We study the problem of designing multiwinner voting rules that are candidate monotone and proportional. We show that the set of committees satisfying the proportionality axiom of proportionality for solid coalitions is candidate monotone. We further show that Phragm\'en's Ordered Rule can be turned into a candidate monotone probabilistic rule which randomizes over committees satisfying proportionality for solid coalitions.

翻译：我们研究设计具有候选人单调性和比例性的多赢家投票规则问题。我们证明满足"团结联盟比例性"公理的委员会集合具有候选人单调性。进一步研究表明，Phragmén的有序规则可转化为候选人单调的概率规则，该规则在满足团结联盟比例性的委员会集合上进行随机化选择。