Penoyar, J.
¶1 Psychiatric security nurses and psychiatric security attendants1 who work in the forensic wards at the state’s psychiatric hospitals filed this suit against the Department of Social and Health Services (DSHS), the Department of Personnel (Personnel), and officials of both agencies,2 seeking an increase in their salary ranges. The employees alleged that the State violated their equal protection rights, violated the comparable worth statutes, and acted arbitrarily and capriciously by setting their salary ranges lower than their counterparts in the civil commitment wards. The trial court agreed with the employees and, following a bench trial, found that the State had violated the employees’ equal protection rights and their rights under the comparable worth statutes. The State appeals the trial court’s verdict and award of attorney fees to the employees, arguing that (1) there is a rational basis for paying forensic and civil nurses differently, (2) the employees have no right to adjustment of their wages under the comparable worth statutes, (3) the trial court improperly [20]*20granted a writ of certiorari, (4) the trial court erred by finding that the State was collaterally estopped by a 1983 order, and (5) the trial court erred by awarding the employees attorney fees under both the common fund doctrine and fee-shifting statutes. The employees cross appeal, arguing that the trial court erred by finding that they are not entitled to double damages under RCW 49.52.070.3
¶2 Because it is reasonable for the State to pay employees the salaries they collectively bargained for, the employees’ equal protection claim fails. Additionally, the employees are not entitled to any relief under the 1980s era comparable worth statutes. We reverse and hold that the employees are not entitled to attorney fees because they did not prevail.
FACTS
I. Background
¶3 This appeal arises from pay disparities between nurses (PSNs) and nursing attendants (PSAs) in the forensic wards of Eastern and Western State Hospitals and their counterparts in the civil commitment wards — licensed practical nurses (LPNs) and mental health technicians (MHTs). Practical nurses on both the forensic and civil wards share similar duties and responsibilities, but there are a few administrative differences. The LPN series has 3 levels: 1, 2, and 4. LPN4s are designated lead workers on the civil wards. There is only one LPN4 on duty per shift. By contrast, there is only one level of PSN, and each shift has multiple PSNs who share the LPN4 responsibilities. As of 2007, when the complaint was filed in this case, PSNs were in the same salary range as LPN2s.4 The PSNs argue that [21]*21their salary range should at least match LPN4s’ salary range.
¶4 Attendants on both the forensic and civil wards also share similar duties and responsibilities. Like the practical nurses, the attendants on the civil wards — MHTs—have different levels: 1, 2, and 3, while the forensic attendants— PSAs — have only one level. MHT3s have additional administrative duties beyond those assigned to MHT2s and MHTls. For example, MHT3s are responsible for placing work orders and ordering supplies, and they serve as ward fire marshals.5 PSAs perform these same tasks, but they are shared among multiple PSAs. As of 2007, PSAs were one salary range above MHT2s and two ranges below MHT3s. PSAs argue that their salary range should at least match MHT3s’ salary range.
II. History of PSN and PSA Salary Setting
¶5 In 1973, Personnel adopted the PSN and PSA classifications for nurses and attendants working in the mental health unit of corrections institutions. Personnel placed forensic PSNs and PSAs in higher salary ranges than civil LPNs and hospital attendants6 in recognition “of the added danger involved in dealing with felons and the criminally insane.” Ex. 40, at 2.
¶6 In 1976, the State moved the mental health units from corrections institutions to state psychiatric hospitals and reclassified PSNs and PSAs as LPNs and hospital attendants. The former PSNs and PSAs petitioned Personnel to reallocate them to their former, higher-paying, classifications. The Personnel Board denied their request and the employees sued. The superior court ordered the employees reallocated back to PSNs and PSAs and awarded them back pay for the time they were misclassified as LPNs and hospital attendants.
[22]*22¶7 In 1985, the legislature ratified a broad settlement agreement implementing comparable worth.7 The agreement calculated an average salary line and provided incremental raises for state employees in job classifications that were below the average line. LPNs and MHTs received raises under comparable worth because their salary ranges were below the average salary line. PSNs and PSAs did not receive raises under comparable worth because their salary ranges were already above the average salary line. As a result, LPN4s and MHT3s are now in a higher salary range than PSNs and PSAs.
