前句讲什么样的人适合执政，这句公职人员的选拔方式，两句从不同的视角来佐证民主的本质。

Public officials shall be chosen not by votes, not by secret cliques pulling the unseen wires of democratic pretense, but by their own ability as demonstrated in the fundamental democracy of an equal race.
公职人员的选拔，不应通过投票，也不应由隐密的小团体借民主的幌子暗中操控，而是依据他们在机会平等的竞赛这一根本民主原则中所展现的自身能力来决定。

细节解析

1、clique: a small group of people who spend time together and who are not friendly to other people派系；小集团
He was withdrawn awkward and did not mingle easily with the theatrical clique.他性格孤僻，不善交际，不易与戏剧界的小圈子混在一起。《著名历史人物传记》
2、pulling the unseen wires of:高频表达，由“拉看不见的线”到“幕后操纵”。高频主要是因现实社会现象。
类似的表达有：“pull the invisible wires”“pull the string behind the scenes”
Many of Nikhil's officials were also secretly on our side, pulling the wires in our interest.Nikhil的许多官员也暗中站在我们这边，为我们的利益暗箱操作了。
3、pretense: a false reason or explanation that is used to hide the real purpose of something伪装
pretense与前面的hypocrisy相响应，均有点虚伪的意思。
He laughed at everything she did, encouraged her extravagances and insolences, jeered at her pretenses — and paid the bills.他笑她所做的一切，纵容她的挥霍无度与傲慢无视，还嘲讽她的矫揉造作——但所有开销都由他来买单。《飘》

所在段落

The Story of Philosophy《哲学的故事》第1章Plato第7节VI. The Political Solution第1段第4句：

Automatically — without any hypocrisy of voting. Democracy means perfect equality of opportunity, especially in education; not the rotation of every Tom, Dick and Harry in public office. Every man shall have an equal chance to make himself fit for the complex tasks of administration; but only those who have proved their mettle (or, in our myth, their metal), and have emerged from all tests with the insignia of skill, shall be eligible to rule. Public officials shall be chosen not by votes, not by secret cliques pulling the unseen wires of democratic pretense, but by their own ability as demonstrated in the fundamental democracy of an equal race. Nor shall any man hold office without specific training, nor hold high office till he has first filled a lower office well(Gorgias, 514-5).
浙江大学译本： 公共管理职位不应通过选举产生，不应让隐蔽的利益集团假借民主之名、行暗箱操控之实，而要以在这绝对平等的民主竞赛中展现出的真正实力来定夺。

上句见：Day433