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We examine the origin of electrons in a weakly outgassing comet, using Rosetta mission data and a 3D collisional model of electrons at a comet. We have calculated a new data set of electron-impact ionization (EII) frequency throughout the Rosetta escort phase, with measurements of the Rosetta Plasma Consortium's Ion and Electron Sensor (RPC/IES). The EII frequency is evaluated in 15-min intervals and compared to other Rosetta data sets. EII is the dominant source of electrons at 67P away from perihelion and is highly variable (by up to three orders of magnitude). Around perihelion, EII is much less variable and less efficient than photoionization at Rosetta. Several drivers of the EII frequency are identified, including magnetic field strength and the outgassing rate. Energetic electrons are correlated to the Rosetta-upstream solar wind potential difference, confirming that the ionizing electrons are solar wind electrons accelerated by an ambipolar field. The collisional test particle model incorporates a spherically symmetric, pure water coma and all the relevant electron-neutral collision processes. Electric and magnetic fields are stationary model inputs, and are computed using a fully kinetic, collision-less Particle-in-Cell simulation. Collisional electrons are modelled at outgassing rates of Q = 1026 s-1 and Q = 1.5 × 1027 s-1. Secondary electrons are the dominant population within a weakly outgassing comet. These are produced by collisions of solar wind electrons with the neutral coma. The implications of large ion flow speed estimates at Rosetta, away from perihelion, are discussed in relation to multi-instrument studies and the new results of the EII frequency obtained in this study.