JUSTICE SOUTER delivered the opinion of the Court.[fn1] [fn1]605JUSTICE SCALIA does not join Part III-B-1-b of this opinion.

Respondent Construction Laborers Pension Trust for Southern California (Plan) is a multiemployer pension trust fund established under a Trust Agreement executed in 1962. Petitioner Concrete Pipe and Products of California, Inc. (Concrete Pipe), is an employer and former contributor to the Plan that withdrew from it and was assessed "withdrawal liability" under provisions of the Employee Retirement Income Security Act of 1974 (ERISA), 29 U.S.C. § 1301-1461 (1988 ed. and Supp. III), added by the Multiemployer Pension Plan Amendments Act of 1980 (MPPAA), Pub.L. 96-364, 94 Stat. 1208. Concrete Pipe contends that the MPPAA's assessment and arbitration provisions worked to deny it procedural due process. And, although we have upheld the MPPAA against constitutional challenge under the substantive component of the Due Process Clause and the Takings Clause, Pension Benefit Guaranty Corporation v. R.A. Gray Co., 467 U.S. 717 (1984); Connolly v. Pension Benefit Guaranty Corporation, 475 U.S. 211 (1986), Concrete Pipe contends that, as applied to it, the MPPAA violates these provisions as well. We see merit in none of Concrete Pipe's contentions.

I

A pension plan like the one in issue, to which more than one employer contributes, is characteristically maintained to fulfill the terms of collective bargaining agreements. The contributions made by employers participating in such a multiemployer plan are pooled in a general fund available to pay any benefit obligation of the plan. To receive benefits, an employee participating in such a plan need not work for one employer for any particular continuous period. Because service credit is portable, employees of an employer participating in the plan may receive such credit for any work done for any participating employer. An employee obtains a vested right to secure benefits upon retirement after accruing a certain length of service for participating employers; benefits vest under the Plan in this case when an employee accumulates 10 essentially continuous years of credit. See Brief for Petitioner 28.

Multiemployer plans like the one before us have features that are beneficial in industries where

"there [is] little if any likelihood that individual employers would or could establish single-employer plans for their employees . . .[,] where there are hundreds and perhaps thousands of small employers, with countless numbers of employers going in and out of business each year, [and where] the nexus of employment has focused on the relationship of the workers to the union to which they belong, and/or the industry in which they are employed, rather than to any particular employer." Multiemployer Pension Plan Termination Insurance Program: Hearings before the Subcommittee on Oversight of the House Committee on Ways and Means, 96th Cong., 1st Sess., 50 (1979) (statement of Robert A. Georgine, Chairman, National Coordinating Committee for Multiemployer Plans).

Multiemployer plans provide the participating employers with such labor market benefits as the opportunity to offer a pension program (a significant part of the covered employees' compensation package) with cost and risk-sharing mechanisms advantageous to the employer. The plans, in consequence, help ensure that each participating employer will have access to a trained labor force whose members are able to move from one employer and one job to another without losing service credit toward pension benefits. See 29 C.F.R. § 2530.210(c)(1) (1991); accord, Washington Star Co. v. International Typographical Union Negotiated Pension Plan, 582 F. Supp. 301, 304 (DC 1983).

Since the enactment of ERISA in 1974, the Plan has been subject to the provisions of the statute as a "defined benefit plan." Such a plan is one that does not qualify as an "'individual account plan' or 'defined contribution plan,'" which provide, among other things, for an individual account for each covered employee and for benefits based solely upon the amount contributed to the covered employee's account. See 29 U.S.C. § 1002(35), 1002(34), 1002(7). Concrete Pipe has not challenged the determination that the Plan falls within the statutory definition of defined benefit plan, and no issue as to that is before the Court.

A

We have canvassed the history of ERISA and the MPPAA before. See Pension Benefit Guaranty Corporation v. R.A. Gray Co., supra; (1984); Connolly v. Pension Benefit Guaranty Corporation, supra. ERISA was designed "to ensure that employees and their beneficiaries would not be deprived of anticipated retirement benefits by the termination of pension plans before sufficient funds have been accumulated in [them]. . . . Congress wanted to guarantee that, if a worker has been promised a defined pension benefit upon retirement — and if he has fulfilled whatever conditions are required to obtain a vested benefit — he will actually receive it." Id., at 214 (citations and internal quotation marks omitted). As enacted in 1974, ERISA created the Pension Benefit Guarantee Corporation (PBGC) to administer and enforce a pension plan termination insurance program, to which contributors to both single-member and multiemployer plans were required to pay insurance premiums. 29 U.S.C. § 1302(a), 1306 (1988 ed. and Supp. III). Under the terms of the statute as originally enacted, the guarantee of basic benefits by multiemployer plans that terminated was not to be mandatory until 1978, and for terminations prior to that time, any guarantee of benefits upon plan termination was discretionary with PBGC. 29 U.S.C. § 1381(c) (2)(4) (1976 ed.). If PBGC did choose to extend a guarantee when a multiemployer plan terminated with insufficient assets to pay promised benefits, an employer that had contributed to the plan in the five preceding years was liable to PBGC for the shortfall in proportion to its share of contributions during that 5-year period, up to 30 percent of the employer's net worth. 29 U.S.C. § 1362(b), 1364 (1976 ed.). "In other words, any employer withdrawing from a multiemployer plan was subject to a contingent liability that was dependent upon the plan's termination in the next five years and the PBGC's decision to exercise its discretion and pay guaranteed benefits." Gray, 467 U.S., at 721.

"As the date for mandatory coverage of multiemployer plans approached, Congress became concerned that a significant number of plans were experiencing extreme financial hardship." Ibid. Indeed, the possibility of liability upon termination of a plan created an incentive for employers to withdraw from weak multiemployer plans. Connolly, 475 U.S., at 215. The consequent risk to the insurance system was unacceptable to Congress, which, in 1978, postponed the mandatory guarantee pending preparation by the PBGC of a report "analyzing the problems of multiemployer plans and recommending possible solutions." Ibid. PBGC issued that report on July 1, 1978. Pension Benefit Guaranty Corporation, Multiemployer Study Required by P.L. 95-214 (1978). "To alleviate the problem of employer withdrawals, the PBGC suggested new rules under which a withdrawing employer would be required to pay whatever share of the plan's unfunded liabilities was attributable to that employer's participation." Connolly, 475 U.S., at 216 (citation and internal quotation marks omitted).

Congress ultimately agreed, see id., at 217, and passed the MPPAA, which was signed into law by the President on September 26, 1980. Under certain provisions of the MPPAA (which when enacted had an effective date of April 29, 1980, 29 U.S.C. § 1461(e)(2)(A) (1976 ed., Supp. V)), if an employer withdraws from a multiemployer plan, it incurs "withdrawal liability" in the form of "a fixed and certain debt to the pension plan." Gray, supra, at 725. An employer's withdrawal liability is its "proportionate share of the plan's 'unfunded vested benefits,'" that is, "the difference between the present value of vested benefits" (benefits that are currently being paid to retirees and that will be paid in the future to covered employees who have already completed some specified period of service, 29 U.S.C. § 1053) "and the current value of the plan's assets. 29 U.S.C. § 1381, 1391." Gray, supra, at 725.

