An elected official who votes the way his or her constituents would want is a delegates.
A paradigm of a representative democracy is the delegate system of representation. In this setup, voters choose their representatives to serve as delegates on their behalf. These delegates solely serve as a spokesperson for their state's or constituency's desires, and the only autonomy they enjoy is the right to vote for the state's actual representatives.
Representatives under this arrangement are constrained by mandatory mandates and do not have the luxury of acting in accordance with their conscience. In essence, the representative speaks for people who are (literally) absent.
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