¶8 Statutory changes mandated that in 2004, the employees, through their union, would begin collectively bargaining with the governor over their salary ranges. See RCW 41.80.001, .010(1), .020(1) (providing the matters subject to bargaining, including wages). The governor represents DSHS during collective bargaining negotiations. RCW 41.80.010(1).
III. Procedural History
¶9 Two PSNs and a PSA filed a class action complaint with the superior court, alleging that by paying PSNs and PSAs less than their LPN and MHT counterparts, the State violated their equal protection rights, acted arbitrarily and capriciously, and violated the comparable worth doctrine. The employees sought declaratory relief directing the State to pay them at the same rate as comparable job classes, double damages for lost wages, and attorney fees.
¶10 Following a bench trial, the trial court concluded that the State had violated the employees’ equal protection rights, had violated their rights to comparable pay under the comparable worth statute, and had acted arbitrarily and capriciously. The trial court ordered the State to adjust the PSNs’ pay range to match the LPN4s’ pay range and to adjust the [23]*23PSAs’ pay range to match the MHT3s’ pay range beginning on May 16, 2004, and continuing prospectively. The trial court granted the employees prospective relief under 42 U.S.C. § 1983 and back pay under its inherent authority to compel other branches of government to comply with the law.
¶11 The trial court denied the employees’ request for double damages but awarded them attorney fees and costs. The trial court awarded employees’ counsel one-third of the employees’ back pay and interest under the common fund doctrine. Under the fee-shifting statutes, the trial court ruled that the State was responsible for a portion of the common fund fees, and it calculated this amount using the lodestar method.
¶12 The State appeals. The employees cross appeal, arguing that the trial court should have awarded double damages under RCW 49.52.070.
ANALYSIS
I. Equal Protection
¶13 The State first argues that the trial court erred by finding that the State violated the employees’ equal protection rights.8 There is substantial evidence to support the trial court’s findings that PSNs and LPN4s share similar duties and that PSAs and MHT3s share similar duties. Although historical salary range setting practices are not a rational basis for distinguishing between employees, it is rational for the State to pay the employees what they have bargained to be paid through their union. We reverse the trial court’s finding that the employees have shown an equal protection violation.
[24]*24¶14 Equal protection guarantees that persons similarly situated with respect to a legitimate purpose of the law receive like treatment. State v. Hamer, 153 Wn.2d 228, 235, 103 P.3d 738 (2004). In analyzing an equal protection claim, we must first determine the applicable standard of review. Wash. Pub. Emps. Ass’n v. Pers. Res. Bd., 127 Wn. App. 254, 263, 110 P.3d 1154 (2005). Both parties agree that rational basis review applies here, where the classification involves finite state resources and does not concern a fundamental right or suspect classification. Under rational basis review, a state action is constitutional if (1) it applies alike to all members of the designated class, (2) there are reasonable grounds to distinguish between those within and without the class, and (3) the classification has a rational relationship to the State’s purpose. Wash. Pub. Emps. Ass’n, 127 Wn. App. at 263. The burden is on the challenging party to show that the classification is purely arbitrary. Gossett v. Farmers Ins. Co. of Wash., 133 Wn.2d 954, 979, 948 P.2d 1264 (1997).
A. Designated Class
¶15 The parties disagree about how to define the designated class. The State argues that each job classification (PSN, PSA, LPN4, and MHT3) constitutes a designated class and that there are rational reasons to treat each job classification differently. The employees argue that the designated class consists of PSNs and PSAs, who do the same work as LPN4s and MHT3s but are paid less. Thus, in order to define the class, it is necessary to first determine whether PSNs and PSAs do the same work as LPN4s and MHT3s.
¶16 The trial court found that PSNs’ duties are-“essentially the same” as LPN4s’ duties and that PSAs’ duties are “essentially the same” as MHT3s’ duties. II Clerk’s Papers (CP) at 2160 (Finding of Fact (FF) 19, 21). The trial court characterized any differences between the positions as “de minim[i]s.” II CP at 2160 (FF 18). We review [25]*25challenged findings of fact to determine whether they are supported by substantial evidence. City of Tacoma v. William Rogers Co., 148 Wn.2d 169, 191, 60 P.3d 79 (2002) (quoting Fred Hutchinson Cancer Research Ctr. v. Holman, 107 Wn.2d 693, 712, 732 P.2d 974 (1987)). “Substantial evidence” is evidence sufficient to persuade a fair-minded person of the truth of the matter asserted. William Rogers Co., 148 Wn.2d at 191 (quoting Fred Hutchinson Cancer Research Ctr., 107 Wn.2d at 712). As long as substantial evidence supports a finding, it does not matter that other evidence may contradict it. In re Marriage of Burrill, 113 Wn. App. 863, 868, 56 P.3d 993 (2002). Here, there is substantial evidence to support the trial court’s findings regarding the similarities among the positions.
