Let Failure Voting and Demand Revelation All this relies upon agents revealing their true valuations for the public good. Would they Recall agents would like to free ride. They would like the good to be provided but they would rather not pay for it. Private provision of the public good is therefore unlikely to take place. Voting for a particular level of the public good might be a way to reveal the preferences of individuals. But remember Agent 1 Agent 2 Agent 3 If a, b and c represent different levels of the public good, then there is majority who prefer a to b, a majority whe prefer b to c and a majority who prefer c to a Social preferences are not transitive. More generally, even when transitivity is imposed on a voting system, the level of public good provision voted for is the median preferred level - which is not necessarily the efficient level Valuation mis-representation to manipulate the vote remains an issue. How can true valuations be revealed? Market- Market Failture a Revelation mechanism There is a solution: Revelation mechanisms. Suppose there are n agents, each with a true valuation for the public good of ui. Each will pay a commonly known share si of the cost c if the good is provided Their net valuations are v=ui-sic. Consider the following mechanism 1. Each agent is asked their net valuation vf. They report a valuation bi which may or may not be their true valuation. (They can misrepresent their preferences if they wish) 2. The public good is provided if i_, bi>0. If the reported valuations add to more than zero the good is prowided -this would be efficient if everyone told the truth 3. Each agent a side-payment equal to the sum of the other agents reported valuations(2i+b). Each agent will tell the truth. The incentive to do so is provided by the side-payments at the end. Given that eac agent tells the truth the public good will be provided efficiently. This mechanism is expensive, however. There are cheaper alternatives: The Clarke tar is similar but only gives side-payments to pivotal agents. As an exercise, show why no agent has an incentive to report b i vi in the abowe mechanism.Market — Market Failure 11 Voting and Demand Revelation • All this relies upon agents revealing their true valuations for the public good. Would they? • Recall agents would like to free ride. They would like the good to be provided but they would rather not pay for it. • Private provision of the public good is therefore unlikely to take place. Voting for a particular level of the public good might be a way to reveal the preferences of individuals. But remember: Agent 1 Agent 2 Agent 3 a b c b c a c a b • If a, b and c represent different levels of the public good, then there is majority who prefer a to b, a majority who prefer b to c and a majority who prefer c to a. Social preferences are not transitive. • More generally, even when transitivity is imposed on a voting system, the level of public good provision voted for is the median preferred level — which is not necessarily the efficient level. • Valuation mis-representation to manipulate the vote remains an issue. How can true valuations be revealed? Market — Market Failure 12 A Revelation Mechanism • There is a solution: Revelation mechanisms. Suppose there are n agents, each with a true valuation for the public good of ui . Each will pay a commonly known share si of the cost c if the good is provided. • Their net valuations are vi = ui − sic. Consider the following mechanism: 1. Each agent is asked their net valuation vi . They report a valuation bi which may or may not be their true valuation. (They can misrepresent their preferences if they wish). 2. The public good is provided if Pn i=1 bi ≥ 0. If the reported valuations add to more than zero the good is provided — this would be efficient if everyone told the truth. 3. Each agent receives a side-payment equal to the sum of the other agents’ reported valuations ( P j6=i bj ). • Each agent will tell the truth. The incentive to do so is provided by the side-payments at the end. Given that each agent tells the truth the public good will be provided efficiently. This mechanism is expensive, however. • There are cheaper alternatives: The Clarke tax is similar but only gives side-payments to pivotal agents. • As an exercise, show why no agent has an incentive to report bi 6= vi in the above mechanism