
667 S.E.2d 587 (2008)
FULLER et al.
v.
THOMAS et al.
No. S08A0898.
Supreme Court of Georgia.
October 6, 2008.
Michael B. King, for appellants.
Insley & Race, Deana S. Johnson, Aynsley M. Harrow, Wayne Hall, for appellees.
*588 THOMPSON, Justice.
The City of Riverdale held its general election on November 6, 2007. In the Ward 2 race, Georgia Randall Fuller ran against three other candidates, Michael Bruce, Wayne Hall, and Roberto Advincula. In the Ward 4 contest, the candidates were Stan Harris and Kenny Ruffin. Bruce and Hall received the most votes in the Ward 2 race, but neither candidate received enough votes to avoid a runoff. Ruffin won the Ward 4 race outright. One week later, Fuller and Harris filed a petition to contest the general election on grounds of fraud, misconduct, irregularity and illegality. They sought a judgment declaring the results of the November 6 general election invalid, and staying the December 4 runoff election.
The case proceeded to trial on December 3, 2007. Finding no evidence of fraud, misconduct, irregularity or illegality, the court rendered judgment in favor of defendants, and refused to enjoin the runoff election. Later that day, petitioners asked this Court for a stay, which was denied. The runoff election, which Hall won, took place the next day, December 4. Petitioners filed an "expedited notice of appeal" on December 10.
1. Election results are presumed to be valid. Thus, "one challenging the results bears the burden of showing that the results are invalid due to an irregularity sufficient to place the entire election in doubt." McCranie v. Mullis, 267 Ga. 416, 478 S.E.2d 377 (1996). In this case, where the focus is on improperly cast ballots or irregularities in the conduct of the election, the number of illegal or irregular ballots necessary to cast doubt on an election is derived by taking the difference between the total votes cast in the election and the race at issue, and adding the margin of victory in the race at issue. Id., n. 5. Compare Mead v. Sheffield, 278 Ga. 268, 601 S.E.2d 99 (2004) (where alleged irregularity focuses on the ballots themselves, not the manner in which they were cast, the number of votes necessary to cast the result of the election in doubt is ascertained only by the margin of victory).
In Ward 2, a total of 792 ballots were cast. Out of those ballots, Bruce received 312 votes, Hall 204, Fuller 171, and Advincula 70. Thus, 757 votes were cast for the candidates in the Ward 2 race, a difference of 35 votes between the total number of ballots cast in Ward 2, and the number of ballots cast for the candidates. Adding that number to the number of votes needed by Fuller to gain a runoff spot, 33, it appears that Fuller needs to show 68 invalid ballots to cast doubt on the election.
In Ward 4, a total of 792 ballots were cast. Ruffin received 414 votes and Harris received 348 votes. Thus, 762 votes were cast for the candidates in the Ward 4 race, 30 less than the total number of ballots cast. Adding that number to the margin of victory in the race66we find that Harris needs to show 96 invalid ballots to cast doubt on the election.
Petitioners claim that (a) 23 absentee ballots were cast illegally because they were not marked to show that proper identification was presented; (b) 4 absentee ballots were illegally rejected on the ground that the voters failed to sign an oath stating that they would not be voting in person; and (c) 21 absentee ballot applications were received without anyone making a determination as to whether the applicants were eligible to cast the ballots. Adding these claims together, petitioners at best cast doubt upon 48 absentee ballots. Assuming, arguendo, that all 48 of these ballots are illegal, petitioners are still far short of showing that the results of the Ward 2 and Ward 4 races are in doubt.
Petitioners contend that other irregularities cast doubt on the election results. In this regard, they allege that Bruce, who used the name Michelle, misled voters into believing that he was a woman; that Ruffin campaigned at Riverdale's Fall Fest while he wore a campaign shirt; that the mayor and council failed to appoint a new manager for the November 6 election;[1] and that the absentee ballot clerk was appointed improperly. None of these alleged irregularities is specific enough to cast doubt on the *589 results of the election. See Middleton v. Smith, 273 Ga. 202, 203, 539 S.E.2d 163 (2000); Henderson v. County Bd. of Registration etc., 126 Ga.App. 280, 190 S.E.2d 633 (1972). "It is not sufficient to show irregularities which simply erode confidence in the outcome of the election. Elections cannot be overturned on the basis of mere speculation, [cit.], or an appearance of impropriety in the election procedures." Middleton, supra.
2. A jury trial is not required in an election case when the alleged irregularities are insufficient to put the results of the election in doubt. OCGA § 21-2-526(a); Henderson, supra at 285, 190 S.E.2d 633. The trial court did not err in denying petitioners' demand for a jury trial.
3. The results of a runoff election will not be set aside simply because the trial court, in its written order, neglected to state which candidates would be eligible to compete in the runoff. See OCGA § 21-2-527(a).
Judgment affirmed.
All the Justices concur.
NOTES
[1]  We note that, contrary to this assertion, the city council is not required to appoint a new election manager for each election. See OCGA § 21-2-90.
