
240 Wis.2d 438 (2000)
2001 WI App 20
623 N.W.2d 195
Everett CARLSON, Plaintiff-Appellant,
v.
OCONTO COUNTY BOARD OF CANVASSERS, Respondent-Respondent,
Barbara SMITH, Intervenor-Respondent-Respondent.
No. 00-1788.
Court of Appeals of Wisconsin.
Submitted on briefs November 13, 2000.
Decided December 5, 2000.
*441 On behalf of the plaintiff-appellant, the cause was submitted on the briefs of Aaron M. Krzewinski of Judge Law Offices, S.C., Oconto.
On behalf of the respondent-respondent, the cause was submitted on the brief of Alyson K. Zierdt of Davis & Kuelthau, S.C., Oshkosh.
On behalf of the intervenor-respondent-respondent the cause was submitted on the brief of Vance M. Waggoner, Oconto Falls.
Before Cane, C.J., Hoover, P.J., and Peterson, J.
¶ 1. PETERSON, J.
Everett Carlson appeals the portion of the judgment affirming the findings of the Oconto County Board of Canvassers and declaring his opponent, Barbara Smith, the winner of the election for Oconto County Board of Supervisors, District 20. On appeal, Carlson argues that (1) he does not have the burden of proving that the votes of the challenged electors would have changed the election results pursuant to WIS. STAT. chs. 5-12;[1] and (2) the trial court erred by determining that it lacked legal authority to order a special election. We disagree and affirm the judgment.

BACKGROUND
¶ 2. The election for Oconto County Board of Supervisors, District 20, resulted in 125 votes for Smith and 123 votes for Carlson. Pursuant to WIS. STAT. § 9.01, Carlson petitioned the Board of Canvassers *442 for a recount and alleged that between two and four persons illegally voted in District 20. The board set aside one vote for Smith that was not properly initialed, reducing the margin of victory to one vote. The board further found that two of the ballots Carlson challenged were cast by voters who did not reside in District 20 and had voted there by mistake. The board refrained from taking further action because Carlson had already announced his intention to appeal to the circuit court.
¶ 3. Carlson appealed the recount to the circuit court, alleging that he was entitled to a special election because the invalid votes could have changed the results of the election.[2] At trial, Carlson called as witnesses, the two District 20 voters who the board had determined voted by mistake. The witnesses stated their current addresses, confirmed that these were their addresses on the day of the election, and were the addresses given to election officials on election day. Carlson did not ask them who they voted for or whether they were willing to waive the privilege against non-disclosure of an election vote.
¶ 4. The trial court ruled that Carlson had failed to show how the challenged ballots would have made a difference in the outcome of the election and that the board had not erroneously interpreted the law. The trial court declared Smith the winner and found that a contrary result would disenfranchise the District 20 electorate. This appeal followed.


*443 STANDARD OF REVIEW
[1, 2]
¶ 5. The validity of an election raises questions of statutory interpretation that this court reviews independently without deference to the trial court. See Logerquist v. Board of Canvassers for Town of Nasewaupee, 150 Wis. 2d 907, 912, 442 N.W.2d 551 (Ct. App. 1989). On appellate review of a WIS. STAT. § 9.01 proceeding, the question is whether the board's findings are supported by substantial evidence. See id. at 918.