B

The MPPAA provides the procedure for calculating and assessing withdrawal liability. The plan's actuary, who is subject to regulatory and professional standards, 29 U.S.C. § 1241, 1242; 26 U.S.C. § 7701(a)(35), must determine the present value of the plan's liability for vested benefits. In the absence of regulations promulgated by the PBGC, the actuary must employ "actuarial assumptions and methods which, in the aggregate, are reasonable (taking into account the experience of the plan and reasonable expectations) and which, in combination, offer the actuary's best estimate of anticipated experience under the plan." 29 U.S.C. § 1393(a)(1). The assumptions must cover such matters as mortality of covered employees, likelihood of benefits vesting, and, importantly, future interest rates. After settling the present value of vested benefits, the actuary calculates the unfunded portion by deducting the value of the plan's assets. § 1393(c).

In order to determine a particular employer's withdrawal liability, the unfunded vested liability is allocated under one of several methods provided by law. § 1391. In this case, the Plan used the presumptive method of § 1391(b), which bases withdrawal liability on the proportion of total employer contributions to the plan made by the withdrawing employer during certain 5-year periods. See §§ 1391(b)(2)(E)ii, (b)(3)(B), (b)(4)(D)(ii). In essence, the withdrawal liability imposes on the withdrawing employer a share of the unfunded vested liability proportional to the employer's share of contributions to the plan during the years of its participation.

Withdrawal liability is assessed in a notification by the "plan sponsor" (here the trustees, see § 1301(a)(10)(A)) and a demand for payment. § 1399(b). The statute requires notification and demand to be made "[a]s soon as practicable after an employer's complete or partial withdrawal." § 1399(b)(1). A "complete withdrawal"

"occurs when an employer —

"(1) Permanently ceases to have an obligation to contribute under the plan, or

"(2) permanently ceases all covered operations under the plan. § 1383(a).

"[T]he date of a complete withdrawal is the date of the cessation of the obligation to contribute or the cessation of covered operations." § 1383(e).

The statute provides that, if an employer objects after notice and demand for withdrawal liability, and the parties cannot resolve the dispute, § 1399(b)(2), it shall be referred to arbitration. See § 1401(a)(1). Two presumptions may attend the arbitration. First, "any determination made by a plan sponsor under [ 29 U.S.C. § 1381-1399 and 405 (1988 ed. and Supp. III)] is presumed correct unless the party contesting the determination shows by a preponderance of the evidence that the determination was unreasonable or clearly erroneous." 29 U.S.C. § 1401(a)(3)(A). Second, the sponsor's calculation of a plan's unfunded vested benefits

"is presumed correct unless a party contesting the determination shows by a preponderance of evidence that —

"(i) the actuarial assumptions and methods used in the determination were, in the aggregate, unreasonable (taking into account the experience of the plan and reasonable expectations), or

"(ii) the plan's actuary made a significant error in applying the actuarial assumptions or methods." § 1401(a)(3)(B).

The statute provides for judicial review of the arbitrator's decision by an action in the district court to enforce, vacate, or modify the award. See § 1401(b)(2). In any such action "there shall be a presumption, rebuttable only by a clear preponderance of the evidence, that the findings of fact made by the arbitrator were correct." § 1401(c).

II

The parties to the Trust Agreement creating the Plan in 1962 are the Southern California District Council of Laborers (Laborers) and three associations of contractors, the Building Industry of California, Inc., the Engineering Contractors Association, and the Southern California Contractors Association, Inc. App. 75, ¶ 6 (stipulation of facts filed in the District Court). Under § 302(c)(5)(B) of the Labor Management Relations Act, 1947 (LMRA), 29 U.S.C. § 186(c)(5)(B), when a union participates in management of a plan permitted by the LMRA, the plan must be administered jointly by representatives of labor and management. Accordingly, half of the Plan's trustees are selected by the Laborers, and half by these contractors' associations. Concrete Pipe has never been a member of any of the contractors' associations that are parties to the Trust Agreement.

In 1976, Concrete Pipe, which is a wholly owned subsidiary of Concrete Pipe and Products Co., Inc., purchased certain assets of another company, Cen-Vi-Ro, including a concrete pipe manufacturing plant near Shafter, California, which Concrete Pipe continued to operate much as Cen-Vi-Ro had done. Cen-Vi-Ro had collective bargaining agreements with several unions including the Laborers, and Concrete Pipe abided by the agreement with the latter by contributing to the Plan at a specified rate for each hour worked by a covered employee. In 1978, Concrete Pipe negotiated a new 3-year contract with the Laborers that called for continuing contributions to be made to the Plan based on hours worked by covered employees in the collective bargaining unit. The collective bargaining agreement specified that it would remain in effect until June 30, 1981, and thereafter from year to year unless either Concrete Pipe or the Laborers gave notice of a desire to renegotiate or terminate it. "'Such written notice [was to] be given at least sixty (60) days prior to June 30 . . ., [and if] no agreement [was] reached by June 30 . . ., the Employer or the [Laborers might] thereafter give written notice to the other that on a specified date [at least] fifteen (15) days [thereafter], the Agreement [should] be considered terminated.'" App. 76.

In August, 1979, Concrete Pipe stopped production at the Shafter facility. Although the details do not matter here, by October, 1979, work by employees covered by the agreement with the Laborers had virtually ceased, and Concrete Pipe eventually stopped making contributions to the Plan. In the spring of 1981, Concrete Pipe and the Laborers each sent the other a timely notice of a desire to renegotiate the collective bargaining agreement. Concrete Pipe subsequently bargained to an impasse and, on November 30, 1981, sent the Laborers a letter withdrawing recognition of that union as an employee representative and giving notice of intent to terminate the 1978 collective bargaining agreement. At about the same time, however, in November, 1981, Concrete Pipe reopened the Shafter plant to produce 7,000 tons of concrete pipe needed to fill two orders for which it had successfully bid. It hired employees in classifications covered by its prior agreement with the Laborers, but did not contribute to the Plan for their work.

In January, 1982, the Plan notified Concrete Pipe of withdrawal liability claimed to amount to $268,168.81. See id., at 89-94. Although the demand letter did not specify the date on which the Plan contended that "complete withdrawal" from it had taken place, it referred to the failure of Concrete Pipe to make contributions to the Plan since February, 1981, and stated that "[w]e are further advised that you have not signed a renewal of a collective bargaining agreement obligating you to continue contributions to the Plan on behalf of the Construction laborers currently in your employ." Id., at 90.

The Plan filed suit seeking the assessed withdrawal liability. Concrete Pipe countersued to bar collection, contending that "complete withdrawal" had occurred when operations at the Shafter plant ceased in August, 1979, a date prior to the effective date of the MPPAA, and challenging the MPPAA on constitutional grounds. These cases were consolidated in the United States District Court for the Central District of California, which sua sponte ordered the parties to arbitrate the issue of whether withdrawal occurred prior to the effective date of the MPPAA.

The arbitration took place in two phases. In the first, the arbitrator determined that Concrete Pipe had not withdrawn from the Plan prior to the effective date of the MPPAA. App. 216. In the second phase, explicitly applying the presumption of 29 U.S.C. § 1401(a)(3)(B), the arbitrator found that Concrete Pipe had failed to meet its burden of showing the actuarial assumptions and methods to be unreasonable in the aggregate. App. 400. For reasons not at issue here, the arbitrator did rule partially in Concrete Pipe's favor, and reduced the withdrawal liability from $268,168.81 to $190,465.57.

