ){F(cC(sC))p(hC)a + [1 - F(cC(sC))]sC}. The first inequality follows from the fact that s* maximizes (22); the second inequality from the fact that h* maximizes (1); the third inequality from the facts that c*(s) < cC(s) (see (21) and (27)) and p(hC)a - whC < sC (see the sentence in the text following (27)); and the first equality follows from (29). - 16 - where hN is determined according to (11) and cN(s) = s - p(hN)a. (31) Since hN = h* (see (12)), it follows that cN(s) = c*(s). Thus, (30) can be expressed as γ{F(c*(s))[p(h*)a - wh*] + [1 - F(c*(s))]s}, (32) where the expression in braces is the expected receipts of the plaintiff in the benchmark (see (22)). Therefore, the lawyer will choose the same settlement demand in the no-conflict fee system as in the benchmark: sN = s*. (33) This also implies that the probability of settlement is the same as in the benchmark, since cN(s) = c*(s). As previously, we assume that the up-front payment t will be the outcome of a bidding process among lawyers and that the winning bid will leave the winner indifferent between taking and not taking the case. Hence, t will equal the lawyer’s share of the expected value of the case, which now is the sum of the value of trial and value of settlement, weighted by their respective probabilities, less the fixed cost of litigation: t = γ{F(cN(sN))[p(hN)a - whN] + [1 - F(cN(sN))]sN - k}. (34) Next consider the distribution of payments among the parties under the no-conflict fee system. If the case settles, the defendant pays the third-party administrator the settlement sN. The administrator then pays (1 - γ)sN to the plaintiff and γsN to the plaintiff’s lawyer for his share of the settlement. If the case goes to trial, the payments made to and from the administrator are those described in section II.C. Aside from the up-front payment t, therefore, the administrator’s net payout is (1 - γ)k if the case settles and (1 - γ)(whN + k) if the case goes to trial. Including the up-front payment and taking account of the probabilities of settlement and trial, the administrator’s expected net revenue is t - {F(cN(sN))(1 - γ)(whN + k) + [1 - F(cN(sN))](1 - γ)k}, (35) which, using (34), can be expressed as γ{F(cN(sN))p(hN)a + [1 - F(cN(sN))]sN} - F(cN(sN))whN - k. (36) Thus, the administrator’s net revenue is increasing in γ. Competition among potential - 17 - administrators will cause γ to decline until the net revenue of an administrator equals zero: γ{F(cN(sN))p(hN)a + [1 - F(cN(sN))]sN} - F(cN(sN))whN - k = 0. (37) There exists a unique γ between zero and one satisfying (37).26 Lastly, observe that the outcomes for all of the parties under our system again duplicate those in the benchmark. The expected cost to the defendant is the same because the probability of trial and settlement are the same, as are the trial and settlement outcomes. The value of the case to the plaintiff also equals that in the benchmark. If the case settles, she obtains (1 - γ)sN, while if the case goes to trial she receives (1 - γ)a if there is a trial victory. Thus, the plaintiff’s expected receipts in the no-conflict fee system are F(cN(sN))p(hN)(1 - γ)a + [1 - F(cN(sN))](1 - γ)sN. (38) The value of the case to the plaintiff in the benchmark is F(c*(s*))[p(h*)a - wh*] + [1 - F(c*(s*))]s - k. (39) That (38) equals (39) follows from hN = h*, cN(s) = c*(s), sN = s*, and the zero net revenue condition for the administrator (37). The lawyer also is identically situated since his compensation in excess of his hourly wage in the no-conflict fee system — which is the right-hand side of (34) — is exactly offset by his up-front payment t.27,28 26 For any positive γ, the lawyer will choose to work hN = h* hours. As γ goes to zero, the left-hand side of (37) goes to -F(cN(sN))whN - k < 0. If γ = 1, the left-hand side of (37) must equal or exceed p(h*)a - wh* - k > 0 (for the reason given in note 23 above). Since the left-hand side of (37) is continuous and strictly increasing in γ for all positive γ, there must exist a unique γ between zero and one such that (37) holds. 27 The Clermont and Currivan (1978) article attempts to resolve the conflict of interest between the lawyer and the client in a different way than we do. Under their proposal, the lawyer is compensated only if he obtains a settlement or a judgment on behalf of the client, in which case his compensation equals the value of his time plus a fraction of the difference between the settlement or judgment and the value of his time. This payment scheme is only fully successful, however, if the plaintiff is certain to obtain a settlement or a trial victory; Clermont and Currivan recognize this point (for example, at pp. 561-66 and 619-22) but argue that it is not a significant qualification to their proposal (“In sum, after the introduction of uncertainty the proposed fee no longer perfectly aligns the economic interests of lawyer and client, but it still substantially improves upon the two present fee systems.”). 