Recent analyses of collective choice predict convergence among the outcomes of simple-majority decisions. I estimate the extent of convergence under restricted preference maximizing through a computer simulation of majority choice by committees in which individual decisions on proposal location and voting are constrained. The simulation generates distributions of majority-adopted proposals in two-dimensional space: nondeterministic outcomes of simple-majority choice. The proposal distributions provide data for a quantitative evaluation of the effects on convergence of relaxing conventional preference-maximizing assumptions. I find convergence of majority-adopted proposals in all cases, and that convergence increases under restricted proposal location. Moreover, under some voting restrictions, experiments yield stable outcomes that demonstrate remarkable convergence. I conclude that restricted preference maximizing generally increases the probability that simple-majority outcomes reflect the central tendency of member preference distributions. Since committees and legislatures are important formal procedures for democratic collective choice, this conclusion applies to a large class of political decisions.