Concrete Pipe then filed a third action in the District Court, to set aside or modify the arbitrator's decision, and again raised its constitutional challenge. Id., at 406. The District Court treated Concrete Pipe's subsequent motion for summary judgment as a petition to vacate the arbitrator's award, which it denied, and granted a motion by the Plan to confirm the award. Construction Laborers Pension Trust for Southern California v. Cen-Vi-Ro Concrete Pipe and Products, CV-82-5184HLH (CD Cal., July 5, 1989), App. 416-425. On Concrete Pipe's appeal, the judgment of the District Court was affirmed. Board of Trustees of Construction Laborers Pension Trust for Southern California v. Concrete Pipe and Products of California, Inc., 936 F.2d 576 (CA9 1991), App. 431-432, judgt. order reported at 936 F.2d 576. We granted certiorari limited to two questions presented, which are set out in the margin. 504 U.S. 940 (1992).

III

Concrete Pipe challenges the assessment of withdrawal liability on several grounds, the first being that, by placing determination of withdrawal liability in the trustees, subject to the presumptions provided by § 1401, the MPPAA is unconstitutional because it denies Concrete Pipe an impartial adjudicator. This is not the first time this legal question has been before the Court. See Pension Benefit Guaranty Corporation v. Yahn McDonnell, Inc., 481 U.S. 735 (1987), aff'g by an equally divided Court United Retail Wholesale Employees Teamsters Union Local No. 115 Pension Plan v. Yahn McDonnell, Inc., 787 F.2d 128 (CA3 1986).

A

1

Concrete Pipe and its amici point to several potential sources of trustee bias toward imposing the greatest possible withdrawal liability. The one they emphasize most strongly has roots in the fact that "all of the trustees, including those selected by employers, are fiduciaries of the fund, 29 U.S.C. § 1002(21)([A]), and thus owe an exclusive duty to the fund." Id., at 139 (emphasis omitted). As we said in another case discussing employee benefit pension plans permitted under LMRA:

"Under principles of equity, a trustee bears an unwavering duty of complete loyalty to the beneficiary of the trust, to the exclusion of the interests of all other parties. To deter the trustee from all temptation and to prevent any possible injury to the beneficiary, the rule against a trustee dividing his loyalties must be enforced with 'uncompromising rigidity.'

* * * *

"In sum, the duty of the management-appointed trustee of an employee benefit fund under § 302(c)(5) is directly antithetical to that of an agent of the appointing party. . . . ERISA essentially codified the strict fiduciary standards that a § 302(c)(5) trustee must meet. [Title 29 U.S.C. § 1104(a)(1)] requires a trustee to 'discharge his duties . . . solely in the interest of the participants [ i.e., covered employees] and beneficiaries.'" NLRB v. Amax Coal Co., 453 U.S. 322, 329-332 (1981) (citations omitted; and footnote omitted).

The resulting tug away from the interest of the employer is fueled by the threat of personal liability for any breach of the trustees' fiduciary responsibilities, obligations, or duties, 29 U.S.C. § 1109, which may be enforced by civil actions brought by the Secretary of Labor or any covered employee or beneficiary of the plan. § 1132(a)(2).

The trustees could act in a biased fashion for several reasons. The most obvious would be in attempting to maximize assets available for the beneficiaries of the trust by making findings to enhance withdrawal liability. The next would not be so selfless, for if existing underfunding was the consequence of prior decisions of the trustees, those decisions could, if not offset, leave the trustees open to personal liability. See Brief for American Trucking Associations, Inc., as Amicus Curiae 9. A [risk] of bias may also inhere in the mere fact that, fiduciary obligations aside, the trustees are appointed by the unions and by employers. Union trustees may be thought to have incentives, unrelated to the question of withdrawal, to impose greater, rather than lesser, withdrawal liability. Employer trustees may be responsive to concerns of those employers who continue to contribute, whose future burdens may be reduced by high withdrawal liability, and whose competitive position may be enhanced to boot. See Brief for Midwest Motor Express, Inc., et al. as Amici Curiae 8, citing Note, Trading Fairness for Efficiency: Constitutionality of the Dispute Resolution Procedures of the Multiemployer Pension Plan Amendments Act of 1980, 71 Geo.L.J. 161, 168 (1982).

As against these supposed threats to the trustees' neutrality, due process requires a "neutral and detached judge in the first instance," Ward v. Village of Monroeville, 409 U.S. 57, 61-62 (1972), and the command is no different when a legislature delegates adjudicative functions to a private party, see Schweiker v. McClure, 456 U.S. 188, 195 (1982). "That officers acting in a judicial or quasi-judicial capacity are disqualified by their interest in the controversy to be decided is, of course, the general rule." Tumey v. Ohio, 273 U.S. 510, 522 (1927). Before one may be deprived of a protected interest, whether in a criminal or civil setting, see Marshall v. Jerrico, Inc., 446 U.S. 238, 242, and n. 2 (1980), one is entitled as a matter of due process of law to an adjudicator who is not in a situation "'which would offer a possible temptation to the average man as a judge . . . which might lead him not to hold the balance nice, clear and true. . . .'" Ward, supra, at 60 (quoting Tumey, supra, at 532). Even appeal and a trial de novo will not cure a failure to provide a neutral and detached adjudicator. 409 U.S., at 61.

"[J]ustice," indeed, "must satisfy the appearance of justice, and this stringent rule may sometimes bar trial [even] by judges who have no actual bias and who would do their very best to weigh the scales of justice equally between contending parties." Marshall v. Jerrico, Inc., supra, at 243 (citations and internal quotation marks omitted). This, too, is no less true where a private party is given statutory authority to adjudicate a dispute, and we will assume that the [possibility] of bias, if only that stemming from the trustees' statutory role and fiduciary obligation, would suffice to bar the trustees from serving as adjudicators of Concrete Pipe's withdrawal liability.

2

The assumption does not win the case for Concrete Pipe, however, for a further strand of governing law has to be applied. Not all determinations affecting liability are adjudicative, and the "'rigid requirements' . . . designed for officials performing judicial or quasi-judicial functions, are not applicable to those acting in a prosecutorial or plaintiff-like capacity." 446 U.S., at 248. Where an initial determination is made by a party acting in an enforcement capacity, due process may be satisfied by providing for a neutral adjudicator to "conduct a de novo review of all factual and legal issues." Cf. id., at 245; see also id., at 247-248, and n. 9; cf. Withrow v. Larkin, 421 U.S. 35, 58 (1975) ("Clearly, if the initial view of the facts based on the evidence derived from nonadversarial processes as a practical or legal matter foreclosed fair and effective consideration at a subsequent adversary hearing leading to ultimate decision, a substantial due process question would be raised").

The distinction between adjudication and enforcement disposes of the claim that the assumed bias or appearance of bias in the trustees' initial determination of withdrawal liability alone violates the Due Process Clause, much as it did the similar claim in Marshall v. Jerrico. Although we were faced there with a federal agency administrator who determined violations of a child labor law and assessed penalties under the statute, we concluded that the administrator could not be held to the high standards required of those "whose duty it is to make the final decision and whose impartiality serves as the ultimate guarantee of a fair and meaningful proceeding in our constitutional regime." 446 U.S., at 250. Of the administrator there we said "He is not a judge. He performs no judicial or quasi-judicial functions. He hears no witnesses and rules on no disputed factual or legal questions. The function of assessing a violation is akin to that of a prosecutor or civil plaintiff." Id., at 247.