¶17 PSNs’ duties are similar to LPN4s’ duties. According to DSHS’s position descriptions and testimony from Western State Hospital’s nurse executive, PSNs and LPN4s have similar education and experience requirements and similar nursing responsibilities. The State points out that LPN4s are designated as lead workers and perform certain administrative tasks, such as assisting registered nurses (RNs) with assigning work. However, PSNs testified that they perform many of the same tasks as LPN4s, and they too act as lead workers when there is no RN present.
¶18 Likewise, PSAs’ duties are similar to MHT3s’ duties. Again, according to DSHS’s position descriptions and testimony from a nurse executive, PSAs and MHT3s require similar education and skills and have similar responsibilities. Although the State argues that there was some testimony contradicting the similarities — there are multiple PSNs per shift and only one LPN4, PSNs and PSAs have increased security concerns, and the daily needs of the patients vary by ward — as long as there is substantial evidence to support a finding, we will affirm it despite contradictory evidence.
¶19 Because PSNs and PSAs do the same work as LPN4s and MHT3s but are paid less, we agree with the [26]*26employees that the designated class consists of PSNs and PSAs. In Washington Public Employees Ass’n, we held that the designated class was defined by those employees who receive disparate treatment. 127 Wn. App. at 264. Here, the PSNs and PSAs are receiving disparate treatment — they are paid at a lower salary range than the LPN4s and MHT3s even though their duties are comparable.
B. Reasonable Grounds and Rational Relationship
¶20 The next issue is whether there are reasonable grounds to distinguish between those within the designated class — PSNs and PSAs — and those without — LPN4s and MHT3s. The State gives two reasons why it is reasonable to pay the forensic and civil nurses differently: (1) they are in separate job classifications and (2) the employees bargained for their wages.
¶21 The State’s first argument fails because historical rate setting practices are not reasonable grounds for distinguishing between those within and without the designated class. In Washington Public Employees Ass’n, we held that the State violated employees’ equal protection rights by paying certain employees in general government less than similarly situated employees in higher education and vice versa. 127 Wn. App. at 257, 268. The State argued that because general government and higher education employees have historically been treated differently, this was a rational basis for paying them differently. Wash. Pub. Emps. Ass’n, 127 Wn. App. at 267. We rejected this analysis, reasoning that no rational basis existed to set different salaries for state employees doing the same work where the disparities are based on historical practice rather than job differences. Wash. Pub. Emps. Ass’n, 127 Wn. App. at 268.
¶22 Similarly, here, the State’s argument for paying PSNs and PSAs less than LPN4s and MHT3s is based on historical rate setting practices and not an evaluation of their job differences. Personnel’s classification and compensation program director testified that “[t]he salary ranges [27]*27that [PSNs and PSAs are] paid are based on the actions that occurred over time [such as comparable worth and collective bargaining], ... so I guess the fact that they’ve ended up this way is a fact of the system and how ... it works.” 5 Report of Proceedings at 493. We rejected a similar explanation in Washington Public Employees Ass’n, and we do so here.
¶23 However, the State’s second argument is persuasive. A classification that is “ ‘neither capricious nor arbitrary, and rests upon some reasonable consideration of difference or policy’ ” does not violate equal protection. Forbes v. City of Seattle, 113 Wn.2d 929, 944, 785 P.2d 431 (1990) (quoting Allied Stores of Ohio, Inc. v. Bowers, 358 U.S. 522, 527, 79 S. Ct. 437, 3 L. Ed. 2d 480 (1959)). Here, the State’s actions are not arbitrary; they are based on the collective bargaining agreement between the employees and the State. The employees have collectively bargained for their wages since 2004, three years before they filed this suit. It is reasonable for the State to pay the employees the rates their union negotiated for them during collective bargaining.
