The defendant, the Town of Sanbornton (town), appeals from an order of the Superior Court (Perkins, J.) denying the town’s motion for summary judgment and allowing the plaintiffs to proceed on collective petitions. See RSA 76:17 (Supp. 1999)(amended 2002). Additionally, the town appeals from an order of the Superior Court (McHugh, J.) on the merits, rescinding the town’s reassessment of the plaintiffs’ properties and abating in full the taxes previously paid on those properties. We affirm in part and reverse in part.
The plaintiffs are 125 owners of waterfront properties bordering Lake Winnisquam. On July 26, 1999, at a meeting of the board of selectmen (board), the board determined, based upon the recommendation of the town’s assessor, Scott Littlefield, that it would reassess the plaintiffs’ properties upward by 14%.
At a subsequent meeting on August 23, numerous property owners challenged the reassessment. Littlefield explained his reasoning for the reassessments, reviewed figures that demonstrated that the assessed values on Lake Winnisquam were at 81% of market value, and pointed out that other sections of the town were at 94% of market value.
The board reviewed the assessments at another meeting held on September 7. At the meeting, David McLaughlin, a lakefront property owner who was not an expert on methods of assessing property, spoke on behalf of the property owners. He presented figures that he had compiled that “led him to believe that those figures used by the selectmen to reach their decision of a 14% increase in waterfront values was [sic] incorrect.” Littlefield then explained the procedure he used that “showed the [waterfront properties] as being 20% under accessed [sic] at present.” The *366board discussed the situation with the property owners and voted to rescind the 14% increase. The board stated, however, that “if the figures presented by Mr. McLaughlin to refute those of Mr. Littlefield, did not when evaluated do so, the board would again vote in an increase.”
The board met with Littlefield again on September 13 and September 20 to review the discrepancies that had developed concerning the waterfront properties. Littlefield told the board that he had reviewed the assessment figures offered by McLaughlin and advised the board of several areas where McLaughlin’s sales or assessed values were incorrect. Littlefield also reported that he had revisited the 1999 sales, including new sales completed after the original evaluation, and indicated that based upon his re-analysis of all 1999 sales, the waterfront properties were assessed at 78% to 79% of market value. On September 27, the board convened a meeting that many of the property owners attended. Littlefield recommended that the board increase the assessment on the waterfront properties between 16% and 18%. The board reconvened on September 29 and increased assessments of the waterfront properties by 18%.
The plaintiffs filed a single petition for abatement pursuant to RSA 76:17, contending that the 18% across-the-board increase caused their assessments to be disproportionate compared to the assessments of property of other classes of owners within the town. Originally, all of the plaintiffs joined in the petition. Some plaintiffs, however, had not filed inventories with the town. They were removed from the original petition and filed a new petition for abatement for the following year. The two cases were consolidated for trial. The trial court allowed all 125 plaintiffs to proceed on two petitions for abatement.
Littlefield was unavailable to testify at trial because of serious illness. The town, instead, offered the testimony of Gregory Heyn, who had replaced Littlefield as the town’s assessor. Although Heyn was unable to reconstruct Littlefield’s exact methodology, he offered his own methodology to support the 18% increase.
The plaintiffs offered Russell Thibeault, an experienced real estate appraiser and consultant on assessment issues, who testified about what he claimed were flaws in the town’s methodology. The trial court found his testimony persuasive, and ruled that the assessment was disproportionate, under RSA 76:17, because it lacked a sound methodology, was arbitrary and lacked a good faith basis.
On appeal, the town argues that RSA 76:17 requires each individual property owner to file a petition for abatement. All parties agree that the town may collectively reassess property. See RSA 75:8 (1991)(amended 2001). The plaintiffs, however, argue that because the town undertook a *367collective reassessment, they should be allowed to collectively challenge the reassessment.
On questions of statutory interpretation, we are the final arbiter of the legislature’s intent as expressed in the words of a statute considered as a whole. In re Baby Girl P., 147 N.H. 772, 775 (2002). It is well established that the intention of the legislature expressed by the words in the statute itself is the touchstone to its meaning. Id.
RSA 76:17, discussing abatements, provides that “if the selectmen neglect or refuse so to abate, any person aggrieved ... may ... apply by petition to the superior court... which shall make such order thereon as justice requires.” The town argues that the phrase “any person” should be interpreted in the singular and restricts the plaintiffs to bringing only individual petitions. RSA 21:3 (2000), however, states that “[w]ords importing the singular number may extend and be applied to several persons or things.” See also RSA 21:1 (2000).
Individually, each plaintiff meets the statutory requirements for petitioning the court under RSA 76:17. The town does not argue that it suffered any prejudice from the plaintiffs bringing their multiple petitions as two collective petitions. Finally, if the plaintiffs had brought 125 separate petitions, the trial court could have consolidated them for trial because they “share the same issues of fact or law,” 5 R. WlEBUSCH, NEW Hampshire Practice, Civil Practice and Procedure § 42.02, at 268 (1998), and nothing in RSA chapter 76 prevents consolidation.