This analysis applies with equal force to the trustees, who, we find, act only in an enforcement capacity. The statute requires the plan sponsor, here the trustees, to notify the employer of the amount of withdrawal liability and to demand payment, 29 U.S.C. § 1399(b)(1), actions that bear the hallmark of an assessment, not an adjudication. The trustees are not required to hold a hearing, to examine witnesses, or to adjudicate the disputes of contending parties on matters of fact or law. In Marshall, we observed that an employer "except[ing] to a penalty . . . is entitled to a de novo hearing before an administrative law judge." 446 U.S., at 247, and we concluded that this latter proceeding was the "initial adjudication," id., at 247, n. 9. Likewise, here we conclude that the first adjudication is the proceeding that occurs before the arbitrator, not the trustees' initial determination of liability.

B

This does not end our inquiry, however, for Concrete Pipe goes on to argue that the statutory presumptions [preserve] the trustees' bias by limiting the arbitrator's autonomy to determine withdrawal liability, and thereby work to deny the employer a fair adjudication.

1

Under the first provision at issue here, "any determination made by the plan sponsor under [ 29 U.S.C. § 1381-1399 and 1405] is presumed correct unless the party contesting the determination shows by a preponderance of the evidence that the determination was unreasonable or clearly erroneous." 29 U.S.C. § 1401(a)(3)(A). Concrete Pipe argues that this presumption denied it an impartial adjudicator on the issue of its withdrawal date, thus raising a constitutional question on which the Courts of Appeals have divided.

The parties apparently agree that this presumption applies only to factual determinations, see Reply Brief for Petitioner 17; Brief for Respondent 24 (deferring to brief for the PBGC as amicus curiae); Brief for Pension Benefit Guaranty Corporation as Amicus Curiae 10, and n. 11, and this position is consistent with a PBGC regulation requiring the arbitrator, "[i]n reaching his decision, [to] follow applicable law, as embodied in statutes, regulations, court decisions, interpretations of the agencies charged with the enforcement of the Act, and other pertinent authorities," 29 C.F.R. § 2641.4(a)(1) (1992). We will assume for purposes of this case that the regulation reflects a sound reading of the statute.

a

It is clear that the presumption favoring determinations of the plan sponsor shifts a burden of proof or persuasion to the employer. The hard question is what the employer must show under the statute to rebut the plan sponsor's factual determinations, that is, how and to what degree of probability the employer must persuade the arbitrator that the sponsor was wrong. The question is hard, because the statutory text refers to three different concepts in identifying this burden: "preponderance," ["clearly erroneous,"] and ["unreasonable."]

The burden of showing something by a "preponderance of the evidence," the most common standard in the civil law, "simply requires the trier of fact "to believe that the existence of a fact is more probable than its nonexistence before [he] may find in favor of the party who has the burden to persuade the judge of the fact's existence." In re Winship, 397 U.S. 358, 371-372 (1970) (Harlan, J., concurring) (brackets in original) (citation omitted). "A finding is "clearly erroneous" when, although there is evidence to support it, the reviewing [body], on the entire evidence, is left with the definite and firm conviction that a mistake has been committed." United States v. United States Gypsum Co., 333 U.S. 364, 395 (1948). A showing of "unreasonableness" would require even greater certainty of error on the part of a reviewing body. See, e.g., Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 252 (1986).

In creating the presumption at issue, these terms are combined in a very strange way. As our descriptions indicate, the first, "preponderance," is customarily used to prescribe one possible burden or standard of proof before a trier of fact in the first instance, as when the proponent of a proposition loses unless he proves a contested proposition by a preponderance of the evidence. The term thus belongs in the same category with "clear and convincing" and "beyond a reasonable doubt," which are also used to prescribe standards of proof (but when greater [degrees of certainty] are thought necessary). Before any such burden can be satisfied in the first instance, the factfinder must evaluate the raw evidence, finding it to be sufficiently reliable and sufficiently probative to demonstrate the truth of the asserted proposition with the requisite degree of certainty.

The second and third terms differ from the first in an important way. They are customarily used to describe not a degree of certainty that some fact has been proven in the first instance, but a [degree of certainty] that a factfinder in the first instance made a mistake in concluding that a fact had been proven under the applicable standard of proof. They are, in other words, standards of review, and they are normally applied by reviewing courts to determinations of fact made at trial by courts that have made those determinations in an adjudicatory capacity (unlike the trustees here). See, e.g., Fed. Rule Civ. Proc. 52(a). As the terms readily indicate, a reviewing body characteristically examines prior findings in such a way as to give the original factfinder's conclusions of fact some degree of deference. This makes sense because, in many circumstances, the costs of providing for duplicative proceedings are thought to outweigh the benefits (the second would render the first ultimately useless), and because, in the usual case, the factfinder is in a better position to make judgments about the reliability of some forms of evidence than a reviewing body acting solely on the basis of a written record of that evidence. Evaluation of the credibility of a live witness is the most obvious example.

Thus, review under the "clearly erroneous" standard is significantly deferential, requiring a "definite and firm conviction that a mistake has been committed." And application of a reasonableness standard is even more deferential than that, requiring the reviewer to sustain a finding of fact unless it is so unlikely that no reasonable person would find it to be true, to whatever the required degree of proof.

The strangeness in the statutory language creating the first presumption arises from the combination of terms from the first category (burdens of proof) with those from the second (standards of review). It is true, of course, that this apparent [confusion] of categories may have resulted from the [hybrid] nature of the arbitrator's proceeding in which it is supposed to be applied. The arbitrator here does not function simply as a reviewing body in the classic sense, for he is not only obliged to enquire into the soundness of the sponsor's determinations when they are challenged, but may receive new evidence in the course of his review and adopt his own conclusions of fact. He may conduct proceedings in the same manner and with the same powers as an arbitrator may do under Title 9 of the United States Code, see 29 U.S.C. § 1401(b)(3), being authorized, for example, to hear (indeed to subpoena) witnesses and to take evidence. See 9 U.S.C. § 7; 29 U.S.C. § 1401(b) (3) (making specific reference to subpoena power). He is, then, a reviewing body (as is clear from his obligation, absent a contrary showing, to deem certain determinations by the plan sponsor correct), but a reviewing body invested with the further powers of a finder of fact (as is clear from his power to take evidence in the course of his review and from the presumption of correctness that a district court is bound to give his "findings of fact," § 1401(c)). The arbitrator may thus provide a dual sort of trial and review, ultimately empowered to draw his own conclusions, and it would make sense to describe his different functions respectively by the language of trial and the language of review.

It does not, however, make sense to use the language of trial and the language of review as the statute does, for the statute does not refer to different arbitrator's functions in language appropriate to each; it refers, rather, to one single conclusion that must be drawn about a determination previously made by a plan sponsor. By its terms, the statute purports to provide a standard for reviewing the sponsor's findings, and it defines the nature of the conclusion the arbitrator must draw by using a combination of terms that are categorically ill-matched. They are also inconsistent with each other on any reading. As used here, as distinct from its more usual context, the statutory phrase authorizing the arbitrator to reject a factual conclusion upon proof by a "preponderance" implies review of the sponsor's determination on the basis of the record, supplemented by any new evidence, for simple error. If this statutory phrase were given effect, and the arbitrator concluded from a review of the record and of new evidence that a finding of fact was more probably wrong than not, it would be rejected, and a different finding might be substituted. On the other hand, requiring a showing that the sponsor's determination was "clearly erroneous" or "unreasonable" would grant the plan sponsor's factual findings a great deal of deference. But to say in this context that one must demonstrate that something is more probably clearly erroneous than not or more probably than not unreasonable is [meaningless.] One might as intelligibly say, in a trial court, that a criminal prosecutor is bound to prove each element probably true beyond a reasonable doubt. The statute is thus [incoherent with respect to the degree of [probability] of error required of the employer to overcome a factual conclusion made by the plan sponsor.]

