*224 Nelson Esimar Martinez Manzanares ("Martinez") unsuccessfully applied for asylum, withholding of removal, and protection under the Convention Against Torture ("CAT"). He now asks us to review the government's decision and to vacate the removal order. We deny the petition.

I.

In May 2014, Martinez entered the United States near McAllen, Texas, without the necessary entry documents. The Department of Homeland Security ("DHS") began removal proceedings. Martinez applied for asylum, withholding of removal, and CAT protection. He argued he had suffered persecution in Honduras based on his membership in a particular social group related to his former work in law enforcement.

A.

Before an Immigration Judge ("IJ"), Martinez testified that he worked as a volunteer auxiliary police officer from 2005 to 2009 in the Honduran village of San Isidro, a small community located in the city of Victoria, in the department of Yoro. On May 14, 2009, he arrested Edwin Giovanni Megdoreta Montcodo, known as Edis, who was suspected of killing a man with a machete. Honduran authorities detained Edis for seventeen days before releasing him. According to Martinez, once released, Edis fled San Isidro for several years to avoid being tried and convicted for murder.

Nearly five years later, however, Edis returned to San Isidro. In January 2014, as Martinez was about to leave church, people informed him Edis was outside. When Martinez left the building, Edis pulled out a gun. Bystanders intervened, however, and "didn't allow [Edis] to do anything to [Martinez]."

About a month later, Edis threatened Martinez again. Martinez was driving with his uncle and brother when he saw Edis outside of a bar-like establishment. Edis yelled that he was going to kill Martinez, pulled out a gun, and fired shots at the car. The bullets missed Martinez and the car. Martinez then pulled out his own gun, and Edis fled.

Approximately two weeks later, on February 14, 2014, Martinez was riding a motorcycle to work when Edis emerged from tall grass with a shotgun. Edis pointed the shotgun at him. Martinez jumped into a nearby lake. When Edis approached the lake, Martinez swam away.

Martinez testified before the IJ that he never reported any of the incidents to the police because the Honduran police do "not function." Martinez did, however, report the first two incidents to a local mayor. Both times the mayor told Martinez that he could "take vengeance in [his] own hands" and that he "had the authority to kill [Edis] if [he] wanted to."

After the third incident, Martinez moved to an apartment in the building where he worked. When asked whether he had any more problems with Edis there, Martinez said no. He explained security guards protect the building so "nothing happens *225 there." For the remaining month and a half Martinez remained in Honduras, Edis did not bother him again. On April 4, 2014, Martinez left Honduras and traveled to the United States.

Martinez sought immigration relief based on persecution on account of membership in a particular social group. Specifically, Martinez alleged membership in three possible groups:

(1) ex-law enforcement officials of San Isidro, Victoria, Yoro, Honduras who are persecuted for having performed their law enforcement duties; (2) ex-law enforcement officials of San Isidro, Victoria, Yoro, Honduras who participated in the capture of [Edis]; and (3) ex-law enforcement officials of San Isidro, Victoria, Yoro, Honduras who participated in the capture of persons accused of committing a crime.

Resp't's Submission in Supp. of Appl., Ex. M. The IJ concluded these groups are not cognizable as particular social groups under the Immigration and Nationality Act ("INA"). But even if they were, the IJ determined Martinez failed to demonstrate persecution on account of membership in these proposed groups. It found Martinez "is not being singled out because of his status as a former law enforcement officer, but instead for his role in arresting a particular individual." Accordingly, the IJ denied relief.

B.

Martinez appealed to the Board of Immigration Appeals ("BIA"). The BIA dismissed, concluding the IJ correctly denied the asylum and withholding claims because Martinez failed to "show ... the requisite nexus between the harm he suffered and a protected ground for asylum or withholding of removal." Regarding the nexus requirement, Martinez admitted he had been harmed because of specific actions he took, not because he belonged to a certain group. Regarding the protected ground, Martinez failed to show his proposed social groups are "socially distinct groups in Honduras." The BIA additionally upheld the IJ's conclusion that Martinez did not show the Honduran government was unable and unwilling to protect him. It further noted Martinez did not suffer harm rising to the level of persecution.

