There are two ways to generate competition; through selection and through comparison. Selection is the usual one of a having a variety of products and choosing between them. Comparison can be effective for goods and services which are generic and lack flavor.
The idea of comparison is to create a monopoly and then divide the customer base geographically into units of roughly even size and then have the customers vote annually, rating the service on a scale of 0 to 10. Each service district, for government services, would receive an equal amount of money, the amount actually spent would be divided by the average rating then the highest cost areas would have their management change.
Let us say that each district is budgeted $10 000 000 for a given service. The manager could spend as much or as little as he wants. Let us say that a manager spends $9 000 000 and has an average rating of 6. That would be $9 000 000/ 6 = $1 500 000. If another manager spends $8 500 000 and also gets a rating of 5.8, it would be $1 466 000, the second manager wins. This method eliminates the perverse incentive to spend the full budget while holding the manager accountable for performance.
There are a variety of statistical methods for determining the cut-off for dismissal, one is the standard deviation. For a normally distribution about 0.17 would be 1 deviation below average. That would mean a change in management, on average every 6 years. That might be a good rate of turn over. The turn over must be high enough that each manage feels an urgent need to perform and improve but it should not be so often that management continuity is reduced to shambles. The other need that should be addressed is the manager gaming the system by, for instance, only spending $1 000 000 and getting a rating of 1 and winning at $1 000 000. The goal is to get good quality service at the minimal cost. To prevent gaming a second criterion could be established on just the rating. 1 deviation is 16%, 2 deviations is 3% and 1.5 deviations is 7%, setting the rating cut-off at 1.5 or 2 deviations should prevent a manager deliberately providing low service.
Managers below the cut-offs would be removed and those empty slots transferred, with maybe 1/2 going to new managers and the others being offered to the best managers. The more districts a manager manages, the higher his pay.
Neighboring, or proximate, districts could also rate each other to force cooperation, eventually , the chain of district groups would stretch across the country, interlocking all districts to some extent, The rating could be done by either the senior managers of each district, or by all employees in that district. There could also be a rating within each district of the different services within that district, again, forcing cooperation.
Elected government could then provide the money and do audits to ensure compliance, letting the district residents fire people when they are unhappy with services. The one stumbling block is trying to allow for people within a given district who want to put more money into a given service. The rating could then be done on percentage of spending, unspent moneys being returned in proportion to there source. If the state allotment is
$10 000 000 and the district gives another $4 000 000 for a total of $14 000 000 and the manager spends
$12 000 000 for a rating of 7, then $12 000 000/ $14 000 000 = 86% / 7 = 12.2%. He would then compete with other managers based on their percentages. The $2 000 000 unspent would be divided $2 000 000 X 4/14= $570 000 to the district, and the remainder $1 430 000 to the state.
If the manager has more money, he clearly has an advantage over other managers, but people in his district would most likely expect better service for the more money and may very well rate him lower for the same performance. So, it might work out evenly, this system would have to be set up and run to be sure.
The managers could also be rated by their own employees to insure they are working with them. There are different ways of averaging the different ratings of customers, neighboring districts, groups in the district and employees. The two easiest are the arithmetic average which is just adding and averaging them, and the geometric average which is multiplying them together and taking the fourth root. The geometric average is more responsive to a single bad rating and is therefore probably the better,
The overall idea is to promote competence and force managers to adopt the best methjods of others at the most cost effective rate.
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