In the context of a probabilistic voting model with dichotomous choice, we investigate the consequences of choosing among voting rules according to the maximin criterion. A voting rule is the minimum number of voters who vote favorably on a change from the status quo required for it to be adopted. We characterize the voting rules that satisfy the maximin criterion as a function of the distribution of voters' probabilities to favor change from the status quo. We prove that there are at most two maximin voting rules, at least one is Pareto efficient and is often different to the simple majority rule. If a committee is formed only by "conservative voters" (i.e. voters who are more likely to prefer the status quo to change) then the maximin criterion recommends voting rules that require no more voters supporting change than the simple majority rule. If there are only "radical voters", then this criterion recommends voting rules that require no less than half of the total number of votes. © Springer-Verlag 2005.