The BIA likewise upheld the IJ's determination that Martinez did not qualify for CAT protection. It noted the Honduran police "initially arrested and detained Edis," and the mayor "effectively authorized" Martinez to kill Edis. Based on "these circumstances," the BIA concluded Martinez "did not show that it is more likely than not that he will be subject to mistreatment rising to the level of torture by Edis by or with the acquiescence of public officials in Honduras."

C.

Martinez petitioned this Court for review. But before the Court could reach the issues presented, Martinez and the government filed a joint motion to remand. The parties wanted the BIA to (1) explain the apparent assumption that Martinez's authorization to kill Edis made it less likely Martinez would suffer harm, (2) reconsider its reasoning regarding Martinez's failure to establish a particular social group and nexus, and (3) "consider whether the alleged harm suffered by [Martinez] 'rises to the level' of persecution." Over Judge Jones's dissent, the Court granted the parties' joint motion without discussion.

On remand, the BIA said the parties misinterpreted its original decision. Regarding the parties' first remand issue, the BIA said it did not assume permission to kill Edis made it less likely Martinez would be killed. The BIA explained the authorization to kill Edis was only one *226 basis for its conclusion that Martinez didn't establish the "Honduran authorities would acquiesce or be willfully blind to any harm inflicted on [Martinez] that rose to the level of torture." Regarding the second issue, the BIA declined to reconsider its analysis regarding Martinez's alleged group because, "regardless of whether former Auxiliary Policemen constitute a cognizable particular social group, [Martinez] did not show that he was harmed on account of his membership in that group." Finally, regarding the third issue, the BIA explained it properly concluded Martinez's harm did not rise to the level of persecution despite the IJ's failure to make that explicit finding. It further noted that conclusion was ultimately immaterial because Martinez could not connect any alleged persecution to a protected ground. Therefore, the BIA again dismissed Martinez's appeal. Martinez again petitioned this Court for review.

II.

We review the BIA's decision; we consider the IJ's decision only to the extent it influenced the BIA. See Nunez v. Sessions , 882 F.3d 499 , 505 (5th Cir. 2018) (per curiam). We will reverse the BIA's factual determinations "only if the evidence is so compelling that no reasonable fact finder could fail to find the petitioner statutorily eligible for relief." Qorane v. Barr , 919 F.3d 904 , 909 (5th Cir. 2019) (quotation omitted). In contrast, we "review[ ] the BIA's legal determinations de novo." Ghotra v. Whitaker , 912 F.3d 284 , 288 (5th Cir. 2019).

We begin by addressing Martinez's claims for asylum and withholding of removal before turning to his CAT claim. We deny the petition on each ground.

A.

To be eligible for asylum, Martinez must establish he is a refugee. 8 U.S.C. § 1158 (b)(1)(B)(i). That requires showing "[past] persecution or a well-founded fear of [future] persecution on account of ... membership in a particular social group." Id. § 1101(a)(42)(A). Similarly, to obtain withholding of removal, he must show his "life or freedom would be threatened" in Honduras "because of ... membership in a particular social group." Id. § 1231(b)(3)(A); accord 8 C.F.R. § 208.16 (b).

1.

A "particular social group" must be "a group of persons [who] share a common immutable characteristic that they either cannot change or should not be required to change." Hernandez-De La Cruz v. Lynch , 819 F.3d 784 , 786 (5th Cir. 2016) (quotation omitted). Furthermore, the relevant society must "perceive those with the characteristic in question as members of a social group" (social distinction), and the proposed group must be a limited, "discrete class of persons" (particularity). Id. at 786-87 .

We doubt any of Martinez's proposed groups qualify as a particular social group. After all, "[w]hen the harm visited upon members of a group is attributable to the incentives presented to ordinary criminals rather than to persecution, the scales are tipped away from considering those people a 'particular social group' within the meaning of the INA." Ucelo-Gomez v. Mukasey , 509 F.3d 70 , 73 (2d Cir. 2007) (per curiam).

At least one proposed group, "ex-law enforcement officials of San Isidro, Victoria, Yoro, Honduras who participated in the capture of [Edis]," is clearly not cognizable. As the BIA noted, there is no record evidence this group is socially distinct. Likewise, it is not clear from the record that anyone other than Martinez *227 would fall into that group. But a "particular social group " necessarily requires "more than one person." Fatin v. INS , 12 F.3d 1233 , 1238 (3d Cir. 1993) (Alito, J.) (emphasis added); see also Memoglu v. Holder , 556 F. App'x 52 , 53 (2d Cir. 2014) (summary order) (concluding a proposed social group of one "lacks the requisite social visibility").

