I am trying to translate the English expression "left to their own
devices"/"left to themselves"/"in a vacuum" into Japanese, and the best I
could come up with would be something involving 「ひとりで」, but I am trying to
describe a group of people who I am treating as a unit (effectively 一族). Is
there any way to say "alone" when talking about a group of people (in this
case 四人), as in "without the influences/presence of an out-group"?
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translation idioms plurals
Equivalent of 【一人で】for a multi-person group unit
“独自{どくじ}に” might fit best. Other possibilities are “自分{じぶん}たちの裁量{さいりょう}で” or
“自力{じりき}で”. If you provide us a whole sentence, it would be easier to answer.
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After poking around I found this [webpage with a translation of 'left to his
own
devices'](http://ejje.weblio.jp/content/leave+a+person+to+his+own+devices).

To quote the site:

> (助言や援助を与えないで)人を思うようにさせておく

There are possibly other translations that could be used in context, but that
seems to be adequate as a general translation.

Other specific examples are:

> あの男は放任しておいたら酒を飲んで死んでしまう

If left to himself, he will drink himself to death. (Weblio)

> 気ままに園児を遊ばせる

Children are left to their own devices to play. (Linguee)

> 私をほうっておいて!

Leave me alone! (Weblio)

> ...監督が無いと.../...世話が不行届き...

Left to themselves (i.e. no supervision). (Weblio)

The best translation will depend on what fits with the whole sentence.
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Where ひとりで/1人で works, 4人で also should work. 4人だけで might be better if you want
to indicate 4人 is a small number. A more generic and neutral expression would
be 自分たちだけで, but I'm not sure if this is usable for the sentence you have in
mind. 孤立して or 隔絶して might be even better in certain contexts (e.g., living in
an desert island).
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