How exactly do しよう and しようか differ in usage?

Question

I personally consider the different usages of 「～しよう」 「～しようか」 「～しないか」 「～する」 「～してもいいか」 「～してください」 etc. one of the most difficult parts in Japanese grammar, alongside 敬語 and particles (e.g. は/が, で/に). It surprises me that there seemingly haven't been detailed discussions on this on our site. Several things stood out to me as I was reading a paper on the difficulty of these phrases and teaching the nuances of these phrases to Japanese learners——山下(2001), my primary source and the genesis of this question

安達(1995)や日本語記述文法研究会編(2003)では〈勧誘〉を次の表 3 のように、話し手と聞き手が共同で行為の実行をする「グループ型」と、話し手の行為に聞き手を引き込もうとする「引き込み型」に分けている。この中で「しようか」が「引き込み型」には使用できない例を以下に示す。

山下(2001), citing 安達(1995) and 日本語記述文法研究会編(2003), claims that, unlike 「～しよう」, 「～しようか」 can't be used as an invitation for the listener to join something that the speaker is already part of. But as @naruto points out in this answer, 「佐藤さんも入ろうか」 makes sense but sounds peremptory. I wonder how 山下(2001) and 安達(1995) differentiate between 「～しようか」 and 「～しよう」, and why they exclude 「～しようか」 from 引き込み型.

Is it because in this usage 「～しようか」 is stronger than 「～しよう」, crossing over into the domain of commands rather than an invitation? For example, a parent may say to their kid: 学校を休もうか

In 表４ the difference between 意志決定に伴う宣言 and 意志未定の表出 appears clear enough. So the source of confusion still lies with 勧誘(引き込み型).

The following seems to be a totally different usage where the speaker is making a suggestion that the listeners do something.

山下 did a survey with hundreds of native speakers (NS) and non-native speakers (NNS) where the subjects were asked to indicate how suitable some phrases are in certain contexts. In this example from 山下(2001),

試験が終わったら、お疲れ様会でも（　　　）

the vast majority (93%) of native speakers surveyed indicated their preference for しようか, in stark contrast to a much smaller group (20%) who went for しよう. Non-native speakers, on the other hand, were not able to tell that しようか was the most suitable term in this context.

Why is しようか preferred in this sentence?

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参考文献

• 山下由美子. "「しよう」「しようか」 の意味・用法: 日本語教育への提案." 創価大学大学院紀要= The bulletin of the Graduate School, Soka University 33 (2011): 299-327.
• ——————(2004)「「しよう」の意味・用法 ―〈非難〉・〈願望表出〉の「しようよ」」『日本語／日本語教育研究（ココ出版）』5, pp. 91-106

Answer 1

お疲れ会でもしよう would sound as if the professor is already pretty much determined to hold a party and expects the students to agree to join him. でも sounds a bit out of place in this case because the speaker already knows what they are going to have and there is no need to make it vague with でも. He would more likely say お疲れ会（を）しよう. This could be part of the reason more native speakers chose しようか than しよう.

By saying お疲れ会でもしようか, the professor is suggesting that they have a party (or something) together, but leaving the final decision to the students. It goes well with でも because whether what they are going to have is indeed お疲れ会 is less certain than in the first case. Someone might suggest an alternative.

The professor would be more embarrassed in the first case if the students refused his suggestion. The か (along with でも) could be seen as a hedge against this risk.

Between friends, お疲れ会でもしようよ would sound most natural. The final よ ensures the decision is a mutual one.

しようか sounds like a command, or even intimidation, when the listener has no choice under the given circumstances. This is not the case here or in the example of 学校を休もうか. In the latter, the parent is trying to convince the kid to agree to her suggestion by involving the kid in the decision, instead of unilaterally pushing her decision upon the kid.

Answer 2

Possibly the tag "提案" is misleading in the paper. In the suggestion of the professor, 行為者=SH and 受益者=SH/H and 決定権者=H, so it is actually 勧誘（グループ型）.

Between しよう and しようか, the presence of か makes it more explicit that the decision maker is the hearer, the students in the example. As such it sounds softer, and seems more appropriate because otherwise it sounds like a command (if implicit) from above (the professor).

On the other hand, お疲れ様会でもしよう sounds more friendlier, like the speaker and the hear(s) are on equal terms. So if the speaker is another student, しよう would be preferred.