How would you convince someone to do something they didn't want to do?

First, thanks for invitation.

On job level,this situation is perceived under the concept of "open allocation" . Basically, this theory assumes that you let people pick what they want to work on, and when you get to the stuff that no one wants to do, you have to provide incentives to get it done. Nevertheless, from my view everyone has a different "currency", and it's not always cash (nor does it always have a cash equivalent). Even so, If you're picked your team correctly, there will be a spirit of "we're all in this together" and someone will step forward because if they don't, it all goes down the tubes.

This thing rest on someone's convincing power. If someone didn't want to do it then try to state first the advantages and  benefits that it would cause him/her if the task is completed. Approach him/her in a friendly manner and avoid being bossy otherwise it might irritate him.her and would end up refusal to perform the job. Just try to be nice, after all you need him/her to get the job done. 

Thanks for your invitation.

If the individual is not willing to do the task means he should have grievances  related to official / personnel. This needs to be identified.  He has to be handled very nicely also he should not get disturbed others. When we came to know immediately to be counseled and advised to do his role. If its getting failed, needs to be taken disciplinary action to improve the situation. 

I wouldn't try to convince someone to do something they don't want to do. There is no point of getting in an argument and whoever has more power will win. I involve the people I manage or I work closely with in a team setting in the decision making and goal setting process so they have ownership of the work and I won't have to convince them later to do stuff they don't want to do. 

I have to explain the purpose of having this task done

Unify the vision of your team and your team

Hear their reason of rejection

At the end we have to accept the right point of view

It’s pretty darn hard to convince someone to do something he or she doesn’t want to do. Also, pretty frustrating. Maybe your colleague doesn’t want to work on a certain part of your joint project, meaning you get stuck doing the entire thing. Or, maybe your boss wants to go in a totally different direction for the client presentation you’re giving. Nine times out of 10, you're going to end up going with her vision.

Or, maybe not. Persuasion expert Dan Pink brings up two questions that, when used together, are dramatically effective in persuading others. Learn his secrets, and then go get your colleague to do his fair share.

Persuasiveness is an important skill everyone should learn because it is useful in countless situations. At work, home, and in your social life, the ability to be persuasive and influence others can be instrumental for achieving goals and being happy. Learning about the tricks of persuasion can also give you insight into when they're being used on you. The biggest benefit of this is that money will stay in your pocket as you realize just how sales people and advertisers sell you products that you don't necessarily need. Here are several techniques that work on a subconscious level.

The trick is to get them wondering why they're saying no -- and with the right tactics, you can do it

very nice answers,

first find the cause of their refuse and then rectify the problem.

some individuals need to be trained, some need more salary, or there might be a need for convergence between different culture. 

I agree with experts answers, thanks for the invitation. 

by small tricks

set with him and give order like idea by non direct way and in end of meeting ask him to give u advise his mind give u his idea plus ur order then u can discuses with him to do it

and with explain to him the benefit from this idea

For example, in marketingThat which drives the desire of customers to prefer a specific product or service is not enjoyed by product attributes or features Features, but what can be obtained from the benefits.