The proper response to this [incomprehensibility] is obviously important in deciding this case. If it permitted an employer to rebut the plan sponsor's factual conclusions by a preponderance, merely placing a burden of persuasion on the employer, and permitting adjudication of the facts by the arbitrator without affording deference to the plan sponsor's determinations, the provision would be constitutionally unremarkable. For although we have observed that, "[w]here the burden of proof lies on a given issue is, of course, rarely without consequence, and frequently may be dispositive to the outcome of the litigation or application, . . . [o]utside the criminal law area, where special concerns attend, the locus of the burden of persuasion is normally not an issue of federal constitutional moment." Lavine v. Milne, 424 U.S. 577, 585 (1976) (footnote omitted). Concrete Pipe points to no special interest that would distinguish this from the normal case. It is indeed entirely sensible to burden the party more likely to have information relevant to the facts about its withdrawal from the Plan with the obligation to demonstrate that facts treated by the Plan as amounting to a withdrawal did not occur as alleged. Such was the rule at common law. W. Bailey, Onus Probandi 1 (1886) (citing Powell on Evidence 167-171) ("In every case, the onus probandi lies on the party who wishes to support his case by a particular fact which lies more peculiarly within his knowledge, or of which he is supposed to be cognizant").

On the other hand, if the employer were required to show the trustees' findings to be either "unreasonable or clearly erroneous," [there would be a substantial question of procedural fairness under the Due Process Clause.] In essence, the arbitrator provided for by the statute would be required to accept the plan sponsor's findings, even if they were probably incorrect, absent a showing at least sufficient to instill a definite or firm conviction that a mistake had been made. Cf. Withrow v. Larkin, 421 U.S., at 58. In light of our assumption of possible bias, the employer would seem to be deprived thereby of the [impartial] adjudication in the first instance to which it is entitled under the Due Process Clause. See supra, at 617-618.

b

Having found the statutory language itself incoherent, we turn, as we would in the usual case of textual ambiguity, to the legislative purpose as revealed by the history of the statute, for such light as it may shed. Unsurprisingly, we have found no direct discussion in the legislative history of the degree of certainty on the part of the arbitrator required for the employer to overcome the sponsor's factual conclusions. The Report of the House Committee on Education and Labor on the bill that became the MPPAA describes the presumption as applying to "a determination of withdrawal liability by a plan," and lumps it together with the statutory presumption, discussed below, that applies to the choice of actuarial assumptions and methods. See H.R. Rep. No. 96-869, pt. 1, p. 86 (1980); 29 U.S.C. § 1401(a)(3)(B). The Report states that

"[t]hese rules are necessary in order to ensure the enforceability of employer liability. In the absence of these presumptions, employers could effectively nullify their obligation by refusing to pay and forcing the plan sponsor to prove every element involved in making an actuarial determination. The committee believes it is extremely important that a withdrawn employer begin making the annual payments even though the period of years for which payments must continue will be based on the actual liability allocated to the employer." H.R. Rep. 96-869, pt. 1, supra, at 86.

The only other comment that we have found in the legislative history occurs in a Report prepared by the Senate Committee on Labor and Human Resources, which first purports to speak about both statutory presumptions, but directs its brief discussion to problems unique to "technical actuarial matters." See S. 1076: The Multiemployer Pension Plan Amendments Act of 1980: Summary and Analysis of Consideration, 96th Cong., 2d Sess., 2021 (Comm. Print 1980) (hereinafter Committee Print); see also infra, at 635, and n. 20.

The legislative history thus sheds little light on the odd language chosen to describe the employer's burden. All it tells us is that the provision's purpose is to prevent the employer from "forcing the plan sponsor to prove every element involved in making an actuarial determination." Since this purpose would be served simply by placing the burden of proof as to historical fact on the employer, however light or heavy that burden may be, the legislative history does nothing to make sense of the drafter's failure to choose among the standards included in the text.

c

The only way out of the muddle is by a different rule of construction. It is a hoary one that, in a case of statutory ambiguity, "where an otherwise acceptable construction of a statute would raise serious constitutional problems, the Court will construe the statute to avoid such problems unless such construction is plainly contrary to the intent of Congress." Edward J. DeBartolo Corp. v. Florida Gulf Coast Building Construction Trades Council, 485 U.S. 568, 575 (1988). "Federal statutes are to be so construed as to avoid serious doubt of their constitutionality." 'When the validity of an act of Congress is drawn in question, and even if a serious doubt of constitutionality is raised, it is a cardinal principle that this Court will first ascertain whether a construction of the statute is fairly possible by which the question may be avoided.' Crowell v. Benson, 285 U.S. 22, 62 (1932). Machinists v. Street, 367 U.S. 740, 749-750 (1961). Cf. Parsons v. Bedford, 28 U.S. (3 Pet.) 433, 448-449 (1830) (Story, J.) (a construction that would render a statute unconstitutional should be avoided); Murray v. Schooner Charming Betsy, 6 U.S. (2 Cranch) 64, 118 (1804) (Marshall, C.J.).

Although we are faced here not with ambiguity within the usual degree, but with incoherence, we have a common obligation in each situation to resolve the uncertainty in favor of definite meaning, and the canon for resolving ambiguity applies with equal force when terminology renders a statute incoherent. In applying that canon here, we must give effect to the one conclusion clearly supported by the statutory language, that Congress intended to shift the burden of persuasion to the employer in a dispute over a sponsor's factual determination. This objective can be realized without raising serious constitutional concerns simply by construing the presumption to place the burden on the employer to disprove a challenged factual determination by a preponderance. In so construing the statute we make no pretense to have read the congressional mind to perfection. We would not, indeed, even have this problem if an argument could not obviously be made that Congress intended greater deference than the preponderance standard extends. But one could hardly call the intent clear after wondering why the preponderance standard was also included. In these circumstances, it is enough that the choice to attain coherence by obviating constitutional problems is not "plainly contrary to the intent of Congress." DeBartolo, supra, at 575.

Because the statute as we construe it does not foreclose [any factual issue] from independent consideration by the arbitrator (the presumption is, again, assumed by all to be inapplicable to issues of law), there is no constitutional infirmity in it. For the same reason, that an employer may avail itself of independent review by the concededly neutral arbitrator, we find no derivative constitutional defect infecting the further presumption that a district court must afford to an arbitrator's findings of fact. See 29 U.S.C. § 1401(c).

d

Before applying the presumption to this case, one must recognize that, in spite of Concrete Pipe's contention to the contrary, determining the date of "complete withdrawal" presents not a mere question of fact on which the arbitrator was required in the first instance to apply the § 1401(a)(3)(A) presumption, but a mixed question of fact and law. The relevant facts are about the closure of the Shafter plant (such as the intent of Concrete Pipe with respect to the plant, its expression of that intent, its activities while the plant was not operating, and the circumstances of the plant's reopening), while the question whether these facts amount to a "complete withdrawal" is one of law.

