1. The government official can hardly find sufficient grounds on which to base in his arguments in favor of the revision of the tax law.

——这个句子，base 是不及物动词，加介词on 后才可接宾语。base on which = base on sufficient grounds。例如：

Fluctuating prices usually base on a fickle public's demand.  

物价的波动往往是由于群众需求的不稳定而引起的。

来自《现代英汉综合大词典》

注意：in his arguments “在他的论点中”，in 不可去掉。his arguments 不是base 的宾语。

【直译】这位政府官员很难找到在支持修改税法的论点时所依据的充分理由。

2. We can't make a decision based on hearsay and guesswork.

——based on hearsay and guesswork，是过去分词短语作定语，修饰a decision；相当于一个定语从句：which is based ...    这时 base 是及物动词，主动语态是：base a decision on hearsay and guesswork。被动语态是：a decision is based on hearsay and guesswork.

这个句子比较特殊。在结构上，based on hearsay and guesswork 是过去分词作定语。在理解时，based on hearsay and guesswork 按照方式状语翻译。即：

【翻译】我们不能根据传闻和猜测作出决定。