DISCUSSION
I. BURDEN OF PROOF
¶ 6. Carlson first argues that he did not have the burden of proving that the votes of the challenged electors would have changed the election results. We disagree.
[3, 4]
¶ 7. In Wisconsin, relief for the losing candidate is confined to the recount statute. See WIS. STAT. § 9.01. The statute is the exclusive remedy for any claimed election fraud or irregularity. See WIS. STAT. § 9.01(11);[3]see also State ex rel. Shroble v. Prusener, 185 Wis. 2d 102, 112-13, 517 N.W.2d 169 (1994).
[5]
¶ 8. Interpretation of WIS. STAT. § 9.01 is based on public policy articulated in early legal decisions that *444 predated § 9.01. See State ex rel. Wold v. Hanson, 87 Wis. 177, 58 N.W. 237 (1894). In Wold, our supreme court stated "[a]n election honestly conducted under the forms of law ought generally to stand, notwithstanding individual electors may have been deprived of their votes, or unqualified voters have been allowed to participate." Id. at 179. This statement of policy was approved as a general rule by the supreme court in McNally v. Tollander, 100 Wis. 2d 490, 500, 302 N.W.2d 440 (1981).
[6]
¶ 9. The public policy articulated in Wold was codified in WIS. STAT. § 5.01(1).[4] Our supreme court has interpreted § 5.01(1) to mean that only substantial violations of the election law should operate to vacate an election. See State ex rel. Pelishek v. Washburn, 223 Wis. 595, 600, 270 N.W. 541 (1936). In Pelishek, the court stated that § 5.01(1) was "a mandate to the judicial tribunal before whom the proceedings are pending that mere informality or failure to comply with some of the provisions of the title shall not defeat the will of the electors." Id. at 601.
A. OUTCOME TEST V. REASONABLE UNCERTAINTY TEST
[7]
¶ 10. Carlson argues that Wisconsin courts have not chosen the standard that a challenger must meet to overturn an election, but that they lean toward the reasonable uncertainty test as opposed to the outcome *445 test. The reasonable uncertainty test requires only that the challenger demonstrate that the outcome of the election is impossible to determine with mathematical certainty. See Helm v. State Election Bd., 589 P.2d 224, 228 (Okla. 1979). The result of an election is sufficiently uncertain if the number of voided ballots cast exceeds the margin of victory between the candidates. See id. Under the outcome test, to successfully challenge an election, the challenger must show the probability of an altered outcome, in the absence of the challenged irregularity. See Tollander, 100 Wis. 2d at 505.
[8]
¶ 11. Contrary to Carlson's argument, our supreme court has approved the outcome test for most election irregularities. See id. In Tollander, our supreme court declined, however, to apply the outcome test because certain public officials had deprived 40% of the electorate the right to vote. While the court reaffirmed the outcome test, it articulated a fact dependent exception to the general application to the test:
But in a case where deprivations of the right to vote are so significant in number or so egregious in character as to seriously undermine the appearance of fairness, we hold such an election must be set aside, even where the outcome of the election might not be changed.
Id. Therefore, this case is not one in which Carlson is relieved from his burden of presenting affirmative evidence to show how the outcome of this election would have been changed if the votes of the two illegal electors had not been counted in District 20. This is not a case where deprivations of the right to vote are significant in number.
*446 ¶ 12. Carlson claims Logerquist, 150 Wis. 2d at 919, controls because it specifically addresses the problem of voter disqualification due to residency requirements. Carlson contends that Logerquist implicitly endorses the reasonable uncertainty test and clearly contemplates a special election had the number of disqualified voters exceeded the margin of victory. We disagree.
¶ 13. The issue in Logerquist was whether WIS. STAT. § 9.01 provides one elector with the opportunity to challenge another elector's eligibility after an election. We held that "[e]ven with one disqualified elector, a new referendum election would not change the results in favor of annexation." Id. at 920. However, relying on Clapp v. Joint Sch. Dist. No. 1, 21 Wis. 2d 473, 124 N.W.2d 678 (1963), we reaffirmed the proposition that post-election eligibility challenges pursuant to WIS. STAT. § 9.01 are permissible "provided they may affect the election results." Logerquist, 150 Wis. 2d at 916.
¶ 14. Contrary to Carlson's argument, Logerquist does not address whether a special election would be appropriate if the number of disqualified voters exceeded the margin of victory. We stated only that the vote of the one elector for whom adequate evidence of disqualification had been submitted would not have changed the election outcome. See id. at 920. This observation is not a holding that a special election is required if the number of disqualified voters exceeds the margin of victory.
B. VOTER PRIVILEGE AGAINST DISCLOSURE
¶ 15. Despite our determination that the outcome test is to be applied in Wisconsin, Carlson argues that a Wisconsin voter's absolute privilege to ballot *447 secrecy compels adoption of the reasonable certainty test. We disagree.
[9]
¶ 16. Article III, § 3, of the Wisconsin Constitution provides that all votes shall be by secret ballot. However, this constitutional provision does not control the question of whether a voter may, under certain circumstances, disclose, or be compelled to disclose, the manner in which he or she voted. WISCONSIN STAT. § 905.07 provides, "Every person has a privilege to refuse to disclose the tenor of the person's vote at a political election conducted by secret ballot unless the vote was cast illegally." Therefore, under the express provisions of WIS. STAT. § 905.07, neither of the two persons who had illegally voted in this election was entitled to the privilege against disclosing how he or she voted in the election.
¶ 17. Carlson further argues that election results would be unreliable and arbitrary if persons who voted illegally were allowed to testify about how they voted because they would know in advance how their testimony would affect the election outcome. See Reich v. District Lodge 720, 11 F.3d 1496, 1500 (9th Cir. 1993). We disagree.
¶ 18. In support of this argument, Carlson cites a footnote in Appeal of Bd. of Canvassers, 147 Wis. 2d 467, 474-75 n.2, 433 N.W.2d 266 (Ct. App. 1988). The footnote expressed concern about the "potential for mischief" if a voter can testify about a vote, knowing that it can affect the election outcome. Id. However, this was not our holding in Board of Canvassers. We did not rule on whether an elector can testify how he or she voted. See id. at 471.
*448 [10]
¶ 19. While Carlson's concerns are not unfounded, there is no case law that prohibits voter testimony in a post election challenge. If there are questions about the credibility of a voter's testimony, those questions may be tested on cross-examination, weighed by the finder of fact, and reviewed on appeal. We reject Carlson's argument that Wisconsin courts lean toward the reasonable certainty test.
II. SPECIAL ELECTION
¶ 20. Last, Carlson argues that the trial court erred by determining that it lacked the authority to order a special election. Carlson contends that the trial court erroneously gave legal weight to the board's recount results and that it relied on outdated case law to deny Carlson his remedy. We disagree.
[11]
¶ 21. Carlson misreads the trial court's ruling. The trial court did not determine that it lacked the authority to order a special election. Rather, it stated that Carlson had failed to meet his burden of proving how the two votes affected the outcome so as to warrant invalidation of the election. The trial court stated:
Nevertheless, in my judgment, it cannot be cured. There is nothing in the record at this time, and there was nothing in the record at the recount proceeding before the Board of Canvassers, to show how the two invalid electors, Umentum and Warrichaiet voted. Accordingly, there is no way for the Board of Canvassers or this court to know how those two invalid votes effected [sic] the final result of the election tally.
....