As to the truly factual issues, the arbitrator's decision fails to reveal the force with which factual conclusions by the trustees here were presumed correct, and in such a case, we would ordinarily reverse the judgment below for consideration of the extent to which the arbitrator's application of the presumption was contrary to the construction we adopt today. But two reasons (urged upon us by neither party) persuade us not to take this course: the Plan's letter to Concrete Pipe contains no statement of facts justifying the trustees' demand, and the parties entered into a factual stipulation in the District Court prior to commencing the arbitration. Because of these two circumstances, there were virtually no contested factual determinations to which the arbitrator might have deferred. And, on the one question of fact that may have been disputed, the arbitrator found, apparently in the first instance, that Concrete Pipe's intent in closing the Shafter plant had been to cease operations permanently. App. 213-214.

While we express no opinion on whether the facts in this case constitute a "complete withdrawal" within the meaning of the statute, a question not before us today, the approach taken by the arbitrator and the courts below is not inconsistent with our interpretation of the first presumption. The determination of the date of withdrawal by the arbitrator did not involve a misapplication of the statutory presumption, and it did not deprive Concrete Pipe of its right to procedural due process.

2

The second presumption at issue attends the calculation of the amount of withdrawal liability. The statute provides that, in the absence of more particular PBGC regulations, the plan is required to use "actuarial assumptions and methods which, in the aggregate, are reasonable (taking into account the experience of the plan and reasonable expectations) and which, in combination, offer the actuary's best estimate of anticipated experience under the plan." 29 U.S.C. § 1393(a)(1). The presumption in question arises under § 1401(a)(3)(B), which provides that

"the determination of a plan's unfunded vested benefits for a plan year, [is] presumed correct unless a party contesting the determination shows by a preponderance of evidence that —"

"(i) the actuarial assumptions and methods used in the determination were, in the aggregate, unreasonable (taking into account the experience of the plan and reasonable expectations), or

"(ii) the plan's actuary made a significant error in applying the actuarial assumptions or methods."

Concrete Pipe's concern is with the presumptive force of the actuarial assumptions and methods covered by subsection (i).

While this provision is like its counterpart creating the presumption as to factual determinations in placing the burden of proof on the employer, the issues implicated in applying it to the actuary's work are not the same. As the text plainly indicates, the assumptions and methods used in calculating withdrawal liability are selected in the first instance not by the trustees, but by the plan actuary. For a variety of reasons, this actuary is not, like the trustees, vulnerable to suggestions of bias or its appearance. Although plan sponsors employ them, actuaries are trained professionals subject to regulatory standards. See 29 U.S.C. § 1241, 1242; 26 U.S.C. § 7701(a)(35). The technical nature of an actuary's assumptions and methods, and the necessity for applying the same assumptions and methods in more than one context, as a practical matter limit the opportunity an actuary might otherwise have to act unfairly toward the withdrawing employer. The statutory requirement (of "actuarial assumptions and methods — which, in the aggregate, are reasonable . . .") is not unique to the withdrawal liability context, for the statute employs identical language in 29 U.S.C. § 1082(c)(3) to describe the actuarial assumptions and methods to be used in determining whether a plan has satisfied the minimum funding requirements contained in the statute. The use of the same language to describe the actuarial assumptions and methods to be used in these different contexts tends to check the actuary's discretion in each of them.

"Using different assumptions [for different purposes] could very well be attacked as presumptively unreasonable both in arbitration and on judicial review.

"[This] view that the trustees are required to act in a reasonably consistent manner greatly limits their discretion, because the use of assumptions overly favorable to the fund in one context will tend to have offsetting unfavorable consequences in other contexts. For example, the use of assumptions (such as low interest rates) that would tend to increase the fund's unfunded vested liability for withdrawal liability purposes would also make it more difficult for the plan to meet the minimum funding requirements of § 1082." United Retail Wholesale Employees Teamsters Union Local No. 115 Pension Plan v. Yahn McDonnell, Inc., 787 F.2d, at 146-147 (Seitz, J., dissenting in part).

This point is not significantly blunted by the fact that the assumptions used by the Plan in its other calculations may be "supplemented by several actuarial assumptions unique to withdrawal liability." Brief for Respondent 26. Concrete Pipe has not shown that any method or assumption unique to the calculation of withdrawal liability is so manipulable as to create a significant opportunity for bias to operate, and arguably the most important assumption (in fact, the only actuarial assumption or method that Concrete Pipe attacks in terms, see Reply Brief for Petitioner 18-20) is the critical interest rate assumption that must be used for other purposes as well.

The second major difference attending the two presumptions lies in the sense of reasonableness that must be disproven by an employer attacking the actuary's methods and assumptions, as against the reasonableness of the trustees' determinations of historical fact. Following the usual presumption of statutory interpretation, that the same term carries the same meaning whenever it appears in the same Act, see Atlantic Cleaners Dyers, Inc. v. United States, 286 U.S. 427, 433 (1932), we might expect "reasonable" in § 1401(a)(3)(B) to function here just as it did in § 1401(a)(3)(A), to denote a certain range of probability that a factual determination is correct. For several reasons, however, we think it clear that this second presumption of reasonableness functions quite differently.

First, of course, the statute does not speak in terms of disproving the reasonableness of the calculation of the employer's share of the unfunded liability, which would be the finding of future fact most obviously analogous to the findings of historical fact to which the § 1401(a)(3)(A) presumption applies. Section 1401(a)(3)(B) speaks instead of the aggregate reasonableness of the assumptions and methods employed by the actuary in calculating the dollar liability figure. Because a "method" is not "accurate" or probably "true" within some range, "reasonable" must be understood here to refer to some different kind of judgment, one that it would make sense to apply to a review of methodology as well as of assumptions. Since the methodology is a subject of technical judgment within a recognized professional discipline, it would make sense to judge the reasonableness of a method by reference to what the actuarial profession considers to be within the scope of professional acceptability in making an unfunded liability calculation. Accordingly, an employer's burden to overcome the presumption in question (by proof by a preponderance that the actuarial assumptions and methods were in the aggregate unreasonable) is simply a burden to show that the combination of methods and assumptions employed in the calculation would not have been acceptable to a reasonable actuary. In practical terms, it is a burden to show something about standard actuarial practice, not about the accuracy of a predictive calculation, even though consonance with professional standards in making the calculation might justify confidence that its results are sound.

As thus understood, the presumption in question supports no due process objection. The employer merely has a burden to show that an apparently unbiased professional, whose obligations tend to moderate any claimed inclination to come down hard on withdrawing employers, has based a calculation on a combination of methods and assumptions that falls outside the range of reasonable actuarial practice. To be sure, the burden may not be so "mere" when one considers that actuarial practice has been described as more in the nature of an "actuarial art" than a science, Keith Fulton Sons v. New England Teamsters, 762 F.2d 1137, 1143 (CA1 1985) (en banc) (internal quotation marks omitted), and that the employer's burden covers "technical actuarial matters with respect to which there are often several equally 'correct' approaches," Committee Print 20-21. But since imprecision inheres in the choice of actuarial methods and assumptions, the resulting difficulty is simply in the nature of the beast. Because it must fall on whichever party bears the burden of persuasion on such an issue, at least where the interests at stake are no more substantial than Concrete Pipe's are here, its allocation to one party or another does not raise an issue of due process. See supra, at 625-626.

IV

Concrete Pipe argues next that, as applied, the MPPAA violates substantive due process and takes Concrete Pipe's property without just compensation, both in violation of the Fifth Amendment. As to these issues, our decisions in Gray and Connolly provide the principal guidance.

