The issue before us in this case is whether Balmoral Racing Club, Inc. and Balmoral Park Trot, Inc. (collectively Bal-moral) must arbitrate a labor dispute between itself and IBEW Local 176 (Local 176) arising out of Balmoral’s brief direct employment of certain camera workers. As is normal with such cases, the answer depends on the language of the agreement — both its arbitration clause and other related provisions. In addition, in this particular instance the resolution of the arbitrability question is closely tied to the merits of the underlying dispute. That is because the central question — whether the camera workers were covered by the relevant agreement — is also the most important issue for the merits of the dispute. Our responsibility, however, is limited to the arbitrability issue, even if there are some inevitable overlaps between that and the merits. The district court found that the relevant workers fell within the scope of a collective bargaining agreement that Balmoral had with Local 176 and that the dispute is therefore arbitrable; it therefore dismissed the case entirely. We agree and accordingly affirm the district court’s judgment.
I
Balmoral has owned and run horse racing facilities in Illinois since at least 1983. It employs electricians at its race tracks who perform a variety of tasks customarily assigned to electricians. At all relevant times, the electricians at the race track were covered by a collective bargaining agreement (the Agreement) between Bal-moral and Local 176. Balmoral also uses the services of camera workers who record the races and transmit them to off-track betting parlors. For a number of years, Balmoral contracted with a separate company, World Wide Broadcasting (World Wide), to provide the personnel needed to perform the camera work; until 1996, World Wide’s camera workers were covered by a separate agreement between World Wide and Local 176, to which Bal-moral was not a party.
In September 1996, the World Wide camera workers honored the picket line of another union that was on strike at the time. Because World Wide could not provide its employees to Balmoral during this period, Balmoral terminated its contractual relationship with World Wide and announced to the union that it no longer had any use for Local 176 members for camera work; around the same time, it hired nonunion personnel to perform those tasks. Local 176 was not happy with this arrangement and began discussing alternatives with Balmoral. On September 26, Balmoral agreed to hire the former World Wide camera workers and to give them the same pay and benefits that World Wide had provided under its contract with Local 176. The workers thereafter performed both camera work and occasional general electrical work of a type normally done by “inside electrical workers” (a term defined in the IBEW Constitution, about which we have more to say later).
Balmoral and Local 176 met to try to reduce this temporary agreement to a more permanent one, but they failed. At this point, Balmoral decided once again to terminate the union camera workers who had previously worked for World Wide and to employ non-union camera workers instead.
The standstill, coupled with Balmoral’s actions, prompted Local 176 in November *4041996 to file two grievances with Balmoral pursuant to the Agreement, in which it challenged the termination of the former World Wide camera workers and the pay-practices of Balmoral with respect to these workers. The union took the position that the World Wide camera workers had come within the coverage of the Agreement, and because the Agreement contains a broad arbitration clause, its dispute with Balmo-ral was therefore subject to the full grievance procedure set forth in the Agreement, up to and including arbitration. Balmoral disagreed, claiming that the camera workers had never come within the scope of the Agreement, and for that reason it refused to arbitrate. Local 176 then filed this action seeking an order compelling arbitration of the grievances.
II
Both parties moved for summary judgment on whether the workers were covered by the Agreement, which in turn (all agreed) governed whether arbitration was required. The district court entered summary judgment for Balmoral and denied Local 176’s motion on June 24,1998. It did not rule on the merits per se; instead, the court found that a condition precedent to arbitration had not been satisfied. Under the terms of the Agreement, the International President of the IBEW had to make a formal determination concerning the jurisdictional scope of the Agreement before the camera workers’ grievance could be entertained, and no such determination had been requested or produced by the time the grievance was filed. In that procedural posture, Local 176 was not entitled to prevail in its effort to compel arbitration. Nonetheless, the district court hinted in its decision that Local 176 (which by the time of the decision had obtained the necessary ruling from the IBEW President) could refile its grievances against Balmoral.
Local 176 took the hint and filed a new action. Presented with new cross-motions for summary judgment, in an order dated March 27, 2001, the district court this time agreed with the union. The court relied on a letter from the International President that (the court was satisfied) concluded that the camera workers were covered by Local 176 and that Balmoral was required to arbitrate the disputes. Balmoral appeals that judgment.