*449 In this case, the appellant has failed to show the defect of the invalid ballots. The appellant has made no showing in the entire record as to how the due challenge [sic] ballots were cast and that they would have made a difference in the election.
The trial court correctly defined the scope of review of the board's decision, stating that it was required to set aside or modify the board's determination if it found that the board had erroneously interpreted a provision of law and that a correct interpretation compelled a particular action. See WIS. STAT. § 9.01(8).[5]
*450 ¶ 22. Carlson argues that the trial court based its holding on the very early language of Wold.[6] However, the trial court's reference to Wold is limited to Wold's expression of general public policy. That public policy favors upholding a flawed election in the absence of fraud, unless there is some proof of the effect the irregularity would have had on the outcome. This principle was reaffirmed in Shroble, 185 Wis. 2d at 116. We reject Carlson's argument that the trial court's decision was not properly based on sound public policy.
[12]
¶ 23. The trial court determined that Carlson failed to meet his burden of proving beyond a reasonable doubt that the election raised any uncertainty concerning the will of the electors. Because the record shows that Carlson did not meet that burden, we affirm the trial court's decision declaring Smith to be the winner.
By the Court.Judgment affirmed.
NOTES
[1]  All references to the Wisconsin Statutes are to the 1997-98 version unless otherwise noted.
[2]  Carlson further alleged that allowing the ineligible electors to vote is an "irregularity, defect, mistake and fraud." The circuit court found that no fraud had occurred. This issue is not challenged on appeal.
[3]  WISCONSIN STAT. § 9.01(11) reads as follows: "EXCLUSIVE REMEDY. This section constitutes the exclusive judicial remedy for testing the right to hold an elective office as the result of an alleged irregularity, defect or mistake committed during the voting or canvassing process."
[4]  WISCONSIN STAT. § 5.01(1) provides: "CONSTRUCTION OF CHS. 5 TO 12. Except as otherwise provided, chs. 5 to 12 shall be construed to give effect to the will of the electors, if that can be ascertained from the proceedings, notwithstanding informality or failure to fully comply with some of their provisions."
[5]  WISCONSIN STAT. § 9.01(8) reads as follows:

SCOPE OF REVIEW. Unless the court finds a ground for setting aside or modifying the determination of the board of canvassers or chairperson of the board, it shall affirm the determination. The court shall separately treat disputed issues of procedure, interpretations of law and findings of fact. The court may not receive evidence not offered to the board of canvassers or chairperson except for evidence that was unavailable to a party exercising due diligence at the time of the recount or newly discovered evidence that could not with due diligence have been obtained during the recount, and except that the court may receive evidence not offered at an earlier time because a party was not represented by counsel in all or part of a recount proceeding. A party who fails to object or fails to offer evidence of a defect or irregularity during the recount waives the right to object or offer evidence before the court except in the case of evidence that was unavailable to a party exercising due diligence at the time of the recount or newly discovered evidence that could not with due diligence have been obtained during the recount or evidence received by the court due to unavailability of counsel during the recount. The court shall set aside or modify the determination if it finds that the board of canvassers or chairperson has erroneously interpreted a provision of law and a correct interpretation compels a particular action. If the determination depends on any fact found by the board of canvassers or chairperson, the court may not substitute its judgment for that of the board of canvassers or chairperson as to the weight of the evidence on any disputed finding of fact. The court shall set aside the determination if it finds that the determination depends on any finding of fact that is not supported by substantial evidence.
[6]  Carlson contends that when State ex rel. Wold v. Hanson, 87 Wis. 177, 58 N.W. 237 (1894), was decided, there were no legislative scheme addressing election problems. Since then, the Wisconsin Legislature has provided that special elections may be held when necessary. See WIS. STAT. §§ 5.02(19) and 8.06.