28 We have been assuming for simplicity that all parties are risk neutral. In reality, the client and the lawyer are likely to be risk averse. (The third-party administrator can be treated as analogous to an insurance company — the administrator presumably handles a large number of cases on behalf of different clients — and therefore presumed to be risk neutral.) In the benchmark, in which the client hires the lawyer on an hourly fee basis, - 18 - IV. Implementation Issues Before discussing two topics related to the implementation of the no-conflict fee system, we summarize here its key features. An individual who has been injured — the plaintiff — enters into a contract with a third-party administrator to hire a lawyer on her behalf. The administrator collects any trial award or settlement, but agrees to pay the fraction γ of this amount to the lawyer and the remainder to the plaintiff.29 In addition, the administrator promises to pay the lawyer for the share (1 - γ) of his legal costs, including the time he spent on the case. Lawyers compete for the right to work under these terms by offering to pay the administrator an up-front fee. Potential administrators compete for plaintiffs by offering to pay a higher fraction of any award or settlement to the plaintiff.30 A. Observing the Lawyer’s Hours Obviously, the no-conflict fee system cannot be implemented unless the third-party administrator knows how many hours the plaintiff’s lawyer devoted to the case. While the lawyer will report his hours in order to receive the compensation due to him from the administrator, a concern is that the lawyer may overstate his time. To reduce the risk of overbilling, the agreement between the administrator and the lawyer presumably would require the lawyer does not bear any risk, whereas the client’s risk is considerable — the client obtains the trial award or a settlement if victorious, and nothing otherwise, but has to pay the lawyer even if the case goes to trial and loses. Under the no-conflict fee system, the client and the lawyer both bear risk. The risk borne by the client is less than in the benchmark because the difference between a favorable and an unfavorable outcome is lessened — the client receives only a fraction of any award or settlement, and does not have to pay the lawyer. The lawyer’s risk bearing, however, obviously is higher under the no-conflict fee system. Thus, to the extent that client risk aversion is more important than lawyer risk aversion, the no-conflict fee system would be superior to the benchmark (of course, the converse proposition holds as well). Note that the risk bearing of the defendant is the same under the no-conflict fee system as in the benchmark, because the no-conflict fee system leads to the same outcome as in the benchmark. 29 Note that the contract between the plaintiff and the administrator is not equivalent to the “sale” of the plaintiff’s case to the administrator. The plaintiff does not receive anything up front from the administrator. The plaintiff’s compensation is contingent on a trial victory or a settlement, just as under the conventional contingent fee system (or under an hourly fee arrangement). 30 Competition among administrators and/or among lawyers is not essential for the no-conflict fee system to work. Even if there were only one administrator who has market power, it would be in that administrator’s interest to adopt the terms of the no-conflict fee system applicable to the lawyer because this would allow the administrator to extract more from the plaintiff (by paying the plaintiff a lower fraction of any trial award or settlement). Similarly, if there were imperfect competition among lawyers, the up-front fee paid to the administrator would be lower than that derived here, but lawyers would still behave as in the benchmark. - 19 - the lawyer to provide detailed billing records and would give the administrator the right to audit the lawyer’s records. The administrator might perform such audits itself or hire a firm that specializes in auditing lawyers’ bills.31 Whoever does the auditing would acquire information about the ordinary range of time reported for different types of cases, and therefore would have a reason to be suspicious if a lawyer billed significantly more than the average for the type of case he handled. An additional constraint on overbilling derives from the ethical and legal obligations of lawyers to not defraud their clients; a lawyer who charges for time not spent working could be barred from the practice of law, as well as civilly and criminally prosecuted. Finally, and perhaps most importantly, there may be a substantial reputational penalty that a lawyer would bear if he is found to have overbilled the administrator. Among other things, the lawyer may be precluded from bidding on future cases. In the light of the preceding considerations, we do not believe that the issue of observing the plaintiff lawyer’s hours is a serious obstacle to the implementation of the no-conflict fee system. Moreover, the fact that lawyers regularly are hired on an hourly fee basis by defendants, and often by plaintiffs as well, suggests that the problem discussed in this subsection is not overwhelming.32 B. Implementation Without a Third-Party Administrator Although our description of the no-conflict fee system involved the use of a third-party administrator, this feature is not essential to the core idea in our article. The main reason for including an administrator in our scheme is to allow the interests of the lawyer and the client to be aligned without the client having to pay anything to the lawyer (or the administrator) if the case goes to trial and loses. If this constraint — that the plaintiff not pay anything in the event of a trial loss — is not imposed, a variation of the no-conflict fee system could be implemented without a third-party administrator. Specifically, the client would enter into a contract with the lawyer in which the client would agree to pay the lawyer for a certain fraction (1 - γ) of his costs, 31 For an example of such a firm, see http://www.stuartmaue.com (web site of Stuart, Maue, Mitchell & James, Ltd., Legal Auditors and Consultants). 