Compose an essay of no less than 500 words discussing the topics covered in this unit

The phenomenon of cycling is very disturbing to our confidence in the democratic institutions of voting and majority rule to reach public choices because it suggests that perhaps no rhyme or reason explains the choices that emerge. Cycling implies that public choices can be influenced by such factors as the order in which issues are placed on the agenda for consideration by voters and legislatures. It also suggests that with three or more alternatives on the agenda, elimination of one of the alternatives can change the way the remaining two are ranked in a public choice. Arrow’s impossibility theorem generalizes the results discussed here for major- ity rule by stating that it is impossible to devise a voting rule that meets a set of conditions that can guarantee a unique political equilibrium for a public choice. To prove his theorem, Kenneth Arrow, who received a Nobel Prize for his ground- breaking work on the properties of political equilibrium, sets up a number of con- ditions for “collective rationality.” These conditions require that public choices meet the same criteria we expect for rational individual choices. Arrow’s work is expressed in terms of mathematics. The analysis here simplifies the theorem. Arrow’s conditions can be roughly summarized to include the following:3 1. All voters must have free choices among alternatives in elections, and the pub- lic choices cannot be made by any one individual who would act as a dictator. 2. A unique political equilibrium must be attained no matter what the preferences of individuals comprising the electorate. We cannot rule out the possibility that some voters have multiple-peaked preferences. 3. If all voters change their rankings of a particular alternative (either moving it up or down), the public choice that emerges must not move in the opposite direction. For example, if all voters now prefer less national defense, we would not expect a public choice to emerge in which more national defense is chosen. 4. Public choices and political equilibrium must not be influenced by the order in which alternatives are presented to voters. 5. Public choices must not be affected by the elimination or addition of an alter- native to the ballot. If voters choose A over B in an election when A and B are the only alternatives, then they must not choose B over A when a third alter- native, C, enters the race. 6. Public choices should be transitive: If A is chosen over B and B is chosen over C, then A should be chosen over C. Arrow’s conditions imply that no “paradox of voting” should exist such that a third-party candidate can act as a “spoiler” in an election. For example, suppose a Republican candidate for president runs against a Democrat and that the Republican would win if the Democrat and the Republican were on the ballot alone. However, a third-party Conservative candidate who enters the race takes votes away from the Republican and the Democrat wins. This means that the ranking between Republicans and Democrats changes when the third-party candidate enters. Arrow’s theorem is disturbing because it implies that any alternative could emerge as a political equilibrium. It also implies that strategies such as controlling the agenda for political debate or manipulating the order in which issues are dis- cussed in a legislature can influence political outcomes. However, Arrow’s theorem does not imply that public choices are always inconsistent. It merely points out that

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