CPO2002 Final Study Guide Chapter 11 I Problems With Group Choice Group Decision Making a Round robin tournament Pits each competing alternative against every other alternative an equal number of times in a series of pair wise votes i Example Suppose councillors vote over all sets of pair wise comparisons using majority rule and the alternative that wins the most pair wise contests is the group choice A set of rational individuals may not act rationally b Condorcet s Paradox when they act as a group i Rational individuals have complete and transitive preference orderings if an individuals preference orderings do NOT meet these conditions they are considered irrational ii COMPLETE PREFERENCE ORDERING MUST choose A or B iii TRANSITIVE PREFERENCE ORDERING Not compared directly first choice trumps the other without comparing iv Condorcet Winner an option that beats all other options in a series of pair wise contests c Majority Rule is Problematic i Many times the majority is unknown ii There is not always a decisive winner iii If preferences are intransitive there s no stable outcome 1 Likelihood of group intransitivity increases with the 2 number of alternatives under consideration the number of voters or both Intransitivity is almost certain when a majority rule is applied to a pair wide competition among alternatives because the set of feasible options grows too large II Institutions Matter a Changes the way a group decides and their decisions b Two reasons we fail to observe instability i Borda Count an alternative decision making rule all voters list their complete preference ordering then assign a numerical value to each item to reflect their preferences 1 Alternative with the most points wins ii A powerful Agenda Setter whichever actor is given the power to set the agenda will choose whatever agenda insures that the contest that produces their most preferred option 1 Plan that determines the order in which votes occur 2 Turns voting process into a sequential game with three 3 Strategic vote players a vote in which an individual votes in favor of a less preferred option because he she believes doing so will ultimately produce a more preferred outcome A vote for an individual s most preferred 4 Sincere vote option 5 Two ways to reach stability a Appoint an agenda setter like a dictator their preferred outcome is always chosen b Placing restrictions on the preferences actors might have tell you what to believe III Median Voter Theorem a States no alternative can beat the one preferred by the median voter in pair wise majority rule elections if i Contest between two individuals ii Voters are arrayed along a single policy dimension 1 When the median voter is the individual who has at least half of all the voters at their position or to their right and at least half of al the voters at his position or to his left iii There are an odd number of voters 1 No median voter exists without an odd number of voters iv Single peaked preferences 1 Voters with single peaked preferences have an ideal point in the policy space and experience declines in utility as policy moves away from that space 2 Some rational preference orderings violate single peaked preferences 3 This is a big constraint on voters 4 The ideal point on the graph is the highest point v All vote sincerely 1 No one should abstain from voting 2 Based on two assumptions a No abstentions b No strategic voting IV Chaos Theorem a States that if there are two or more issue dimensions and three or more voters with preferences in the issue space who all vote sincerely there will be NO Condorcet winner b Whoever controls the order of voting determines the outcome c NOT stable unless you win the lottery d Politics must be reduced to a single issue dimension or i Stable outcomes will NOT occur ii Stable outcomes will be controlled by the agenda setter V Arrow s Theorem a The pathologies of majority rule apply to any group decision procedure that meets some minimal standards of fairness b Minimal Standards Arrow s Fairness Conditions i Non dictatorship 1 There must be no individual who fully determines the outcome of the group decision making process regardless of the preferences of the other group members example professor parent etc ii Universal admissibility condition 1 1 Individuals can adopt any rational preference ordering over the available alternatives iii The unanimity condition If all individuals in a group prefer x to y then the group preference must reflect a preference for x to y as well iv Independence from irrelevant alternatives 1 Group choice should be unperturbed by changes in the rankings of irrelevant alternatives VI Conclusion a Arrow showed that if you accept universal admissibility pareto optimality and independence from irrelevant alternatives as untouchable you have to accept either i Dictatorship usually in the form of Agenda Control ii The potential for intransitivity Chapter 13 I Electoral Systems a Electoral Formula determines how votes are translated into seats b Ballot Structure How the vote structure is presented to the voter on c District Magnitude election day many seats available for voting for must be at least 1 i This is the key variable for determining the proportionality of an Number of representatives elected in a district how electoral system LARGE ii The degree of proportionality is greater when the district magnitude is iii Although proportional representation PR systems use multimember districts the average size varies a large amount Must have at least one district magnitude Elections Regime Type a Elections under Authoritarian Regimes why i To send a national signal that they aren t harmful bad ii With hope that it ll lead to a fragmented position II III Electoral System Families a Majoritarian i System in which the candidates or parties that receive the most votes win ii Need either the majority vote or just more votes than anyone else iii There are eight different majoritarian electoral systems six in which are talked about in class 1 Single Member District Plurality System SMDP a Used in the United Kingdom b It is NOT required to win the majority vote just need more votes than the other candidate s AKA first past the post c Easy for voters to punish representatives based on their current performance they do this by voting for the counter candidate d Advantages simple straight forward accountable single party majority governments e Disadvantages Unrepresentative outcomes disproportionate
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