2.

Even if Martinez's proffered groups are cognizable, substantial evidence supports the BIA's determination that Martinez failed to show a nexus between the alleged persecution and his membership in the groups.

To show persecution was "on account of" a protected ground for asylum and withholding of removal, Martinez must prove the protected ground was "at least one central reason" for the persecution. 8 U.S.C. § 1158 (b)(1)(B)(i) ; Revencu v. Sessions , 895 F.3d 396 , 402 (5th Cir. 2018). The protected ground "cannot be incidental, tangential, superficial, or subordinate to another reason for harm." Shaikh v. Holder , 588 F.3d 861 , 864 (5th Cir. 2009) (quotation omitted).

Martinez did not make this showing. He never once stated Edis persecuted him because he was an ex-law enforcement officer. Instead, all the testimony demonstrates Martinez was targeted because of his specific involvement in Edis's arrest, not his general status as an ex-law enforcement official. Martinez testified that Edis "retaliated against [him]" because he "turned [Edis] over to the authorities." He also described the threats as being "personal, because [he] captured and arrested [Edis] some time back."

Persecution motivated by a personal vendetta or desire for revenge is not persecution "on account of" a protected ground. See Hernandez-Rivera v. Sessions , 721 F. App'x 401 , 402 (5th Cir. 2018) (per curiam) (agreeing applicant did not establish nexus when persecution was based on "revenge," not applicant's "former police officer" status); Sanjaa v. Sessions , 863 F.3d 1161 , 1165 (9th Cir. 2017) ("The personal retribution [applicant] suffered ... because of his role in the drug-trafficking investigation is not cognizable under the INA."); Marin-Portillo v. Lynch , 834 F.3d 99 , 101 (1st Cir. 2016) (concluding no nexus when threats were motivated by "a personal dispute"); Rodriguez-Leiva v. Holder , 607 F. App'x 807 , 810-11 (10th Cir. 2015) (concluding a witness to a murder "was targeted by criminals because he posed a threat to their interest in avoiding prosecution," not "on account of his social status"); Costa v. Holder , 733 F.3d 13 , 17 (1st Cir. 2013) (concluding persecution based on a "personal vendetta" is "not due to ... membership in a social group"); Ayala v. Holder , 640 F.3d 1095 , 1098 (9th Cir. 2011) (per curiam) (concluding persecution based on prior arrest of a drug dealer "is not cognizable under the INA"); Pavlyk v. Gonzales , 469 F.3d 1082 , 1088-89 (7th Cir. 2006) (concluding applicant cannot demonstrate nexus when "persecution stemmed from his conduct in [two] particular investigations").

At most, Edis's desire for retribution is only tangentially related to Martinez's status as an ex-law enforcement officer. Martinez thus cannot show he was persecuted on account of that status. See Shaikh , 588 F.3d at 864 .

Martinez attempts to escape this conclusion by relying on Madrigal v. Holder , 716 F.3d 499 (9th Cir. 2013). Of course, that decision is not binding on us, and in any event, it's readily distinguishable. In that case, the Ninth Circuit concluded the applicant established a nexus between a protected *228 ground and persecution because, "even if revenge partially motivated [the gang members'] mistreatment of him, the record makes clear that their desire to intimidate members of his social group was another central reason for the persecution." Id. at 505-06 . Martinez offered no similar evidence that Edis had a reason for threatening him other than revenge, much less another central reason.

And even if we disagreed with the agency's factual conclusion that Edis was motivated by personal reasons, we still could not say "a reasonable factfinder would be compelled to conclude to the contrary." See Thuri v. Ashcroft , 380 F.3d 788 , 793 (5th Cir. 2004) (per curiam). Because substantial evidence supports the BIA's conclusion that Martinez didn't show the alleged persecution was "on account of" a protected ground, he is not entitled to asylum or withholding of removal.

B.