Ill
The usual Rule 56 standard of review applies to cross-motions for summary judgment, and our review is de novo. Lac Courte Oreilles Band of Lake Superior Chippewa Indians v. Voigt, 700 F.2d 341, 349 (7th Cir.1983). To the extent that Balmoral challenges the court’s decision to grant summary judgment in favor of the union, we construe the record in the light most favorable to Balmoral. Hendricks-Robinson v. Excel Corp., 154 F.3d 685, 692 (7th Cir.1998). To the extent that Balmo-ral asserts that the court erred in refusing to grant its own motion for summary judgment, the record is evaluated in the light most favorable to Local 176. Id. Either way, summary judgment is proper if the record demonstrates that there is no genuine issue as to any material fact and that the moving party is entitled to judgment as a matter of law under the familiar standards of Fed.R.Civ.P. 56(c).
Before turning to the details of this case, it is important to clarify what is and what is not before us. Our focus is on whether this dispute is arbitrable, and to a certain degree it is about who should decide certain issues. Normally, the question of the arbitrability of a labor-management dispute is a matter to be resolved by the courts. Chicago Disk Council of Carpenters Pension Fund v. K & I Construe*405tion, Inc., 270 F.3d 1060, 1066 (7th Cir.2001). A court asked to compel arbitration must “interpret[ ] the relevant language of [the parties’] collective bargaining agreement in light of well-worn principles of labor contract interpretation, including the rule that where the agreement contains a mandatory arbitration provision, there is generally a presumption in favor of finding arbitrability.” Id. See also Local Union 1393 Int’l Bhd. of Elec. Workers v. Utilities Dist. of W. Ind. Rural Elec. Membership Coop., 167 F.3d 1181, 1183 (7th Cir.1999).
Usually it is obvious whether there is some kind of arbitration agreement between the disputing parties, and the only question relates to the scope of that agreement. See, e.g., Penn v. Ryan’s Family Steak Houses, Inc., 269 F.3d 753, 755 (7th Cir.2001). This would have been the case, for example, if a dispute had arisen between Balmoral and its ordinary electricians, in which instance the existence of the arbitration agreement would have been plain. The issue would be equally simple on the other side if an utter stranger were asked to arbitrate: she need not do so, unless she executed an agreement to that effect. Here, however, we face something between those two extremes. The issue before us is whether the camera workers Balmoral employed between September and November 1996 were covered by Bal-moral’s agreement with Local 176. If they are, then this is an arbitrable dispute; if not, then the company was within its rights to refuse to arbitrate.
The starting point in our inquiry is naturally the language of the Agreement — and we stress, in light of some of the arguments Balmoral has made, that we are referring to the agreement Balmoral itself signed with the union, not with any agreement that may have existed between World Wide and the union. We interpret collective bargaining agreements in the same way we approach other contracts. Alexander v. City of Evansville, 120 F.3d 723, 727 (7th Cir.1997). The source of law, however, is different: while the arbitrability of a dispute is ordinarily regulated by state law, see Penn v. Ryan’s Family Steak Houses, Inc., 269 F.3d at 758-59, collective bargaining agreements are interpreted under federal law. Chicago Painters and Decorators Pension, Health and Welfare and Deferred Sav. Plan Trust Funds v. Karr Bros., Inc., 755 F.2d 1285, 1290 (7th Cir.1985); see also Sweeney v. Westvaco Co., 926 F.2d 29, 36 (1st Cir.1991) (Breyer, C.J.) (“Congress has said that courts, when they interpret ... collective bargaining agreements, must apply federal law. Indeed, they are to create a body of federal common law that applies to disputes arising out of collective bargaining agreements.”). As the Supreme Court has made clear, however, we may draw guidance from state law principles if they are compatible with federal labor law policies. See Textile Workers Union v. Lincoln Mills, 353 U.S. 448 at 456-57, 77 S.Ct. 912, 1 L.Ed.2d 972 (1957); see also Merk v. Jewel Food Stores Div. of Jewel Companies, Inc., 945 F.2d 889, 892 (7th Cir.1991) (common law contract principles are brought into the labor context with sensitivity to. considerations of national labor policy).
