While p-n homojunctions in two-dimensional transition metal dichalcogenide materials have been widely reported, few show an ideality factor that is constant over more than a decade in current. In this paper, electric double layer p-i-n junctions in WSe2 are shown with substantially constant ideality factors (2-3) over more than 3 orders of magnitude in current. These lateral junctions use the solid polymer, polyethylene oxide: cesium perchlorate (PEO:CsClO4), to induce degenerate electron and hole carrier densities at the device contacts to form the junction. These high carrier densities aid in reducing the contact resistance and enable the exponential current dependence on voltage to be measured at higher currents than prior reports. Transport measurements of these WSe2 p-i-n homojunctions in combination with COMSOL multiphysics simulations are used to quantify the ion distributions, the semiconductor charge distributions, and the simulated band diagram of these junctions, to allow applications to be more clearly considered.