Although the candidate (made promises) both to cut taxes and improve services,he failed to keep either of them after the

前提：我是凭读出来的感觉得出这个结论的,大致上应该是这样,希望能帮到你（由于我不是很会用文字来表达所以希望你能了解我在说什么）
假如要用promised就要去掉both.
Although the candidate made promises both to cut taxes and improve services,he failed to keep either of them after the election.
尽管候选人曾做出不仅要减税而且还要改善服务的承诺,（但）在选举后他却无法履行其中的一个.
在这句话中both为连词,即为“不仅...而且...”
除了promise to do sth以外,promise有一种用法为promise sb to do sth.
而除了连词both亦可作为代词,表示“两者”
因此promised both to将被理解为“允诺两者要（做某事）”
both作为代词时的例句：
Both are to blame
Orz...==...终于解释完了...被搞得有点头晕了...
P.S.另一个问题我po上另一个英语论坛了,等看有没有消息