¶24 Additionally, the State’s actions are rationally related to its interest in abiding by collective bargaining agreements. The purpose of chapter 41.56 RCW is “to promote the continued improvement of the relationship between public employers and their employees by providing a uniform basis for implementing the right of public employees to join labor organizations of their own choosing and to be represented by such organizations.” RCW 41.56.010. The purpose of the act is not served if the State ignores a collectively bargained agreement and unilaterally sets the employees’ rates.9
¶25 The employees do not provide any authority stating that collective bargaining is not a rational basis for deter[28]*28mining salary rates. At oral argument, the employees compared their situation to one where the State uses a racially discriminatory collective bargaining agreement to justify its discriminatory actions. However, this hypothetical involves a suspect classification, and the State’s actions would be subject to strict scrutiny, not rational review. Am. Legion Post No. 149 v. Dep’t of Health, 164 Wn.2d 570, 608-09, 192 P.3d 306 (2008). Further, although we did not find any Washington case law directly on point, case law from other jurisdictions supports our decision. See Collins v. County of Monroe, 531 F. Supp. 2d 522, 527 (W.D.N.Y. 2008) (dismissing employee’s equal protection complaint, in part, because employer’s conduct conformed to the collective bargaining agreement); St. Cloud Police Relief Ass’n v. City of St. Cloud, 555 N.W.2d 318, 321 (Minn. Ct. App. 1996) (“The guarantee of equal protection does not require equal outcomes in labor-management negotiations.”).
¶26 It is reasonable for the State to pay the employees what their union has bargained for them to be paid. Therefore, we reverse the trial court’s conclusion that the employees have proved an equal protection claim.
II. Comparable Worth
¶27 The State next argues that the trial court erred by granting the employees relief under the comparable worth statutes. Specifically, they argue that (1) the comparable worth statutes did not create a private cause of action, (2) the employees cannot show that the conditions within the statutes have been met, and (3) the trial court cannot “subjectively determine” the comparable worth of positions. Appellant’s Reply Br. at 28. Because legislative intent does not support a remedy in this case and implying a remedy would be inconsistent with the underlying purpose of the legislation, we agree that the comparable worth statutes did not create a private cause of action. And, even if there were a cause of action, the employees cannot show that they are entitled to relief under the statutes.
[29]*29¶28 Former RCW 41.06.020(5) (1993) defines “comparable worth” as “the provision of similar salaries for positions that require or impose similar responsibilities, judgments, knowledge, skills, and working conditions.” The employees argue that the State violated its duty to achieve comparable worth compensation for PSNs and PSAs.
¶29 The employees base their argument on two statutes, former RCW 41.06.133(10) (2002) and RCW 41.06.155. Former RCW 41.06.133(10) states,
The director [of Personnel] shall adopt rules, consistent with the purposes and provisions of this chapter and with the best standards of personnel administration, regarding the basis and procedures to be followed for . . . [a]doption and revision of a state salary schedule to reflect the prevailing rates in Washington state private industries and other governmental units. The rates in the salary schedules or plans shall be increased if necessary to attain comparable worth under an implementation plan under RCW 41.06.155----Such adoption and revision is subject to approval by the director of financial management in accordance with chapter 43.88 RCW.
RCW 41.06.155 states,
Salary changes necessary to achieve comparable worth shall be implemented during the 1983-85 biennium under a schedule developed by the department. Increases in salaries and compensation solely for the purpose of achieving comparable worth shall be made at least annually. Comparable worth for the jobs of all employees under this chapter shall be fully achieved not later than June 30, 1993.
A. Private Cause of Action
¶30 First, the State argues that the comparable worth statutes do not create a private cause of action. The statutes do not explicitly create a cause of action, but “a cause of action may be implied from a statutory provision when the legislature creates a right or obligation without a corresponding remedy.” Ducote v. Dep’t of Soc. & Health Serus., 167 Wn.2d 697, 703, 222 P.3d 785 (2009). To deter[30]*30mine whether a cause of action exists, we consider (1) whether the plaintiffs are within the class of persons for whose benefit the statute was enacted, (2) whether legislative intent supports creating or denying a remedy, and (3) whether implying a remedy is consistent with the underlying purpose of the legislation. Wash. State Coal, for Homeless v. Dep’t of Soc. & Health Servs., 133 Wn.2d 894, 912-13, 949 P.2d 1291 (1997) (citing Bennett v. Hardy, 113 Wn.2d 912, 920-21, 784 P.2d 1258 (1990)).
