Demand Revelation

Dr. Fred Foldvary

Problem: how to make people truthfully reveal their preferences for public goods, when we don't trust them to be benevolent.

Solution: Let the total cost be C. There are N people.

The average cost is C/N. Each person i would pay the average cost c_i.

Each person has some subjective value v_i on the public good.

Each person can state a value s_i which may or may not be v_i.

A person's net value n_i is his stated value s_i minus his share of the cost.

The only people who are a problem are those who change the outcome; they are pivotal.
One changes the outcome when instead of being neutral (stating the average cost) one states something else and causes the outcome to change.

If someone changes the outcome to getting the good, the net total harm they impose is
Hj = sum n_i, i not= j.
(j is the person who changes the outcome)
There can be several pivotal persons, or there might be none.

The payment for the social cost, called the Clarke tax after Edward Clark, who discovered this method, is equal to that harm. It is the social cost the pivotal person pays to change the outcome from what these people wanted.

The rules for using the Clarke tax are:

1. Assign a cost c_i. to each person.

2. Have each person state his value s_i, and calculate his net value n_i.

3. Don't buy or make the good if the sum of the net values are negative.

Buy the good if the sum is positive.
If the sum is zero, flip a coin.

4. Each pivotal person pays the Clarke tax equal to the sum of the n_i other than his own.

The Clarke tax is in addition to the amount paid for the good.

Example: 3 room-mates A, B, and C, deciding on buying a TV.

The TV costs $300. Each pays $100.

A says it is worth $50 to him. His n_i is 50-100 = -50.

Same with B.

C values the TV at $250. His n_i is 250-100 = 150.

The sum of the n_i is 50, so they buy the TV.

Note: if they had done a majority vote, they would not have gotten the TV!

The demand-revealing method is superior to voting!!

C is pivotal. So he pays a Clarke tax equal to 50+50 = $100.

He pays $200 in total, but this is less than his stated value of $250.

C has an incentive to tell the truth, since if his stated value is lower than his true value, they might not get the TV, and he would be worse off.

With the demand-revealing method, it is in the interest of each person to truthfully reveal his or her true value for the public good.