Competition with government contracts

Governments are introducing new measures to improve quality and reduce cost in government departments and services, one way believed to do this is giving out government services to private companies in health, local government, policing and other services, but when government is paying on behalf of a third party how do you make sure companies don't just undercut on quality to undercut on price?

One way to do this is not allowing companies to make bids on contracts based on price but based on

quality, such as satisfaction ratings for social care companies. You would allow individuals to make a choice of what social care company they would like taking care of them, as all social care companies will get paid the same, so people can not just choose the most expensive social care providers bringing up costs.
Companies with a high level of social care ratings will be awarded new contracts and companies not meeting minimum standards and low level of satisfaction rating would not gain new contracts.

How to reduce cost?
In a market where companies do not bid based on price how do you reduce cost? One way to try and reduce cost is having strict rules over their accounts, looking at profits and reducing the tariffs paid out to companies for the same service. 
The main problem are companies hiding profits this is why it might be advised to have stricter rules on these companies to police their accounts, another option is to always have a government competitor making sure government isn't being overpriced by a service we can do better at a lower cost.

Local government vs national
I would like local government to have more accountability so they could decide on the best quality and price for local people, until people are more informed about their local government and hold their local government to account, I believe it's best for central government to decide what tariffs will be given to each region and what companies will be awarded contracts. local government can only provide new contractors ,help companies provide better services and refer people to companies in certain cases.

Being a good consumer
Making informed decisions is vital to improved quality for services, if people are uninformed about the quality competitors offer, or unwilling to change to a competitor this can harm improvements to services.
People have to be informed of the best schools, hospitals, universities, etc so people can choose the best service.

Not in all cases do you want the individual to make the choice on the service they are given such as prisoners choice on prisons and vulnerable people such as drug addicts on rehabilitation services. In certain cases you want local government to choose on behalf of a third party, as tariffs are set by central government local government will more likely choose based on quality as there is no cost element.

When competition doesn't work
When you have a lack of competition, such as high number of children and low level of school places, we will have to be quick to spot such situations and tougher restrictions will come in place to make sure companies still offer good services and in the worse cases government take over if companies do not meet standards.

Sometimes too much competition can create a fractured market that is less productive than what the government can do on it's own, this is why the competition commission would have to take a bigger role in looking at government services to make sure people are getting the best services for their money.