For three different groupsthe rich the poor and the

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for three different groups—the rich, the poor, and the “middle,” assuming a particular tax system. Inthis example, the rich prefer higher levels of expenditure to the middle class, who prefer higherlevels than the poor.
The Problem of Aggregating PreferencesIn the private market, decisions are made on an individual basis. If an individual is willing to pay aprice for a commodity that exceeds the marginal cost of production, it pays for the firm to sell thecommodity to the individual.In the public sector,on the other hand, decisions are made collectively. The problem of reconcilingdifferences arises whenever there must be a collective decision.Because different people want different things, however, how can a social decision be made fromthese divergent views?Democracy vs dictatorshipThe politician’s vote is intended to represent the interests of his or her constituents,In a dictatorship, the answer is easy: the dictator’s preferences dominate.A number of different voting rules have been suggested in a democracy, among them unanimityvoting, simple majority voting, and two-thirds majority voting.CENTRAL PROBLEMS OF PUBLIC CHOICEPreference Revelation-Ascertaining the desired level of public goods of each individual.Aggregating Preferences:-Different individuals have different preferred levels of public expenditure.-Preferred level depends on both individuals’ income and the tax system.-Other things being equal, rich typically prefer higher levels.-However, the cost of increased public expenditure may be higher for the rich.Majority Voting and the Voting ParadoxAs early as the eighteenth century, the famous French philosopher Nicolas de Condorcet noted thatthere may not exist any majority voting equilibrium.Voter 1 prefers A to B to CVoter 2 prefers C to A to BVoter 3 prefers B to C to AThere is no clear winner.This is referred to as the voting paradox, or the paradox of cyclical voting.This analysis leads to two questions.1.First, are there voting rules that will ensure a determinate outcome for any vote?2.Second, are there any circumstances under which simple majority voting will yield adeterminate outcome?
For instance, rank-order voting in which individuals rank the alternatives, then the ranks assigned byall individuals are added together, and the alternative with the lowest score wins.Arrow’s Impossibility TheoremAn endless cycle of voting is clearly an unsatisfactory state of affairs.An ideal political mechanism should have four characteristics:1. Transitivity:If the rule shows that A is preferred to B, and B is preferred to C, then A should bepreferred to C - without this property, we can get into cyclical voting2. non-dictatorial choice:There is a simple way of avoiding voting cycles: give all decision makingpowers to a dictator. As long as the dictator has consistent preferences, then there will never be avoting cycle.3. Independence of irrelevant alternatives:The outcome should be independent of irrelevantalternatives; that is, if we have to make a choice between, say, a swimming pool and a tennis court,the outcome should not depend on whether there is a third alternative, such as a new library.

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