
454 N.W.2d 633 (1990)
Joyce Ann HOULIHAN, et al., Appellants,
v.
Gregory Lawrence FIMON, et al., Respondents.
No. C1-89-2058.
Court of Appeals of Minnesota.
May 1, 1990.
*634 Mark C. Vandelist, Mark Gwinn, Cousineau, McGuire, Shaughnessy & Anderson, Minneapolis, for appellants.
Lance B. Nyberg, Baukol, Nyberg and Thompson, St. Louis Park, for respondents.
Considered and decided by HUSPENI, P.J., and SCHUMACHER and LESLIE,[*] JJ.


*635 OPINION
HUSPENI, Judge.
Joyce and Patrick Houlihan appeal from an award of summary judgment in which the trial court found that they were collaterally estopped from bringing suit against respondents. The trial court found that appellants' suit was precluded by a prior arbitration decision which held Joyce Houlihan 100% at fault for the accident. We reverse and remand for trial.

FACTS
Joyce Houlihan was the driver of a car which went through the intersection at 27th Street and Bloomington Avenue in Minneapolis and collided with a school bus. Houlihan later stated that she did not see the stop sign at the intersection because a large truck was parked at the right side of 27th Street facing the wrong way. The truck belonged to Tamarack Materials, Inc. ("Tamarack") and was driven by an employee, Gregory Fimon.
Both Joyce Houlihan and Thomas Weaver, the driver of the school bus, were injured in the collision. Weaver filed suit against Houlihan, Fimon and Tamarack. Houlihan's insurer, American Family Insurance Co., appointed in-house counsel to represent Houlihan. Houlihan also retained a separate attorney, who advised her to bring a separate action for her injuries at a later time. During trial the parties reached a settlement. The insurance companies were unable to agree on the allocation of liability, and agreed to submit that issue to arbitration. Joyce Houlihan was informed by letter that neither side intended to call her as a witness, but that she was welcome to attend the arbitration proceeding.[1] Houlihan's personal attorneys were not informed of the proceeding and did not participate in the arbitration.
Following the proceeding on September 3, 1987, the arbitrator determined that Houlihan was 100% at fault for the accident. Houlihan's attorneys discontinued her representation after the arbitration decision. Houlihan retained other counsel, and then brought suit against Fimon and Tamarack for her personal injuries. In granting respondents' motion for summary judgment, the trial court concluded that Houlihan was collaterally estopped by the arbitration decision from relitigating her liability.

ISSUE
Did the trial court err in granting summary judgment?