Having determined that the trial court correctly allowed the plaintiffs to proceed on two petitions, we turn to the town’s argument that the trial court improperly ruled that the 18% increase was disproportionate without requiring the plaintiffs to establish that their tax burdens were individually disproportionate. The plaintiffs, by contrast, argue that they should be allowed to prove disproportionality by demonstrating that: (1) the town’s reassessment lacked a sound methodology; or (2) the town acted in an arbitrary fashion and lacked good faith.
New Hampshire tax abatement statutes provide the exclusive remedy to a taxpayer dissatisfied with an assessment. LSP Assoc. v. Town of Gilford, 142 N.H. 369, 374 (1997). To succeed on their tax abatement claim, the plaintiffs have the burden of proving by a preponderance of the evidence that they are paying more than their proportional share of taxes. Society Hill at Merrimack Condo. Assoc. v. Town of Merrimack, 139 N.H. 253, 254 (1994).
*368To carry the burden of proving disproportionality, the taxpayer must establish that the taxpayer’s property is assessed at a higher percentage of fair market value than the percentage at which property is generally assessed in the town. Appeal of Town of Sunapee, 126 N.H. 214, 217 (1985). The plaintiffs produced no evidence regarding the fair market value of their properties. Rather, they attempted to prove disproportionate tax burdens by demonstrating that the town employed a flawed method.
The right to tax abatement and the powers of the superior court in such proceedings are dictated solely by statute. LSP Assoc., 142 N.H. at 373; see RSA 76:17. RSA 76:17 authorizes the superior court in an abatement proceeding to “make such order thereon as justice requires.” This statute confers broad discretion and equitable powers upon the superior court to abate taxes. LSP Assoc., 142 N.H. at 373.
However, the powers of the superior court are not unlimited. See id. at 374. We have long held that however erroneous, in law or in fact, the assessment may be, we will abate only so much of a taxpayer’s tax as in equity the taxpayer ought not to pay. Edes v. Boardman, 58 N.H. 580, 586 (1879). This principle necessarily follows from the language of the statute that commands the abatement of a taxpayer’s taxes as justice requires. Id. Justice requires that an order of abatement will not relieve the taxpayer from bearing his or her share of the common burden of taxation despite any error in the process of determining the amount of that share. Id.
The plaintiffs rely upon Duval v. Manchester, in which we stated that establishing the property’s fair market value is not the only means of proving disproportionality. Duval v. Manchester, 111 N.H. 375, 376 (1971). The plaintiffs contend, and the trial court found, that Duval stands for the proposition that they may prove disproportionate tax burdens by establishing that the town lacked a sound methodology when it established the assessment.
In Duval, the defendant, the City of Manchester, chose to reassess properties as they were sold. Id. In doing so, the defendant failed to reassess properties that were not sold. Id. The result was that 50% to 60% of the properties within the city had not been reassessed for over twenty years. Id. The plaintiffs in Duval proved a disparity between their recently sold property, which was assessed at 40% of its value, and other city properties that remained assessed between 20% to 30% of their value. Id. As a result, we found that the plaintiffs had established disproportionality. Id.
*369In Duval, no one contended that the city did not correctly assess the plaintiffs’ property. Rather, we found disproportionality between those properties that had been recently sold and those properties that had not been sold for more than twenty years. Thus, Duval does not address the methodology that the city used to reassess the plaintiffs’ property; rather, Duval stands for the proposition that taxpayers must prove that they are being required to pay more than their proportionate share of taxes. Id.
In the present case, the trial court impermissibly allowed the plaintiffs to prove disproportionality by establishing that the town could have used a more reliable methodology. While it is possible that a flawed methodology may lead to a disproportionate tax burden, the flawed methodology does not, in and of itself, prove the disproportionate result. Thus, even if multiple petitions are consolidated into a single trial, each plaintiff bears the burden of demonstrating that he or she is paying a higher amount than he or she ought to pay. See Edes, 58 N.H. at 586; Duval, 111 N.H. at 376.
The trial court focused upon the methodology that the town used to arrive at its assessment value, and not upon the actual harm. See Sunapee, 126 N.H. at 217; Sirrell v. State, 146 N.H. 364, 383 (2001). Thus, the trial court erred as a matter of law in ruling that the plaintiffs were entitled to an abatement of their assessments under RSA 76:17.
We next turn to the trial court’s finding that the town lacked good faith and acted in an arbitrary manner when reassessing the plaintiffs’ properties. Like other findings of fact, findings of bad faith and arbitrariness can be set aside on appeal only if they are unsupported by the evidence or erroneous as a matter of law. See In re Estate of Bennett, 149 N.H. 496, 498 (2003).
The trial court found that the 18% reassessment was in retaliation for the taxpayers’ challenge of the initial 14% increase, and, thus, made in bad faith. We presume that boards act in good faith and in conformity with the requirements of law. See Frank v. Assessors of Skowhegan, 329 A.2d 167, 171 (Me. 1974). Bad faith involves more than mere bad judgment or negligence. See Spiegel v. Beacon Participations, 8 N.E.2d 895, 907 (Mass. 1937). Bad faith implies conscious wrongdoing. See id. To carry the heavy burden of proving bad faith in this context, one must demonstrate intent to injure or intent to disregard duties. Cf. Indian Head Nat'l Bank v. Corey, 129 N.H. 83, 87-88 (1986).
