Nice, but are they relevant? The main points of the presentation What are voting Nice but are they relevant? A political rules used for Rationality of rules scientist looks at social choice results Improving old systems Varieties of Hannu Nurmi goodness Spatial modelling results Public Choice Research Centre Principles of and system choice Department of Political Science How often are the University of Turku criteria violated? The no-show paradox COMSOC-2010 Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they Background relevant? The main points of the presentation What are voting rules used for ◮ social choice rules have been studied in somewhat Rationality of rules Improving old systematic manner for more than two centuries systems ◮ over the past half a century the literature grown Varieties of goodness particularly rapidly Spatial modelling results ◮ much of interest in this area is motivated by various Principles of flaws of existing voting rules system choice ◮ yet, very few electoral system reforms have been How often are the criteria violated? observed The no-show paradox Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they Why? relevant? The main points of the presentation What are voting rules used for Some possible answers: Rationality of rules 1. the results tend to be of negative nature Improving old systems 2. the research community is far from unanimous about Varieties of goodness best systems Spatial modelling results 3. the nature of the results makes them difficult to Principles of “apply” system choice 4. the present system brought you to power, so why How often are the criteria violated? change it? The no-show paradox Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they The main points relevant? The main points of the presentation ◮ Voting rules are instruments with many properties What are voting rules used for ◮ Some are mutually compatible, some incompatible Rationality of rules ◮ Not all of the properties are deeded of equal Improving old systems importance Varieties of ◮ Patching existing rules may lead to new problems goodness Spatial modelling ◮ Some counterexamples are harder to come by than results others Principles of system choice ◮ This pertains the relevance of (negative) results How often are the criteria violated? ◮ Systems can be justified by what we aim at The no-show paradox ◮ Systems may influence opinion patterns Learning from ◮ This also pertains to the relevance of results proofs Justifying systems by their goal states Upshot
Nice, but are they What are voting rules used for relevant? The main points of the presentation What are voting rules used for Rationality of rules Improving old ◮ Aggregating opinions. systems ◮ Making collective choices. Varieties of goodness ◮ Making individual choices Spatial modelling results ◮ Settling disagreements. Principles of system choice ◮ Searching for consensus. How often are the criteria violated? The no-show paradox Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they Rules make a difference relevant? The main points of the presentation What are voting rules used for Rationality of rules 4 voters 3 voters 2 voters Improving old A E D systems B D C Varieties of goodness C B B Spatial modelling D C E results E A A Principles of system choice How often are the criteria violated? The no-show 5 options, 5 winners paradox Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they Relevance? relevant? The main points of the presentation What are voting rules used for ◮ this is just a theoretical example Rationality of rules Improving old ◮ with a strong Condorcet winner present, many rules systems result in it Varieties of goodness ◮ even a modicum of consensus increases the Spatial modelling results coincidence probability of choice rules essentially Principles of ◮ (somewhat contradicting the preceding) most rules system choice have advocates who are not moved by the fact that How often are the criteria violated? other rules differ from their favorite The no-show paradox Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they Rationality of rules: what does it mean? relevant? The main points of the presentation What are voting rules used for Some views: Rationality of rules Improving old ◮ Arrovian view: collective opinions should be similar systems to the individual ones Varieties of goodness ◮ Condorcet requirements Spatial modelling results ◮ Consistency Principles of ◮ Choice set invariance system choice How often are the ◮ Monotonicity criteria violated? The no-show paradox Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they Borda’s paradox relevant? The main points of the presentation What are voting rules used for Rationality of rules 4 voters 3 voters 2 voters Improving old A B C systems B C B Varieties of goodness C A A Spatial modelling results Borda’s points: Principles of system choice ◮ plurality voting results in a bad outcome How often are the criteria violated? ◮ a superior system exists (Borda Count) The no-show paradox Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they Improving Borda Count: Nanson’s rule relevant? The main points of the presentation What are voting rules used for Rationality of rules How does it work? Compute Borda scores and eliminate Improving old systems all candidates with no more than average score. Repeat Varieties of until the winner is found. goodness Properties: Spatial modelling results ◮ Guarantees Condorcet consistency Principles of system choice ◮ Is nonmonotonic How often are the criteria violated? The no-show paradox Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they Nanson’s rule is nonmonotonic relevant? The main points of the presentation 30 21 20 12 12 5 What are voting rules used for C B A B A A Rationality of rules A D B A C C Improving old D C D C B D systems B A C D D B Varieties of goodness Spatial modelling The Borda ranking: A ≻ C ≻ B ≻ D with D’s score 97 results being the only one that does not exceed the average of Principles of system choice 150. Recomputing the scores for A, B and C, results in How often are the both B and C failing to reach the average of 100. Thus, A criteria violated? The no-show wins. Suppose now that those 12 voters who had the paradox ranking B ≻ A ≻ C ≻ D improve A’s position, i.e. rank it Learning from proofs first, ceteris paribus . Now, both B and D are deleted and Justifying systems the winner is C. by their goal states Upshot
Nice, but are they Improving plurality rule: plurality runoff relevant? The main points of the presentation What are voting rules used for Properties: Rationality of rules ◮ Does not elect Condorcet losers Improving old systems ◮ Is nonmonotonic Varieties of goodness 6 voters 5 voters 4 voters 2 voters Spatial modelling results A C B B Principles of system choice B A C A How often are the C B A C criteria violated? The no-show paradox Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they Black’s system: a synthesis of two ideas relevant? The main points of the presentation How does it work? Pick the Condorcet winner. If none What are voting rules used for exists, choose the Borda winner. Rationality of rules Properties: Improving old ◮ Satisfies Cordorcet criteria systems Varieties of ◮ Is monotonic goodness ◮ Is inconsistent Spatial modelling results Principles of 4 voters 3 voters 3 voters 2 voters 2 voters system choice How often are the A B A B C criteria violated? B C B C A The no-show paradox C A C A B Learning from proofs Justifying systems by their goal states Upshot
Nice, but are they Some systems and performance criteria relevant? The main points of the presentation What are voting Criterion rules used for Voting system a b c d e f g h i Rationality of rules 1 1 1 1 0 0 0 0 0 Amendment Improving old systems Copeland 1 1 1 1 1 0 0 0 0 Varieties of 1 0 1 0 1 0 0 0 0 Dodgson goodness Maximin 1 0 1 1 1 0 0 0 0 Spatial modelling results 1 1 1 1 1 0 0 0 0 Kemeny Principles of Plurality 0 0 1 1 1 1 0 0 1 system choice How often are the 0 1 0 1 1 1 0 0 1 Borda criteria violated? Approval 0 0 0 1 0 1 1 0 1 The no-show paradox 1 1 1 1 1 0 0 0 0 Black Learning from 0 1 1 0 1 0 0 0 0 Pl. runoff proofs 1 1 1 0 1 0 0 0 0 Nanson Justifying systems by their goal states 0 1 1 0 1 0 0 0 0 Hare Upshot
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