ANALYSIS
Generally,
On appeal from a summary judgment the reviewing court determines whether there are any genuine issues of material fact and whether the trial court erred in its application of the law.
Hubred v. Control Data Corp., 442 N.W.2d 308, 310 (Minn.1989). Where the facts are not in dispute and only questions of law are at issue, no deference need be given to the trial court's decision. Id.
Collateral estoppel is a branch of the res judicata doctrine. Ellis v. Minneapolis Commission on Civil Rights, 319 N.W.2d 702, 703 (Minn.1982).
It applies where (1) the issue was identical to one in a prior adjudication; (2) there was a final judgment on the merits; (3) the estopped party was a party or in privity with a party to the prior adjudication; and (4) the estopped party was given a full and fair opportunity to be heard on the adjudicated issue.
Johnson v. Consolidated Freightways, Inc., 420 N.W.2d 608, 613 (Minn.1988) (citing Ellis, 420 N.W.2d at 613). Neither collateral estoppel nor res judicata should be rigidly applied. Johnson, 420 N.W.2d at 613. As a flexible doctrine, "the focus is on whether its application would work an injustice on the party against whom estoppel is urged." Id. at 613-14 (citing Jeffers v. Convoy Co., 636 F.Supp. 1337, 1339 (D.Minn.1986)).
*636 The parties agree that the issue of Houlihan's liability is identical in both proceedings and thus the first prong of Johnson/Ellis is met. The parties dispute the remaining elements of estoppel.
Regarding the second prong of Johnson/Ellis, the Houlihans argue that the arbitration proceeding should not be considered a "final judgment" on the merits for purposes of applying collateral estoppel. Both this court and the Minnesota Supreme Court have addressed the Johnson/Ellis factors. Aufderhar v. Data Dispatch, Inc., 452 N.W.2d 648 (Minn.1990). The Aufderhar court held that when personal injury damages were previously determined in an arbitration proceeding where the claimant has been afforded a full opportunity to litigate the issue, the claimant may be estopped from relitigating the issue in a later action against a different defendant. The Aufderhar court cited Johnson in stressing that "arbitration is meant to be a final judgment of both law and fact," Johnson, 420 N.W.2d at 613, and stated that its prior refusal to apply collateral estoppel in Johnson was based on the fact that the defendant in that case was not afforded a full and fair opportunity to be heard on the issue, "the crucial fourth prong of the Ellis test." Aufderhar, 452 N.W.2d at 651. See also Art Goebel, Inc. v. Arkay Construction Co., 437 N.W.2d 117 (Minn.Ct.App.1989) (it is appropriate to apply collateral estoppel where parties acquiesced in arbitration award).
We agree that in appropriate circumstances, particularly where the estopped party sought the arbitration, a prior arbitration decision may result in application of collateral estoppel. See Aufderhar; see also Lysholm v. Liberty Mutual Insurance Co., 404 N.W.2d 19 (Minn.Ct.App. 1987) (estoppel may apply where the estopped party actively sought arbitration and later challenged the result).
Even if we assume for the sake of further analysis that the arbitration proceeding here constituted a final judgment, we must determine whether Houlihan was a party to the prior adjudication. Although she was a named party in both actions, we are troubled by whether she was a "party" in more than name only. We believe that being a "party" for purposes of collateral estoppel contemplates more than merely a name on the documents. See Minnesota State Board of Health v. City of Brainerd, 308 Minn. 24, 241 N.W.2d 624 (1976) (city not barred by previous action in which it was a party, where city did not have "full, free, and untrammeled opportunity" to present facts, and city was only a nominal party in first action), appeal dismissed City of Brainerd v. Minnesota State Board of Health, 429 U.S. 803, 97 S.Ct. 35, 50 L.Ed.2d 63 (1976).
Respondents argue that even if the insurance company were the real party in interest, Houlihan was in privity with the insurance company. "There is no prevailing definition of privity which can automatically be applied." Margo-Kraft Distributors, Inc. v. Minneapolis Gas Co., 294 Minn. 274, 278, 200 N.W.2d 45, 47 (1972).
[Privity] expresses the idea that certain nonparties may be so connected with the litigation that the judgment should also determine their interests.
Denzer v. Frisch, 430 N.W.2d 471, 473 (Minn.Ct.App.1988) (quoting Brunsoman v. Seltz, 414 N.W.2d 547, 550 (Minn.Ct.App. 1987)), pet. for rev. denied (Minn. Jan. 15, 1988). Those in privity include "those who control an action although not parties to it * * *; [and] those whose interests are represented by a party to the action." Margo-Kraft, 294 Minn. at 278, 200 N.W.2d at 48. "Privity is usually a question of fact requiring case-by-case determination." Miller v. Northwestern National Insurance Company, 354 N.W.2d 58, 62 (Minn. Ct.App.1984).
Respondents argue that the insurance company and Houlihan shared a common interest in obtaining the lowest percentage of fault attributable to Houlihan. However, "coincidental interests alone are not sufficient to establish privity." Denzer, 430 N.W.2d at 473. Here, Houlihan's interests went beyond the scope of her insurance coverage. Arguably, her interest in recovery for her personal injuries was not *637 fully represented in the arbitration proceeding.
Again, even if we assume for the sake of further analysis that Houlihan was a party or in privity with the real party in interest, we believe that before we may affirm application of the doctrine of collateral estoppel, we must find that the fourth prong of Johnson/Ellis was met. We must find that Houlihan had a "full and fair" opportunity to be heard on the adjudicated issue. It was the fourth prong of this analysis that troubled the court in Johnson. It troubles us also.
We ask, as did the Aufderhar court, "Was [the person estopped] afforded a full and fair opportunity to present evidence * * *." Aufderhar at 652. The Aufderhar court concluded he was. We examine the facts of both that case and this to determine whether it is proper to conclude that Houlihan, too, was afforded the full and fair opportunity to present evidence.
Houlihan's arguments that she did not elect to arbitrate, that her insurance company controlled the decision, that she risked the loss of her insurance coverage if she failed to cooperate, and that she did not acquiesce in the arbitration result are persuasive. We note that the insurance company assigned in-house counsel to represent Houlihan. She had little or no control over the litigation, and virtually no input in the decision-making process. She was not informed of the settlement or the decision to arbitrate liability prior to the time those decisions were made.
In contrast the defendant in Aufderhar sought arbitration; in fact had resorted to court intervention to compel arbitration. Aufderhar's attorney, in essence, concluded that Aufderhar was given a full opportunity to provide evidence.
Although Houlihan had retained private counsel, her attorneys were not notified of the arbitration proceeding and did not participate in it. Houlihan was notified by letter that "the lawsuit brought by Thomas Weaver * * * was resolved by agreement between American Family and representatives for [Tamarack and Fimon]." The letter stated that a settlement was paid with the understanding that "we would arbitrate" liability. Houlihan was informed that neither side intended to call her as a witness, but she could attend if she chose. There is no evidence that Houlihan was informed that the arbitration decision could be binding in a subsequent suit. Apparently she did not realize that her own cause of action against respondents here could be lost as a result of the arbitrator's decision.
Neither is the fact that Houlihan did not appeal the arbitration decision dispositive. If she were unaware of the significance of that decision to issues beyond the scope of her insurance coverage, it is not surprising that she did not appeal.
We are left with the firm conviction that in contrast to the party estopped in Aufderhar, Houlihan had no meaningful participation in the arbitration proceeding. Consequently, she did not have a fair opportunity to be heard and the fourth prong of the Johnson/Ellis test was not met.
We conclude that under the circumstances of this case, application of collateral estoppel would work an injustice. To hold otherwise would also mean that Houlihan's claim was essentially decided in a forum of the insurance company's choosing, without opportunity for a jury trial on the issues. Application of collateral estoppel under these circumstances could result in denial of the constitutional right to trial by jury where a prior arbitration has addressed the same issue. See Aufderhar, 452 N.W.2d 648 (Yetka, J., dissenting).
Finally, while it can be argued that Houlihan should have brought her damage claim against respondents by cross-claim in the original action, to place her in that position makes the claim mandatory. "Cross-claims are not mandatory or compulsory in Minnesota." Denzer, 430 N.W.2d at 475, see Minn.R.Civ.P. 13.07 ("A pleading may state as a cross-claim any claim by one party against a co-party arising out of the transaction or occurrence [at issue]") (emphasis added).


