Es decir, ejercerán su autoridad en toda el área electoral en general sin tomar en cuenta las subdivisiones políticas de ese territorio.

at large
chosen by or representing the whole of an area (as a state or a city) having political subdivisions rather than a particular district or other subdivision -- usually used in combination with a preceding noun

'in the Republican convention each state has four delegates-at-large -- W.S.Sayre

'a congressman-at-large'

Saludos desde Tenerife en Canarias,

V