What does のに比べて mean? In "一人の相手を幸せにするのに比べて"


> 一人の相手を幸せにするのに比べて、倍の時間を彼女のために使える必要があるはず

Compared to giving only one of your partner happiness, you need twice the time
to make your partners happy.

  * Is this の used as a nominalizer?
  * Can の be replaced with こと?




That の is a nominalizer in the sense that it plays the grammatical function of
turning the verb phrase 一人の相手を幸せにする into a noun phrase, just like the の in,
say, 本を読むのが好きです. However, the resulting noun phrase seems to have a more
specific meaning than 一人の相手を幸せにする **こと** , which refers to the act of making
one person happy in general and abstract terms.

Your sentence has no subject or topic, but we can assume it to be a person
because of 使える. It’s _you_ (or someone else) who must be **able to spend**
twice as much time, not the act of making other people happy. For this reason,
the following sentence would sound unnatural (to me, at least).

> （二人の相手を幸せにすることは）一人の相手を幸せにする **こと** に比べて、倍の時間を彼女のために使える必要があるはず。

This would compare one act against another, but the sentence would end up with
a mismatching predicate.

The original sentence must be something like the following in its complete
form.

> （（あなたが）二人の相手を幸せにする（ため）には）一人の相手を幸せにする **の** に比べて、倍の時間を彼女のために使える必要があるはず。

This basically compares two amounts of time or efforts. I would translate
一人の相手を幸せにするの as something along the lines of “the **time** you need to spend
to make one person happy” and this translation is not possible with こと.

In comparison, the following seem both acceptable as the predicate is
matching.

> （二人の相手を幸せにするのは）一人の相手を幸せにする **の** に比べて、倍の時間を要するはず。

> （二人の相手を幸せにすることは）一人の相手を幸せにする **こと** に比べて、倍の時間を要するはず。



  * Yes, this の is a nominalizer.
  * Yes, this の can be replaced with こと.

So is this person talking about how to do 二股? Please always explain the
context when you present a sentence based on an unusual context. Also, note
that 一人の相手 here is "one girl", not "one of your partners" (see
[this](https://japanese.stackexchange.com/q/36012/5010)). Translating 相手 as
"partner" is often misleading (see
[this](https://japanese.stackexchange.com/q/66456/5010)).