*638 DECISION
The trial court erred in determining that Houlihan had a full and fair opportunity to be heard in the arbitration proceeding. Consequently, collateral estoppel is not applicable and the summary judgment must be reversed.
Reversed and remanded.
LESLIE, Judge (dissenting).
The majority concludes that collateral estoppel should not apply in the present case. I disagree. It is undisputed that the identical issue is involved in both actions. Additionally, the arbitration proceeding qualifies as a prior adjudication. The supreme court's decision in Aufderhar v. Data Dispatch, Inc., 452 N.W.2d 648 (Minn.1990) clearly supports application of collateral estoppel under similar circumstances. The court held in Aufderhar that a party who has litigated the issue of personal injury damage with his insurance carrier in an arbitration proceeding may be estopped from relitigating the same issue in a subsequent tort action. The court recognized that, "We have afforded to an arbitration award finality as to both facts and the law." Aufderhar, 452 N.W.2d at 651 (citation omitted).
Arbitration is a procedure favored in the law. Ehlert v. Western National Mutual Insurance Co., 296 Minn. 195, 199, 207 N.W.2d 334, 336 (Minn.1973). The strong public policy in favor of arbitration is not served by permitting parties who participated in the arbitration proceeding, and who did not appeal the result, to attack the arbitrator's decision in a later proceeding.
Here, Houlihan attempts to relitigate the precise issue determined in arbitration. She was notified of the arbitration and informed that the arbitration would address "the question of which party was more at fault in causing the accident." Houlihan was represented by competent counsel; in fact she later retained the same attorney when he entered private practice. Houlihan attended the arbitration and testified on her own behalf. She had ample opportunity to present evidence. There is no allegation that the arbitration proceeding was flawed, or that the decision was based on incomplete evidence. The evidence presented at the hearing revealed that Houlihan approached Bloomington Avenue, a major thoroughfare, and failed to stop before entering the intersection, striking a school bus. Houlihan claimed that she could not see the stop sign blocked by a truck and that she was unfamiliar with the area. A driver in an unfamiliar area, however, should be especially cautious. After hearing all the evidence, the arbitrator determined that Houlihan was 100% at fault. There is no indication that the arbitrator erred.
Moreover, Houlihan did not appeal the result. While we can speculate as to possible reasons for her failure to appeal, the fact remains that she did not contest the arbitrator's finding of 100% liability. Houlihan's actions indicate that she acquiesced in the arbitration decision. See Art Goebel, Inc. v. Arkay Construction Co., 437 N.W.2d 117, 119 (Minn.Ct.App.1989) (collateral estoppel appropriate where party acquiesced in prior arbitration award).
The majority questions whether Houlihan was a party to the suit. Houlihan was an individual named party in both actions. Her participation in the arbitration proceeding went beyond a mere name on the documents. There is no evidence that her interest was not capably represented in the proceeding. While her interest in recovering for her own personal injury may have gone beyond the scope of her insurance coverage, on the crucial issue of her liability for the accident she and the insurance company shared the same objective of obtaining the minimal possible liability. Thus, even if Houlihan were not the real party in interest, she was in privity with the insurance company.
Additionally, I believe that Houlihan had a fair opportunity to be heard on the issue of her liability. Whether she used her opportunity wisely is not the issue here. Instead, the focus is on whether she had a fair chance to present her evidence. Houlihan was fully aware that the specific issue of liability would be determined at the hearing. She had the benefit of not only *639 her appointed counsel, but her privately retained counsel as well. The fact that her counsel apparently advised her to bring a separate action later does not mean that Houlihan was denied the opportunity to be heard in the arbitration hearing. On the contrary, she attended and testified. Under these circumstances, I cannot agree that she did not have a sufficient opportunity to present her side of the case. In my view, both the law and the facts support the trial court's grant of summary judgment. I see no justification for wasting scarce judicial time in a further consideration of this matter and would affirm.
NOTES
[*]  Acting as judge of the Court of Appeals by appointment pursuant to Minn. Const. art. 6, § 2.
[1]  The trial court memorandum indicates that Houlihan did not attend the arbitration hearing. However, the parties at oral argument agreed that she did attend and testify.