A

In Gray, we upheld the MPPAA against substantive due process challenge. Unlike the employer in Gray, Concrete Pipe here has no complaint that the MPPAA has been retroactively applied by predicating liability on a withdrawal decision made before passage of the statute. To be sure, since there would be no withdrawal liability without prewithdrawal contributions to the Plan, some of which were made before the statutory enactment, some of the conduct upon which Concrete Pipe's liability rests antedates the statute. But this fact presents a far weaker premise for claiming a substantive due process violation even than the Gray employer raised, and rejection of Concrete Pipe's contention is compelled by our decisions not only in Gray, but in Usery v. Turner Elkhorn Mining Co., 428 U.S. 1 (1976), upon which the Gray Court relied.

"'It is by now well established that legislative Acts adjusting the burdens and benefits of economic life come to the Court with a presumption of constitutionality, and that the burden is on one complaining of a due process violation to establish that the legislature has acted in an arbitrary and irrational way. See, e.g., Ferguson v. Skrupa, 372 U.S. 726 (1963); Williamson v. Lee Optical Co., 348 U.S. 483, 487-488 (1955).

* * * *

"'[I]t may be that the liability imposed by the Act . . . was not anticipated at the time of actual employment. But our cases are clear that legislation readjusting rights and burdens is not unlawful solely because it upsets otherwise settled expectations. See Fleming v. Rhodes, 331 U.S. 100 (1947); Carpenter v. Wabash R. Co., 309 U.S. 23 (1940); Norman v. Baltimore Ohio R. Co., 294 U.S. 240 (1935); Home Bldg. Loan Assn. v. Blaisdell, 290 U.S. 398 (1934); Louisville Nashville R. Co. v. Mottley, 219 U.S. 467 (1911). This is true even though the effect of the legislation is to impose a new duty or liability based on past acts. See Lichter v. United States, 334 U.S. 742 (1948); Welch v. Henry, 305 U.S. 134 (1938); Funkhouser v. Preston Co., 290 U.S. 163 (1933).'" Gray, 467 U.S., at 729-730, quoting Turner Elkhorn, supra, at 15-16 (footnotes omitted).

To avoid this reasoning, Concrete Pipe relies not merely on a claim of retroactivity, but on one of irrationality. Since the company contributed to the plan for only 3 1/2 years, it argues, none of its employees had earned vested benefits through employment by Concrete Pipe at the time of its withdrawal. See Brief for Petitioner 28. Concrete Pipe argues that, consequently, no rational relationship exists between its payment of past contributions and the imposition of liability for a share of the unfunded vested benefits.

But this argument simply ignores the nature of multiemployer plans, which, as we have said above, operate by pooling contributions and liabilities. An employer's contributions are not solely for the benefit of its employees or employees who have worked for it alone. Thus, Concrete Pipe's presupposition that none of its employees had vested benefits at the time of its withdrawal may be wrong. An employee whose benefits had vested before coming to work for Concrete Pipe may have earned additional vested benefits by the subsequent covered service. Another may have had sufficient prior service credit to obtain vesting of benefits during employment at Concrete Pipe. A third may have attained vesting while working for other employers but based in part on service credits earned at Concrete Pipe.

But even if Concrete Pipe is correct, and none of its employees had earned enough service credits for entitlement to vested benefits by the time of Concrete Pipe's withdrawal, as a Concrete Pipe employee, each had earned service credits that could be built upon in future employment with any other participating employer. In determining whether the imposition of withdrawal liability is rational, then, the relevant question is not whether a withdrawing employer's employees have vested benefits, but whether an employer has contributed to the plan's probable liability by providing employees with service credits. When the withdrawing employer's liability to the plan is based on the proportion of the plan's contributions (and coincident service credits) provided by the employer during the employer's participation in the plan, the imposition of withdrawal liability is clearly rational.

It is true that, depending on the future employment of Concrete Pipe's former employees, the withdrawal liability assessed against Concrete Pipe may amount to more (or less) than the share of the Plan's liability strictly attributable to employment of covered workers at Concrete Pipe. But this possibility [was exactly what Concrete Pipe accepted when it joined the Plan.] A multiemployer plan has features of an insurance scheme in which employers spread the risk that their employees will meet the plan's vesting requirements and obtain an entitlement to benefits. A rational employer hopes that its employees will vest at a rate above the average for all employees of contributing employers, and that, in this way, it will pay less than it would have by creating a single-employer plan. But the rational employer also appreciates the foreseeable risk that circumstances may produce the opposite result. Since the MPPAA spreads the unfunded vested liability among employers in approximately the same manner that the cost would have been spread if all of the employers participating at the time of withdrawal had seen the venture through, the withdrawal liability is consistent with the risks assumed on joining a plan (however inconsistent that liability may be with the employer's hopes). In any event, under the deferential standard of review applied in substantive due process challenges to economic legislation, there is no need for mathematical precision in the fit between justification and means. See Turner Elkhorn, 428 U.S., at 19.

Concrete Pipe's substantive due process claim is not enhanced by its argument that the MPPAA imposes obligations upon it contrary to limitations on liability variously contained in the 1962 Trust Agreement, in a collective bargaining agreement between the Laborens and multiemployer associations (the "1977-1980 Laborer's Craft Master Labor Agreement"), and in an appendix to the "Southern California Master Labor Agreements in 1977-1980." Even assuming that all these provisions apply to Concrete Pipe, its argument runs against the holding in Gray that federal economic legislation, which is not subject to constraints coextensive with those imposed upon the States by the Contract Clause of Art. I, § 10 of the Federal Constitution, Gray, 467 U.S., at 733; United States Trust Co. of N.Y. v. New Jersey, 431 U.S. 1, 17, n. 13 (1977), is subject to due process review only for rationality, which, as we have said, is satisfied in the application of the MPPAA to Concrete Pipe.

Nor does the possibility that trustee decisions made "before [Concrete Pipe] entered [the Plan]" may have led to the unfunded liability alter the constitutional calculus. See Brief for Petitioner 31. Concrete Pipe's decision to enter the Plan after any such decisions were made was voluntary, and Concrete Pipe could at that time have assessed any implications for the Plan's future liability. Similarly, Concrete Pipe cannot rely on any argument based on the fact that, because it was not a member of any of the contractors' associations represented among the Plan's trustees, it had no control over decisions of the trustees after it entered the Plan that may have increased the unfunded liability. Again, Concrete Pipe could have assessed the implications for future liability of the identity of the trustees of the Plan before it decided to enter. The imposition of withdrawal liability here is rationally related to the terms of Concrete Pipe's participation in the Plan it joined, and that suffices for substantive due process scrutiny of this economic legislation.

B

Given that Concrete Pipe's due process arguments are unavailing, "it would be surprising indeed to discover" the challenged statute nonetheless violating the Takings Clause. Connolly, 475 U.S., at 223. Nor is there any violation. Following the analysis in Connolly, we begin with the contractual provisions relied upon from the Trust Agreement and the collective bargaining agreements, which we find no more helpful to Concrete Pipe than those adduced in the facial challenge brought in Connolly, as described in that opinion:

"By the express terms of the Trust Agreement and the Plan, the employer's sole obligation to the Pension Trust is to pay the contributions required by the collective bargaining agreement. The Trust Agreement clearly states that the employer's obligation for pension benefits to the employee is ended when the employer pays the appropriate contribution to the Pension Trust. This is true even though the contributions agreed upon are insufficient to pay the benefits under the Plan." Id., at 218 (citations and footnotes omitted).

