A decision on whether and how to rezone property is left to the sound discretion and good judgment of the elected officials.  The philosophy behind this thinking is that the decision to rezone or not to rezone is a legislative decision, and any recourse against a legislative decision should be at the ballot box. 

However, the protest petition allows citizens a more direct say in a rezoning decision at the time it is made. 

What they can do.  The protest petition law states, generally speaking, that if the owners of a sufficient amount of land most directly affected by a rezoning decision file a protest petition, the rezoning can be adopted only if it is approved by a three-fourths (3/4) majority of the municipality's governing board rather than the usual simple majority.  In other words, if a valid protest petition is filed -- and the rules are strict -- the voting requirement to pass a rezoning goes from a default simple majority to a super majority.

What they can't do.  Protest petitions can only be used to object to changes in the zoning map.  Protest petitions cannot be used to protest changes to the zoning ordinance text, nor can they be used to protest the initial zoning of a parcel or parcels of land, such as in the case of an annexation.  Moreover, protest petitions cannot be used to protest individual permits -- like special and conditional use permits -- nor can they be used to protest minor changes in special and conditional use districts or conditional zoning amendments.   

The law governing protest petitions is at NCGS 160A-385160A-386.

Why are we talking about the protest petition?

Well, they might go away.  And people are mad, or at least skeptical, as you can read herehere and here.

On March 25, 2015, the N.C. General Assembly's House passed HB 201.  The bill now goes to the General Assembly's Senate.  Entitled "An Act to Amend the Process By Which the City Councils Receive Citizen Input In Zoning Ordinance Amendments", if adopted in its current form, the proposed law will remove protest petitions from the statutory processes and the protest petition power will be removed from State law.

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"Please, sir.  Stop asking me about my 'frontage'."