Looking at the Agreement, we find in Section 2.03(a) language defining the scope of the work covered to include the following:
... the installation, operation, maintenance and repair of all'electrical wiring and electrical equipment used in the construction, alteration, and repair of buildings, structures, bridges, street and highway work, tunnels, subways, shafts, dams, river and harbor work, airports, mines, all electrical raceways for electri*406cal wires and cables, and such other work as by custom has been performed by members of IBEW when determined to be within the Inside branch in accordance with section (c) below.
(Emphasis added.) The highlighted phrase with which this section ends is obviously more open-ended than the earlier examples of covered work, but the Agreement also includes a mechanism for resolving coverage disputes. Section 2.03(d) has the following to say on that subject:
The Employer understands that the Local’s jurisdiction both trade and territorial is not the subject for negotiations but rather is determined solely within the IBEW by the International President and therefore, agrees to recognize and be bound by such determination.
Elsewhere in the Agreement, we find Section 2.02, recognizing Local 176’s authority over “all employees in the different employee and work classifications set forth in Section 5.04.” Section 5.04, in turn, provides that “[wjages for Apprentices, Journeymen, Foremen and General Foremen shall be equal to wages paid for Zone I on the Inside Agreement.” Balmoral infers from this that, under common trade usage, “apprentices, journeymen, foremen and general foremen” are terms used for electricians, and not for camera workers, and thus that the contract is at best ambiguous. But it is well established that we are to read collective bargaining agreements as a whole, Irvin H. Whitehouse & Sons Co. v. N.L.R.B., 659 F.2d 830, 835 (7th Cir.1981), and when one reads the list of types of employees covered (Section 5.04) in conjunction with the list of kinds of work covered (Section 2.03(a)), we see no ambiguity that needs to be resolved.
Under a unified reading of Sections 2.03(a) and 2.04(d), as well as the other parts of the Agreement we have just mentioned, we are prepared to agree with Bal-moral that the camera workers were not performing any of the enumerated tasks set forth in Section 2.03(a), and that if they are covered at all, it is because they were doing work customarily performed by members of the IBEW. Balmoral urges that a natural reading of the Agreement does not evince an intent that it cover camera workers, even under the residual clause. This may be correct; the district court expressed exactly that view in its first summary judgment decision. But it would be inappropriate for us to rule on that issue, because that is not the question before us. As we have been emphasizing, we must decide only whether this industrial dispute belongs before an arbitral tribunal, and under this Agreement and in the circumstances here presented, the parties have agreed that the answer to the coverage question is for the International President to give. This court is certainly not in the business of reviewing the wisdom of contractual obligations parties decide to enter into — absent special circumstances, the parties will be bound by their agreement. See Beanstalk Group, Inc. v. AM General Corp., 283 F.3d 856, 860 (7th Cir.2002). We must therefore look to see what the International President of the IBEW had to say on the matter.
Section 2.03(d) of the Agreement gave the International President unfettered discretion to make his determination. Bal-moral is now trying to resist that language, insofar as it is arguing that the court must retain some power to supervise the propriety of the International President’s decision. We disagree. There is no reason why the parties could not contract for the International President’s decision to be final and unreviewable, and the language set forth above shows that they did exactly that in the Agreement. Whether or not the International President had a *407contractual duty of performing his job in good faith, see, e.g., Interim Health Care of Northern III., Inc. v. Interim Health Care, Inc., 225 F.3d 876, 884 (7th Cir.2000), is beside the point. The contract itself put his decision beyond judicial review, and we will respect that limit. It may also be worth noting that the President is not deemed to be a party to this Agreement. Thus, this is not a situation in which one party unilaterally forced another into arbitration. See, e.g., Gibson v. Neighborhood Health Clinics, Inc., 121 F.3d 1126 (7th Cir.1997). Using the procedures on which both sides had agreed, Local 176 had to petition the International President for a ruling; had the ruling been adverse to its position, it would be Balmo-ral now who would be insisting on strict compliance with the Agreement.