¶31 The employees are within the class of persons for whose benefit the comparable worth statutes were enacted. Courts look to statutory language to determine whether plaintiffs are members of the protected class. Tyner v. Dep’t of Soc. & Health Servs., 141 Wn.2d 68, 78, 1 P.3d 1148 (2000) (quoting Schooley v. Pinch’s Deli Mkt., Inc., 134 Wn.2d 468, 475, 951 P.2d 749 (1998)). RCW 41.06.155 requires achievement of comparable worth for the “jobs of all employees under this chapter.” RCW 41.06.070(1) lists employees who are not subject to the provisions of chapter 41.06 RCW. This list does not include PSNs and PSAs; thus, they are “employees under this chapter” and within the class of persons for whose benefit the comparable worth statutes were enacted.
¶32 However, legislative intent does not support the remedy the employees seek here, and implying a judicial remedy is inconsistent with the underlying purpose of the statutes. The legislature enacted the comparable worth statutes to protect its prerogative in setting state employees’ compensation. The legislature enacted RCW 41.06.155, providing a 10-year process for achieving comparable worth, subsequent to a 1982 Title VII suit by a group of state employees. Laws of 1983, 1st Ex. Sess., ch. 75, § 6; see Am. Fed’n of State, County, & Mun. Emps. v. Washington, 578 E Supp. 846 (W.D. Wash. 1983). The litigation continued, so, in 1985, the legislature provided more than $40 million for settlement of the Title VII suit and implementation of statutory comparable worth. Laws of 1985,1st Ex. Sess., ch. [31]*316, § 702. Thus, the legislature enacted the comparable worth statute and appropriated funds for its implementation in order to settle and avoid, not encourage, litigation.
¶33 Moreover, the legislature limited the time frame for implementing comparable worth, indicating that it did not intend to provide an ongoing remedy. RCW 41.06.155 states that “[c]omparable worth . . . shall be fully achieved not later than June 30, 1993.” Since 1993, the State has not made any comparable worth adjustments.
¶34 Because the legislature enacted the comparable worth statutes to avoid litigation and because it limited the time frame for implementing comparable worth, legislative intent does not support an ongoing private cause of action under the comparable worth statutes.
B. Relief
¶35 Even if the comparable worth statutes did create a private cause of action, the employees cannot show that they are entitled to relief. In Washington Public Employees Ass’n, we denied employees relief under a civil service statute because they failed to prove that all the conditions in the statute were met. 127 Wn. App. at 262. There, the employees argued that they had been deprived of equal pay for equal work and sought an order requiring the Personnel Resources Board to adopt a single salary schedule for employees in general government and higher education under former RCW 41.06.150(14) (2002).10 Wash. Pub. Emps. Ass’n, 127 Wn. App. at 261. But, to attain that relief, the employees had to show (1) what schedule the Personnel Resources Board would have adopted, (2) that the director [32]*32of financial management would have approved the adopted schedule, (3) that the governor would have sent the adopted schedule to the legislature, and (4) that the legislature would have implemented it. Wash. Pub. Emps. Ass’n, 127 Wn. App. 261-62. The employees could not prove that any of those conditions would have been met; accordingly, this court denied them relief under former RCW 41.06.150(14).
¶36 Similarly, here, the employees cannot show that all of the conditions necessary to adopt an increased salary schedule under former RCW 41.06.133(10) would have been met. In order to receive increased compensation under the comparable worth increase under former RCW 41.06-.133(10), the employees must show that (1) the director of Personnel11 would have found the increase necessary, (2) the director of financial management would have approved the increase, and (3) the legislature would have funded the increase. See Wash. Pub. Emps. Ass’n, 127 Wn. App. at 262; Teamsters, Chauffers, Warehouse & Helpers Union Local No. 313 v. Dep’t of Corr., 119 Wn. App. 478, 479-80, 81 P.3d 875 (2003). The employees have not done so here.