Indeed, one provision of the Trust Agreement on which Concrete Pipe primarily relies is substantially identical to the one at issue in Connolly. Compare n. 22, supra, with Connolly, supra, at 218, n. 2.

We said in Connolly that

"[a]ppellants' claim of an illegal taking gains nothing from the fact that the employer in the present litigation was protected by the terms of its contract from any liability beyond the specified contributions to which it had agreed. 'Contracts, however express, cannot fetter the constitutional authority of Congress. Contracts may create rights of property, but when contracts deal with a subject matter which lies within the control of Congress, they have a congenital infirmity. Parties cannot remove their transactions from the reach of dominant constitutional power by making contracts about them.'

"If the regulatory statute is otherwise within the powers of Congress, therefore, its application may not be defeated by private contractual provisions." 475 U.S., at 223-224 (citations omitted).

Nothing has changed since these words were first written.

Following Connolly, the next step in our analysis is to subject the operative facts, including the facts of the contractual relationship, to the standards derived from our prior Takings Clause cases. See id., at 224-225. They have identified three factors with particular significance for assessing the results of the required " ad hoc, factual inquir[y] into the circumstances of each particular case." Connolly, id., at 224. The first is the nature of the governmental action. Again, our analysis in Connolly applies with equal force to the facts before us today.

"[T]he Government does not physically invade or permanently appropriate any of the employer's assets for its own use. Instead, the Act safeguards the participants in multiemployer pension plans by requiring a withdrawing employer to fund its share of the plan obligations incurred during its association with the plan. This interference with the property rights of an employer arises from a public program that adjusts the benefits and burdens of economic life to promote the common good and, under our cases, does not constitute a taking requiring Government compensation." Id., at 225.

We reject Concrete Pipe's contention that the appropriate analytical framework is the one employed in our cases dealing with permanent physical occupation or destruction of economically beneficial use of real property. See Lucas v. South Carolina Coastal Council, 505 U.S. 1003, 1015 (1992) (slip op., at 9-10). While Concrete Pipe tries to shoehorn its claim into this analysis by asserting that "[t]he property of [Concrete Pipe] which is taken, is taken in its entirety," Brief for Petitioner 37, we rejected this analysis years ago in Penn Central Transp. Co. v. New York City, 438 U.S. 104, 130-131 (1978), where we held that [a claimant's parcel of property could not first be divided into what was taken and what was left] for the purpose of demonstrating the taking of the former to be complete and hence compensable. To the extent that any portion of property is taken, that portion is always taken in its entirety; the relevant question, however, is whether the property taken is all, or only a portion of, the parcel in question. Accord, Keystone Bituminous Coal Assn. v. DeBenedictis, 480 U.S. 470, 497 (1987) ("[O]ur test for regulatory taking requires us to compare the value that has been taken from the property with the value that remains in the property, [and] one of the critical questions is determining how to define the unit of property 'whose value is to furnish the denominator of the fraction'") (citation omitted).

There is no more merit in Concrete Pipe's contention that its property is impermissibly taken "for the sole purpose of protecting the PBGC [a government body] from being forced to honor its pension insurance." Brief for Petitioner 38; see also Brief for Midwest Motor Express, Inc., et al. as Amici Curiae 12. That the solvency of a pension trust fund may ultimately redound to the benefit of the PBGC, which was set up in part to guarantee benefits in the event of plan failure, is merely incidental to the primary congressional objective of protecting covered employees and beneficiaries of pension trusts like the Plan. "[H]ere, the United States has taken nothing for its own use, and only has nullified a contractual provision limiting liability by imposing an additional obligation that is otherwise within the power of Congress to impose." Connolly, supra, at 224.

Nor is Concrete Pipe's argument about the character of the governmental action strengthened by the fact that Concrete Pipe lacked control over investment and benefit decisions that may have increased the size of the unfunded vested liability. The response to the same argument raised under the substantive Due Process Clause is appropriate here: although Concrete Pipe is not itself a member of any of the management associations that are represented among the trustees of the fund, Concrete Pipe voluntarily chose to participate in the Plan, notwithstanding this fact. See supra, at 641, and n. 26.

As to the second factor bearing on the taking determination, the severity of the economic impact of the Plan, Concrete Pipe has not shown its withdrawal liability here to be "out of proportion to its experience with the plan," 475 U.S., at 226, notwithstanding the claim that it will be required to pay out 46% of shareholder equity. As a threshold matter, the Plan contests this figure, arguing that Concrete Pipe, a wholly owned subsidiary of Concrete Pipe Products Co., Inc., was simply "formed to facilitate the purchase . . . of certain assets of Cen-Vi-Ro," Brief for Respondent 2, and that the relevant issue turns on the diminution of net worth of the parent company, not Concrete Pipe. See Tr. of Oral Arg. 29. But this dispute need not be resolved, for even assuming that Concrete Pipe has used the appropriate measure in determining the portion of net worth required to be paid out, our cases have long established that mere diminution in the value of property, however serious, is insufficient to demonstrate a taking. See, e.g., Village of Euclid v. Ambler Realty Co., 272 U.S. 365, 384 (1926) (approximately 75% diminution in value); Hadacheck v. Sebastian, 239 U.S. 394, 405 (1915) (92.5% diminution).

The final factor is the degree of interference with Concrete Pipe's "reasonable investment-backed expectations." 475 U.S., at 226. Again, Connolly controls. At the time Concrete Pipe purchased Cen-Vi-Ro and began its contributions to the Plan, [pension plans had long been subject to federal regulation,] and "'[t]hose who do business in the regulated field cannot object if the legislative scheme is buttressed by subsequent amendments to achieve the legislative end." FHA v. The Darlington, Inc., 358 U.S. 84, 91 (1958). See also Usery v. Turner Elkhorn Mining Co., 428 U.S., at 15-16, and cases cited therein." Id., at 227. Indeed, at that time, the Plan was already subject to ERISA, and a withdrawing employer faced contingent liability up to 30% of its net worth. See 29 U.S.C. § 1364 (1976 ed.); see also 29 U.S.C. § 1362(b) (1976 ed.); Connolly, supra, at 226-227; Gray, 467 U.S., at 721. Thus while Concrete Pipe argues that requiring it to pay a share of promised benefits "ignores express and bargained-for conditions on [its contractual] promises," Connolly, 475 U.S., at 235 (O'CONNOR, J., concurring), it could have had no reasonable expectation that it would not be faced with liability for promised benefits. Id., at 227 (opinion of the Court). Because "legislation readjusting rights and burdens is not unlawful solely because it upsets otherwise settled expectations . . . even though the effect of the legislation is to impose a new duty or liability based on past acts," Turner Elkhorn, 428 U.S., at 16, Concrete Pipe's [reliance on ERISA's original limitation of contingent liability to 30% of net worth] is misplaced, there being no reasonable basis to expect that the legislative ceiling would never be lifted.

"The employe[r] in the present litigation voluntarily negotiated and maintained a pension plan which was determined to be within the strictures of ERISA." Connolly, supra, at 227. In light of the relationship between Concrete Pipe and the Plan, we find no basis to conclude that Concrete Pipe is being forced to bear a burden "which, in all fairness and justice, should be borne by the public as a whole." Armstrong v. United States, 364 U.S. 40, 49 (1960).

V

Having concluded that the statutory presumptions work no deprivation of procedural due process, and that the statute, as applied to Concrete Pipe, violates no substantive constraint of the Fifth Amendment, we affirm the judgment of the Court of Appeals.

It is so ordered.