The record presented on appeal does not support the trial court’s finding of bad faith. The evidence demonstrates that the board relied upon the recommendations of Littlefield, an expert, in making its original *370decision to increase the assessments by 14%. The board, on the basis of the objections of the property owners, then rescinded that decision, but informed the waterfront property owners that if the evidence they presented did not refute Littlefield’s figures, it would again vote in an increase.
The trial court focused upon Littlefield’s statement to the property owners at the September 7 meeting that his figures indicated that the waterfront properties may be under-assessed by as much as 20%. The trial court concluded that when the plaintiffs challenged the 14% reassessment, Littlefield responded with a threat, thus demonstrating retaliatory intent. The record demonstrates that this was not the case. Littlefield’s statement is consistent with his previous position on August 23 that the waterfront properties were assessed at 81% of fair market value or approximately 20% under-assessed. Indeed, given that the waterfront properties were at 81% of fair market value, the 14% figure chosen by the board was conservative.
The 18% increase was also conservative. By the time the board made its decision to reassess the waterfront properties upward to 18%, Littlefield’s new figures showed that the properties were at 78% to 79% of fair market value. This explains the change from Littlefield’s recommendation of a 14% increase to a recommendation of a 16% to 18% increase. The board conducted a de novo review of the reassessment and was not bound by its previous decision to increase the assessment by 14%. Thus, given the new evidence presented, it was within its discretion to reassess the properties at 18% instead of the original 14%.
At trial, selectman Evelyn Auger stated that she “leaned most heavily on [Littlefield’s] recommendations.” Auger also stated that she “personally ... went over the figures ... but [that] his [recommendation had] the greatest weight.” The record does not contain any evidence that the board intentionally disregarded its duties or intentionally injured the plaintiffs. We find that, in light of the evidence presented, the trial court unreasonably inferred that the 18% increase was in retaliation for the property owners having challenged the 14% increase.
Finally, we review the trial court’s finding that the town acted in an arbitrary fashion. Arbitrary action is: (1) action arising from the unrestrained exercise of the will, caprice, or personal preference; or (2) based upon random or convenient selection or choice, rather than reason or nature. See Webster’s Third New International Dictionary 110 (unabridged ed. 1961).
*371The trial court found arbitrariness because it decided that the board had acted in a retaliatory manner and that the town was unable to explain Littlefield’s methods at trial. We have already concluded that the board did not act in retaliation. We turn, then, to the inability of the town to explain the exact method employed by Littlefield.
To carry the heavy burden of proving arbitrariness one must demonstrate more than poor methodology. The record shows that after agreeing to rescind the 14% increase, the board met three times before deciding upon the 18% increase. Moreover, it is clear that the board gave due consideration to both its initial decision to increase the assessments by 14% and its final decision to increase the assessments by 18%. The board did not choose 18% randomly or out of convenience; nor did its selection depend upon willfulness. Instead, the board relied heavily upon Littlefield’s recommendations when determining the assessments, for as selectman Auger herself stated, “He was the expert.” Although the town could not explain with precision Littlefield’s methodology, and while the record demonstrates that Littlefield could have employed a more reliable method, the board’s reliance upon Littlefield does not demonstrate arbitrariness.
We presume that assessments are conclusive in the absence of fraud, bad faith, or arbitrariness and place the burden on the taxpayer to show that the assessments made against his or her property are disproportionate. Nash Family Inv. Prop. v. Town of Hudson, 139 N.H. 595, 600-01 (1995). A finding of fraud, bad faith, or arbitrariness does not prove a disproportionate tax burden, see In re Appeal of Greens of Pine Glen Ltd., 576 S.E.2d 316, 319 (N.C. 2003), because a taxpayer must prove that he or she is paying more than he or she ought to pay. See Edes, 58 N.H. at 586; Duval, 111 N.H. at 376.
We note, however, that even if the board had acted in bad faith or arbitrarily the inquiry would not have ended there. In cases in which the town has increased a taxpayer’s assessment, a finding of fraud, bad faith, or arbitrariness provides sufficient evidence to shift the taxpayer’s burden of production to the town to produce evidence that demonstrates that, even with a finding of illegitimate action, the assessment is proportionate and the taxpayer has suffered no damages. If the town fails to produce evidence demonstrating proportionality then the taxpayer will be deemed to have met his or her burden of proof and the old assessment will remain in effect until and unless a new assessment is done correctly. If the town meets its burden of production, the burden shifts back to the taxpayer to *372produce evidence, aside from the evidence of illegitimate action, to demonstrate a disproportionate tax burden. If the taxpayer proves a disproportionate tax burden then the amount of the increase will be abated by the amount that is disproportionate. See RSA 76:17.
Affirmed, in part; reversed in part.
Brock, C.J., and Broderick, Nadeau and Duggan, JJ., concurred.