Mikael Goldmann and Marek Karpinski. Simulating threshold circuits by majority circuits. A lower bound for monotone perceptrons. Ravi Kannan, H. Venkateswaran, V. Vinay, and Andrew C. Yao. A circuit-based proof of Toda's theorem.
Geometric arguments yield better bounds for threshold circuits and distributed computing.
On the computational power of depth-2 circuits with threshold and modulo gates. On the computational power of depth 2 circuits with threshold and modulo gates. Alexis Maciel and Toniann Pitassi. Vwani Roychowdhury, Kai-Yeung Siu, Alon Orlitsky, and Thomas Kailath. Vector analysis of threshold functions.