¶37 The dissent argues that Washington Public Employees Ass’n is partially distinguishable because the director of Personnel does not have flexibility in setting pay under the comparable worth scheme. But, the statute at issue in Washington Public Employees Ass’n contains the same language as former RCW 41.06.133(10): “the rates in the salary schedules or plans shall be increased if necessary to attain comparable worth under an implementation plan under RCW 41.06.155.” 127 Wn. App. at 261 n.1. In both cases, the employees argued that this language means the Personnel Resources Board or the directors of Personnel and financial management had to adopt equal pay scales for comparable work. But, we rejected this contention in [33]*33Washington Public Employees Ass’n and we uphold that precedent here.12
III. Collateral Estoppel
¶38 The State also argues that the trial court erred by-concluding that the State-was collaterally estopped from relitigating the issues from a previous case involving classification of PSNs and PSAs. Because both cases involved issues regarding the employees’ duties and work environment, we hold that the trial court did not err.
¶39 The trial court concluded “[t]hat the findings of fact and conclusions of law entered in the action brought in Thurston County Superior Court Cause Number 80-2--00966-1 . . . are established as a matter of law and the State is collaterally estopped from relitigating those issues based upon the record therein.” XI CP at 2170-71 (Conclusion of Law 25).
¶40 In its 1983 decision, the Thurston County Superior Court reversed the Personnel Board and ordered the forensic nurses and attendants reallocated back to PSN and PSA job classifications. The court found that the “duties and responsibilities of the staff of the mentally ill offender programs are enhanced and are more onerous and exacting” and that the mentally ill offender units “can be best described as ‘mini prisons,’ ” requiring greater levels of security. Ex. 27, at 4.
¶41 “Collateral estoppel works to prevent relitigation of issues that were resolved in a prior proceeding.” City of Aberdeen v. Regan, 170 Wn.2d 103, 108, 239 P.3d 1102 (2010). “Collateral estoppel . . . requires ‘(1) [34]*34identical issues; (2) a final judgment on the merits; (3) the party against whom the plea is asserted must have been a party to or in privity with a party to the prior adjudication; and (4) application of the doctrine must not work an injustice on the party against whom the doctrine is to be applied.’” City of Arlington v. Cent. Puget Sound Growth Mgmt. Hr’gs Bd., 164 Wn.2d 768, 792,193 P.3d 1077 (2008) (quoting Shoemaker v. City of Bremerton, 109 Wn.2d 504, 507, 745 P.2d 858 (1987) (quoting Malland v. Dep’t of Ret. Sys., 103 Wn.2d 484, 489, 694 P.2d 16 (1985)).
¶42 The State argues that the first requirement is not met here because the prior litigation involved “the appropriate classification of positions within the State’s classification system” and “[n] either party to the instant case is arguing that the positions should be reallocated.” Appellant’s Br. at 47. Although the State is correct that neither party is challenging PSNs’ and PSAs’ classifications, some of the underlying issues in both cases are identical. In both cases, the PSNs’ and PSAs’ duties and the nature of the forensic ward were at issue. One of the employees who had worked in the forensic ward since before the first litigation testified that her duties have not changed since the time of the first litigation. Thus, the first requirement is met.
¶43 The other collateral estoppel requirements are also met. The prior litigation resulted in a final judgment on the merits. The parties for both actions are the same: nurses and attendants in the forensic wards at the state psychiatric hospitals and Personnel and DSHS. Finally, application of collateral estoppel to the issues of PSNs’ and PSAs’ duties and their work environment would not work an injustice on the State. The State does not argue that an injustice would result, and it does not contest the employees’ characterization of their duties or work environment.13 Therefore, the trial court did not err by finding that collateral estoppel applied to the facts of the previous litigation.
[35]*35TV. Attorney Fees
¶44 The State argues that the trial court erred by awarding attorney fees under both the common fund doctrine and fee-shifting statutes. Because the employees sought fees under the common fund doctrine, RCW 49-.48.030, and 42 U.S.C. § 1988 — all of which require the party to prevail, and the employees have not prevailed — we reverse the trial court’s attorney fee award.
¶45 The employees seek attorney fees on appeal under RAP 18.1, RCW 49.48.030, RCW 49.52.070, and 42 U.S.C. § 1988. We deny the employees’ request. RCW 49.48.030 and 42 U.S.C. § 1988 require a party to prevail, and the employees did not prevail on appeal. RCW 49.52.070 does not apply because the State did not act willfully.
¶46 We reverse the trial court’s verdict for the employees and its award to them of attorney fees.
Hunt, J., concurs.