IV
While the first phase of this litigation was underway, on November 6, 1997, Local 176 wrote the International President formally asking for a determination of jurisdiction pursuant to Section 2.03. It did not specifically ask the International President to find that the camera workers were “within the Inside branch,” even though the final sentence of Section 2.03(a) seems to require such a finding. Nonetheless, the intent to obtain a jurisdictional determination was clear. The International President, Mr. J.J. Barry, responded with the following letter:
This correspondence is in reply to your letter forwarded to this office by International Vice President O’Connor. The IBEW Constitution, Article XXVII, Section 6(a) states:
Sec. 6. These shall include the following divisions and classifications: (a) Radio, television and recording engineers, technicians, operators, installers, inspectors, maintenance and repairmen and service men, engaged in the application of electricity to the transmission and transference of voice, sound and vision for commercial, educational and entertainment purposes, excepting employees of common carrier companies. They shall have jurisdiction over the following work: The installation, operation, inspection, maintenance, repair and service of radio, television, recording, voice, sound and vision production and reproduction apparatus, equipment and appliances used for domestic, commercial, educational and entertainment purposes.
The IBEW and its local unions represent cameramen in all facets of video production. Some members are covered under national agreements between the IBEW and the major telévision networks and many others are covered by collective bargaining agreements with our local unions. Our members are also the cameramen for numerous in-house closed circuit productions at major sport arenas.
To simplify my answers, yes, cameramen are under the jurisdiction of the IBEW and Local 176.
The trouble with this response was that, apart from the last sentence, it had little to do with the Agreement between Balmoral and Local 176. The key question was whether these cameramen were part of the Inside branch: if so, they fell within the scope of the Balmoral agreement; if not, they did not.
To be part of the Inside branch (as the Agreement requires) is not the same as to be part of Local 176 more generally. Local 176 is divided into several branches: the Inside Electrical Workers, the Outside and Utility Workers, the Communications Workers, the Railroad Electrical Workers, and the Electrical Manufacturing Workers. *408Balmoral argues that the International President’s answer was insufficient for purposes of Section 2.03 without a specific sentence about the branch to which the cameramen belonged. Indeed, Balmoral argues that by citing from Section 6(a) of the IBEW Constitution, which is about the Communications branch, it is obvious that the International President was at best confused about the question posed to him.
We agree that there may have been some confusion leading up to the affirmative answer, but we conclude that the correspondence with the International President, taken as a whole, adequately responded to the coverage question. The International President’s letter unambiguously answers one question: that the camera workers were under the jurisdiction of the IBEW and Local 176. Deposition testimony shows that all members of Local 176 were also members of the Inside branch and thus that an affirmative answer to the question about Local 176 was also necessarily an affirmative answer to the question about the Inside branch. Furthermore, even disregarding that deposition testimony, it is appropriate to look at the letter from Local 176 to which the International President was responding. In a two-page letter to the President, Local 176 explained the relation' between itself and Balmoral and the nature of the grievance. Local 176 even quoted the relevant passages of the Agreement, Section 2.03(a) and Section 2.03(c). This gives the necessary context to the International President’s final response, where he stated “yes, cameramen are under the jurisdiction of the IBEW and Local .176.” He was not answering a question in the abstract: he was dealing with the Agreement between Local 176 and Balmoral. As the International President was not unaware of what he was being asked, his answer can only be read to confer jurisdiction to Local 176 over the camera workers at Balmoral in the context of the Agreement. And that determination also settles the question of arbitrability in favor of Local 176.
Whether the International President was right is beside the point. Perhaps Bal-moral is correct that he erroneously looked to Section 6 of'Article XXVII of the IBEW Constitution, which details the coverage of the Communications branch (separate and distinct from the Inside branch), instead of confining himself to the history of the camera work at Balmoral and whether (having always been within the Inside branch under the World Wide contract) it stayed within the Inside branch when Balmoral briefly employed these workers. The right to make an unreviewable decision, for better or for worse, includes the right to make mistakes. Having decided that the International President did make the determination asked of him, we have done all that we can, or should. As he clearly stated, “yes, cameramen are under the jurisdiction of the IBEW and Local 176” in response to a letter seeking to establish jurisdiction for the current dispute, the reasons by which he arrived at this result — right, wrong, or inapposite — are irrelevant.
V
. For these reasons, we Affirm the judgment of the district court.