CPO2002 Final Study GuideChapter 11I. Problems With Group Choice/Group Decision Makinga. Round-robin tournament: Pits each competing alternative against every other alternative an equal number of times in a series of pair-wise votesi. 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 choiceb. Condorcet’s Paradox : A set of rational individuals may not act rationally when they act as a groupi. Rational individuals have complete and transitive preference orderings; if an individuals’ preference orderings do NOT meet these conditions, they are considered irrationalii. COMPLETE PREFERENCE ORDERING: MUST choose A or Biii. TRANSITIVE PREFERENCE ORDERING: Not compared directly, first choice trumps the other without comparingiv. Condorcet Winner: an option that beats all other options in a series of pair-wise contestsc. Majority Rule is Problematici. Many times the majority is unknownii. There is not always a decisive winneriii. If preferences are intransitive, there’s no stable outcome 1. Likelihood of group intransitivity increases with the number of alternatives under consideration, the number of voters, or both2. 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 largeII. Institutions Mattera. Changes the way a group decides and their decisionsb. 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 preferences1. Alternative with the most “points” winsii. 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 option1. Plan that determines the order in which votes occur2. Turns voting process into a sequential game with three players3. Strategic vote : 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 outcome4. Sincere vote : A vote for an individual’s most preferred option5. 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 individualsii. Voters are arrayed along a single policy dimension1. 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 leftiii. There are an odd number of voters1. No “median voter” exists without an odd number of votersiv. 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 space2. Some rational preference orderings violate single-peaked preferences 3. This is a big constraint on voters4. The ideal point on the graph is the highest pointv. All vote sincerely1. No one should abstain from voting2. Based on two assumptions:a. No abstentionsb. No strategic votingIV. Chaos Theorema. 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 winnerb. Whoever controls the order of voting determines the outcomec. NOT stable, unless you win the lotteryd. Politics must be reduced to a single-issue dimension or:i. Stable outcomes will NOT occurii. Stable outcomes will be controlled by the agenda-setterV. 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-dictatorship1. There must be no individual who fully determines the outcome of the group decision-making process regardlessof the preferences of the other group members (example: professor, parent, etc.)ii. Universal admissibility condition1. Individuals can adopt any rational preference ordering over the available alternativesiii. The unanimity condition1. If all individuals in a group prefer x to y, then the group preference must reflect a preference for x to y as welliv. Independence from irrelevant alternatives1. Group choice should be unperturbed by changes in the rankings of irrelevant alternativesVI. Conclusiona. 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 intransitivityChapter 13I. Electoral Systems a. Electoral Formula: determines how votes are translated into seatsb. Ballot Structure: How the vote structure is presented to the voter on election dayc. District Magnitude : Number of representatives elected in a district (how many seats available for voting for *must be at least 1)i. This is the key variable for determining the proportionality of an electoral system ii. The degree of proportionality is greater when the district magnitude is LARGEiii. Although proportional representation (PR) systems use multimember districts, the average size varies a large amount*Must have at least one district magnitudeII. Elections & Regime Typea. Elections under Authoritarian Regimes: why?i. To send a national signal that they aren’t harmful/badii. With hope that it’ll lead to a fragmented positionIII. Electoral System Familiesa. Majoritarian i. System in which the candidates or parties that receive the most votes winii. Need either the majority vote or just more votes than anyone elseiii. 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 Kingdomb. 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
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