We turn now to whether Martinez established his eligibility for CAT protection. To be eligible for CAT relief, Martinez must show it is "more likely than not" he will be tortured if he returns to Honduras. Tamara-Gomez v. Gonzales , 447 F.3d 343 , 350 (5th Cir. 2006). In assessing whether Martinez has made this showing, we look for record evidence regarding any past torture he suffered, whether he could relocate within Honduras to avoid torture, and relevant conditions in Honduras, such as whether there are flagrant human rights violations. See Zhang v. Gonzales , 432 F.3d 339 , 345 n.4 (5th Cir. 2005) (citing 8 C.F.R. § 208.16 (c)(3) ).

Moreover, an applicant must demonstrate there would be "sufficient state action involved in that torture" to be eligible for CAT relief. Tamara-Gomez , 447 F.3d at 351 . That's because torture is defined to include only "pain or suffering ... inflicted by[,] at the instigation of[,] or with the consent or acquiescence of a public official or other person acting in an official capacity." 8 C.F.R. § 208.18 (a)(1).

Substantial evidence supports the BIA's denial of CAT relief. Even if Edis threatened Martinez with a sufficiently "extreme form of cruel and inhuman treatment" to constitute torture, id. § 208.18(a)(2), Martinez failed to show it was "more likely than not" he will be tortured if he returns to Honduras, id. § 208.16(c)(2). For starters, the record demonstrates it is likely he could relocate within Honduras to avoid Edis's mistreatment. See id. § 208.16(c)(3)(ii). Indeed, before he left Honduras, he was able to avoid Edis for a month and a half by relocating a short distance away, close to where he worked. See Ramirez-Mejia v. Lynch , 794 F.3d 485 , 494 (5th Cir. 2015) (agreeing torture was not likely when evidence suggested "any danger of harm could be mitigated through relocation" because a family member had "not been harmed since moving to another part of Honduras").

Martinez also failed to show he suffered past torture. See 8 C.F.R. § 208.16 (c)(3)(i). The record evidence does not prove public officials acquiesced to any pain or suffering inflicted by Edis. Before the IJ, Martinez testified he never reported Edis's threats to the police. Nevertheless, he argues in his brief that the Honduran government was "willfully blind" to his persecution, because the "Mayor failed to mobilize law enforcement or do anything to protect [him]." Martinez offered no testimony, however, showing the mayor of his community could mobilize the police. Nor did Martinez testify that he asked the mayor to have the police investigate the incident-much less that the mayor refused. Instead, he asks this Court to infer the "Mayor of San Isidro is akin to the mayor *229 of a city in the U.S." with "the authority to mobilize the local police." Even if these are reasonable inferences, the IJ and BIA were not required to draw them. See Siewe v. Gonzales , 480 F.3d 160 , 167 (2d Cir. 2007) ; Tesfamichael v. Gonzales , 469 F.3d 109 , 117 (5th Cir. 2006).

Furthermore, Martinez provided evidence demonstrating public officials did not consent to previous harm Edis caused, but rather attempted to combat it. See Chen v. Gonzales , 470 F.3d 1131 , 1142 (5th Cir. 2006) (noting it is proper to consider government efforts "to combat [criminal activity] in the willful blindness inquiry"). He testified the Honduran authorities detained Edis for seventeen days on suspicion of murder in 2009. And they were planning to prosecute Edis-or at least Edis believed they were, because he fled for nearly five years to avoid it. Record evidence also indicates Honduras had been taking steps to reform its criminal justice institutions and better "tackle the crime situation."

At most, Martinez demonstrated Honduras was unable to provide Martinez and other citizens complete protection from criminals like Edis. But that does not suffice because "a government's inability to protect its citizens does not amount to acquiescence." Qorane , 919 F.3d at 911 ; see also Miah v. Mukasey , 519 F.3d 784 , 788 (8th Cir. 2008) (explaining "evidence that Bangladeshi officials have been unable to control the activities of [a] criminal gang" is "insufficient to compel a finding of willful blindness toward the torture of citizens by third parties" (quotation omitted)); Tamara-Gomez , 447 F.3d at 351 (concluding "neither the failure to apprehend the persons threatening the alien, nor the lack of financial resources to eradicate the threat or risk of torture constitute[s] sufficient state action for [CAT] purposes").

The record evidence does not compel the conclusion that Martinez was eligible for CAT relief.

The petition is DENIED.