A 3.65-approximately stable committee always exists in approval-based elections and can be computed using a Lindahl equilibrium and a strongly Rayleigh distribution.
Foley, Lindahl's solution and the core of an economy with public goods, Econometrica 38 (1970), 66--72
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Computation of Approximately Stable Committees in Approval-based Elections
A 3.65-approximately stable committee always exists in approval-based elections and can be computed using a Lindahl equilibrium and a strongly Rayleigh distribution.