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18 Cards in this Set
- Front
- Back
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Weighted Voting Systems
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System where voters or the alternatives may be treated UNequally.
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May's theorem says that ___ rule is the only system with which 4 properties?
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majority
1. All voters treated equally 2. Both candidates or alternatives treated equally 3. Monotone: If I vote "no" on education cuts and "yes" wins, then "yes" on education cuts would still win if I switched my vote to "yes" (provided that no other voters switched their votes.) 4. Only one winner with even number of voters (tie cant occur) |
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Weight
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the number of votes that the participant/voter has
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Quota
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The specific number of votes used in a weighted voting system to determine whether "yes" or "no" has won.
*must be greater than half of total weight of all voters *if the sum of weights of all voters who say "yes" is equal to or greater than the quota, then "yes" wins. |
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Why does the quota need to be greater than half of the total weight of all voters?
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to avoid situations where contradictory motions might pass.
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Why cant the quota be greater than the total weight of participants?
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Because no motion would ever pass
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**Dictator
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*voting weight must be equal to or more than the quota
-all other participants are dummy voters ie: [51 : 40, 60] -weight 60 voter can pass any motion and is a dictator |
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Dummy Voters
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-Votes don't count
ie: [51: 26, 26, 26, 22] *voter 22 not needed when two of the prior weight votes combine; they have enough weight to pass a motion without her. -If 22 joins forces with just one of the other voters, the total weight is still less than the quota- 22 is a dummy voter. |
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Evenly Distributed Power
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i.e.: [9: 5 , 3 , 1]
-the only way this motion will pass if voters A, B and C all agree |
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***Veto Power
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Voter whose vote is necessary to pass any motion.
*Dictator ALWAYS has veto power *It is possible for more than one voter to have veto power |
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Which voter has the veto power in the system:
a. [6: 5,3,1] |
weight 5-voter because the other two don't have enough combined weight to pass a motion.
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Give an example of a voting system where more than one voter has veto power.
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In a criminal trial, each voter has veto power.
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Power Index
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gives a way to measure the share of power that each participant in any voting system has.
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Which voters, if any, have veto power in the weighted voting system [9: 5,4,3]? Is any voter a dummy?
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a. weight-5 and 4 voters (because combined they have exactly enough power to pass a motion)
b. weight-3 vote is a dummy voter |
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Shapley-Shubik power index
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*a voters share of power
consider all possible ways the voters could vote then looking at the proportion of those in which a voters role was pivotal. Number of pivotal voters divided by n! where n is the number of pivotal voters. |
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Pivotal Voter
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The first voter in a permutation who, when joining those coming before him would have enough voting weight to win.
*Each permutation has exactly one pivotal voter. |
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Permutation
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The index in Shapley-Subiks Power Index is translated as a permutation
-an ordering of all the voters in a voting system |
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How are voters ordered in a permutation?
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*in accordance with their commitment to the issue
*starting with most favorably inclined and ending with those who are most opposed ie: an animal rights issue could range from a voter who would outlaw the sale of cow's milk to one who would legalize cockfighting. |
