In Japanese, when you are making requests, it is polite to use forms such as… shite kuremasenka and … itdakemasenka, but in English we prefer not to use “Can’t you” and “Won’t you” in ordinary polite requests. Somehow these forms sound as if the person is pleading, rather than making a simple request.
When we use forms such as “Can you help me?” or “Could you give me a ride?” we are being polite by asking about “possibility.” In other words, we are not asking about the person’s will or desire, but merely whether it is “possible.” This allows the other person to reject the request not as a personal decision, but because of conditions that he or she cannot control. For example, “I would like to help you, but I can’t. I have to go to an appointment.” “I can’t give you a ride because my car is being repaired.” In other words, the situation is out of that person’s control.
With the words “will” and “would” we enter the realm of volition and personal will. “Will you help me?” skips the level of possibility and immediately asks for a personal decision. “Would you give me a ride?” is more polite than “Will you please give me a ride?” but it still goes directly to the person’s intention without allowing an intermediate step.
Therefore, when you are asking a friend for some small favor, it is perfectly all right to ask, “Will (Would) you do me a favor?” But if you are asking someone you do not know well, or a superior, and the request is larger, you should ask, “Can (Could) you do me a favor?” This allows the person to refuse without making it a personal refusal.
To make this a simpler, we have arranged different ways of making the same request in order of increasing politeness. The last is most polite.
Will you please bring me a newspaper?
Please bring me a newspaper.
Can you (please) bring me a newspaper?
Can you bring me a newspaper, please? I’d like to see the TV schedule.
Could you bring me a newspaper, please?
Would you mind bringing me a newspaper, please?
I wonder if you’d mind bringing me a newspaper, please?