32 Note, too, that under the no-conflict fee system the lawyer is reimbursed for only a fraction of his time, so the incentive to overstate hours is less (possibly substantially less) than under an hourly fee arrangement. - 20 - regardless of whether the case is won or lost; the client also would agree to pay the lawyer for the fraction γ of any trial award or settlement. In return, the lawyer would pay the client an up-front payment for the right to represent the client under these terms. This contract between the lawyer and the client would lead the lawyer to act exactly as in the benchmark, though the client will bear costs if the case goes to trial and loses. V. Conclusion Although we have discussed the conflict of interest between lawyers and clients in the context of cases involving a single client, our analysis and conclusions easily extend to class actions. The need to resolve the lawyer-client conflict of interest is even greater in that setting because of the insufficient incentive of any one member of the class to try to supervise and monitor the lawyer. For this reason, courts already intervene to some extent in the lawyer-client relationship in class actions, by selecting the lawyer to represent the class (when multiple lawyers are competing for that position) and reviewing any prospective settlement to assess whether it is in the class’ interest. The no-conflict fee system could be used to compensate lawyers in class action cases and it may provide a superior way to align the lawyer’s interests with the class’ interests than active judicial oversight. While our analysis has focused on the compensation of lawyers representing plaintiffs, an approach similar to the one we have presented could be used to compensate lawyers hired by defendants. The defense analogue to the no-conflict fee system would work as follows. The contract between the defendant and the defense lawyer would require the defense lawyer to bear some fraction — say φ — of any trial award or settlement paid by the defendant. In return, the defendant would agree to pay for the fraction (1 - φ) of the lawyer’s costs and pay the lawyer an up-front fee. Lawyers would compete for the right to work for the defendant on these terms, bidding for the case by offering to work for a lower up-front fee. The lawyer who represents the defendant under this type of contract will have the same incentives with respect to investing time and money in the case, and settling the case, as would a knowledgeable defendant who hires the - 21 - lawyer on an hourly fee basis.33 Thus, this defense version of the no-conflict fee system would overcome the conflict of interest that otherwise would arise if the defendant is not as knowledgeable as the lawyer about the case and hired the lawyer on an hourly fee basis — specifically, that the lawyer would have an incentive to spend an excessive amount of time on the case at trial and will be overly reluctant to accept a settlement demand.34 33 This conclusion follows because the lawyer will, in effect, “own” the fraction φ of the defendant’s obligations resulting from the plaintiff’s claim against the defendant — the lawyer will pay the fraction φ of any trial award or settlement and will bear the fraction φ of the defendant’s litigation costs. 34 Although this description of the defense version of the no-conflict fee system does not employ a third- party administrator, an administrator would be needed if one wanted to ensure that the defendant would not have to pay the lawyer anything if the defendant loses. The administrator would pay the lawyer for the fraction (1 - φ) of his costs regardless of the outcome of the case. - 22 - References Bebchuk, Lucian Arye, "Litigation and Settlement Under Imperfect Information," Rand Journal of Economics, Vol. 15, No. 3 (Autumn 1984), pp. 404-415. Clermont, Kevin M., and John D. Currivan, “Improving on the Contingent Fee,” Cornell Law Review, Vol. 63, No. 4 (April 1978), pp. 529-639. Dana, Jr., James D., and Katherine E. Spier, "Expertise and Contingent Fees: The Role of Asymmetric Information in Attorney Compensation," Journal of Law, Economics, & Organization, Vol. 9, No. 2 (October 1993), pp. 349-67. Danzon, Patricia Munch, “Contingent Fees for Personal Injury Litigation,” Bell Journal of Economics, Vol. 14, No. 1 (Spring 1983), pp. 213-24. Emons, Winand, “Expertise, Contingent Fees, and Insufficient Attorney Effort,” International Review of Law and Economics, Vol. 20, No. 1 (March 2000), pp. 21-33. 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